apple_tv_3rd_gen_setup_f - Manuels - Apple Apple sur FNAC.COM

 

 

 

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http://manuals.info.apple.com/MANUALS/1000/MA1607/fr_FR/apple_tv_3rd_gen_setup_f.pdf

 

 

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Bienvenue. Vous regardez l’Apple TV. Table des matières 3 Table des matières Chapitre 1 : Connectez. 7 Inclus dans le pack 8 Apple TV – Vue d’ensemble 10 Avant toute chose 11 Configuration de votre Apple TV Chapitre 2 : Configurez. 16 Configuration du réseau 17 Connexion à iTunes Chapitre 3 : Regardez. 20 Utilisation de votre télécommande Apple Remote 21 Fonctions élémentaires de la télécommande 21 Jumelage de l’Apple TV et d’une télécommande 22 Désactivation du jumelage de l’Apple TV et de la télécommande 24 Remplacement de la pile de la télécommande 25 Location de films et de séries TV 4 Table des matières Chapitre 4 : Un problème ? Pas de problème. 28 Dépannage 34 Voyant d’état 35 Service et assistance 35 Numéro de série 36 Précautions d’emploi et entretien www.apple.com/fr/support/appletv Connectez. 1 6 Chapitre 1 Connectez. Avec l’Apple TV, vous pouvez louer des films et des séries TV haute définition, visionner du contenu en diffusion directe depuis Netflix, ainsi que des podcasts, des vidéos YouTube et des chaînes de radio en ligne. Vous pouvez également diffuser votre contenu iTunes personnel à partir d’un Mac ou d’un PC, et visionner sans fil des photos sur votre téléviseur HDTV grand écran à partir de votre ordinateur, MobileMe ou Flickr, le tout sans quitter votre fauteuil. Avec AirPlay, vous pouvez en outre dffuser sans fil sur votre Apple TV des vidéos, de la musique et des photos à partir de votre iPhone, iPad ou iPod touch. Remarque : la disponibilité du contenu varie selon les régions. Pour en savoir plus sur Consultez Ce dont vous avez besoin pour démarrer « Avant toute chose » à la page 10 Configuration de votre Apple TV « Configuration de votre Apple TV » à la page 11 Configuration de votre connexion réseau « Configuration du réseau » à la page 16 Utilisation de la télécommande Apple Remote « Utilisation de votre télécommande Apple Remote » à la page 20 Dépannage de l’Apple TV « Dépannage » à la page 28 Chapitre 1 Connectez. 7 Pour en savoir plus sur Consultez Sécurité et garantie de l’Apple TV Guide d’informations importantes sur le produit Apple TV Inclus dans le pack Câble d’alimentation AC Télécommande Apple Remote Remarque : il se peut que le câble d’alimentation dont vous disposez soit légèrement différent du câble illustré ici. 8 Chapitre 1 Connectez. Apple TV – Vue d’ensemble Récepteur à infrarouge Voyant d’état £ Port HDMI d Port Micro USB Port audio numérique optique Port d’alimentation G Port Ethernet Chapitre 1 Connectez. 9 Récepteur à infrarouge À utiliser avec la télécommande Apple Remote fournie pour contrôler l’Apple TV. Voyant d’état Le voyant d’état clignote lentement au démarrage de l’Apple TV. Une fois l’Apple TV allumé, ce voyant ne clignote plus. Reportez-vous à la section « Voyant d’état » à la page 34. d Port Micro USB Destiné à la maintenance et aux diagnostics. ≤ Port d’alimentation Utilisez-le pour brancher le câble d’alimentation sur l’Apple TV. G Port Ethernet Si votre réseau fonctionne avec une connexion Ethernet, connectez un câble Ethernet. £ Port HDMI Connectez l’Apple TV au port HDMI d’un téléviseur haute définition au moyen d’un câble HDMI. Port audio numérique optique Utilisez ce port pour connecter, au moyen d’un câble audio numérique optique (également appelé S/PDIF ou TOSLINK), l’Apple TV à un récepteur home-cinéma doté d’un port audio numérique optique. Z Connectivité sans fil Wi-Fi/AirPort intégrée Connectez l’Apple TV à votre réseau sans fil. 10 Chapitre 1 Connectez. Avant toute chose Pour pouvoir utiliser votre Apple TV, vous devez disposer des éléments cités ci-après. Téléviseur haute définition Un téléviseur haute définition capable d’afficher des vidéo en 720 p. Câblage  Un câble HDMI pour connecter l’Apple TV à votre téléviseur.  Un câble audio numérique optique (si vous pensez en utiliser un). Réseau  Un réseau, AirPort Extreme 802.11b, 802.11g ou 802.11.n, un réseau Wi-Fi sans fil (la diffusion directe de vidéo sans fil requiert 802.11g ou 802.11n) ou un réseau Ethernet 10/100.  Une connexion Internet haut débit (DSL, câble ou réseau local).  Le nom de votre réseau sans fil et le mot de passe (si vous en utilisez un). Logiciels et comptes Pour reproduire le contenu sur l’Apple TV à partir d’un Mac ou d’un PC, votre ordinateur doit satisfaire la configuration requise suivante :  un compte iTunes Store pour la location de films et de séries TV ;  iTunes 10.2 ou ultérieur ;  un compte iTunes Store afin d’utiliser le partage à domicile pour reproduire du contenu à partir d’un Mac ou d’un PC ;  un compte Netflix pour reproduire du contenu Netflix. Chapitre 1 Connectez. 11 Configuration de votre Apple TV L’Apple TV se branche sur votre téléviseur par un port HDMI transmettant l’audio et la vidéo à votre téléviseur. Avant de configurer votre Apple TV, vérifiez les ports placés à l’arrière de votre téléviseur et assurez-vous de posséder les câbles nécessaires. Vous pouvez aussi brancher l’Apple TV sur un téléviseur haute définition ou sur un récepteur home-cinéma possédant un port HDMI à l’aide d’un câble HDMI pour la vidéo et l’audio. Vous pouvez également utiliser un câble audio numérique optique pour connecter l’Apple TV à un récepteur audio. Important : avant de brancher l’Apple TV sur une prise de courant, lisez attentivement toutes les instructions d’installation et les informations relatives à la sécurité dans le Guide d’informations importantes sur le produit livré avec votre produit. 12 Chapitre 1 Connectez. Étape 1 : Connexion des câbles 1 Branchez une extrémité du câble HDMI sur la partie arrière de votre téléviseur. 2 Branchez l’autre sur la partie arrière de votre Apple TV. 3 Si vous utilisez un câble audio numérique optique, connectez une extrémité de celui-ci au port d’entrée audio de votre récepteur ou de votre téléviseur et l’autre au port numérique optique situé à l’arrière de votre Apple TV. Apple TV Télévision Port HDMI Port HDMI Câble HDMI Remarque : les composants Wi-Fi 802.11 intégrés connectent l’Apple TV à votre réseau sans fil. Si votre réseau est un réseau Ethernet, reliez l’Apple TV à votre réseau à l’aide d’un câble Ethernet. Chapitre 1 Connectez. 13 Étape 2 : Connectez le câble d’alimentation Branchez une extrémité du câble sur le port d’alimentation situé à l’arrière de votre Apple TV et l’autre sur une prise de courant. Port d’alimentation Important : veillez à ne rien déposer sur l’Apple TV. Les objets placés sur l’appareil risquent de provoquer des interférences avec le signal sans fil. Ne posez pas l’Apple TV sur d’autres équipements électroniques. Étape 3 : Allumez votre téléviseur et selectionnez l’entrée Lors de la première utilisation de l’Apple TV, il peut être utile de choisir une langue, un réseau et configurer l’Apple TV pour fonctionner avec votre réseau (si nécessaire). Reportez-vous aux chapitre 2, « Configurez. » à la page 15. Si vous voyez apparaître un écran noir la première fois que vous utilisez l’Apple TV, assurez-vous que l’entrée sélectionnée sur votre téléviseur correspond à l’entrée sur laquelle vous avez branché les câbles sur le téléviseur ou sur le récepteur. Pour obtenir des informations sur les différentes entrées de votre téléviseur, consultez le chapitre 4, « Un problème ? Pas de problème. » à la page 27 et lisez la documentation fournie avec votre appareil. www.apple.com/fr/support/appletv Configurez. 2 16 Chapitre 2 Configurez. L’Apple TV vous permet de sélectionner et de configurer votre connexion au réseau sans fil et, si vous cherchez à regarder ou écouter du contenu de votre bibliothèque iTunes, de vous connecter à iTunes sur votre ordinateur. Configuration du réseau Ayez le nom de votre réseau et votre mot de passe (si vous en utilisez un) ainsi que votre télécommande Apple Remote sous la main durant la configuration de votre Apple TV. Assurez-vous que rien ne se trouve entre la télécommande et l’Apple TV. Pour plus d’informations concernant l’utilisation de votre télécommande, reportez-vous aux chapitre 3, « Regardez. » à la page 19. Si vous :  Si vous vous connectez à un réseau Ethernet, l’Apple TV détecte automatiquement votre réseau.  Si vous vous connectez à un réseau sans fil, l’Apple TV vous aide à sélectionner et à configurer votre connexion réseau. Connexion à votre réseau sans fil L’Apple TV vous aide à vous connecter à votre réseau sans fil. Si vous utilisez un nom et un mot de passe pour accéder à votre réseau, ayez-les à portée de main. Utilisez la télécommande Apple Remote pour : 1 Sélectionner votre réseau dans une liste ou saisir le nom du réseau s’il s’agit d’un réseau masqué. 2 Saisir votre mot de passe d’accès au réseau sans fil (le cas échéant). Chapitre 2 Configurez. 17 Si vous ne vous connectez pas via DHCP, vous devrez peut-être saisir votre adresse IP, le masque de sous-réseau, l’adresse du routeur et les adresses DNS. Pour terminer la configuration de la connexion à votre réseau, suivez les instructions à l’écran. Connexion à iTunes Pour accéder au contenu de votre bibliothèque iTunes sur l’Apple TV, iTunes 10.2 ou ultérieur doit être installé sur votre ordinateur. Pour consulter le détail de la configuration requise, veillez vous reporter à la section « Logiciels et comptes » à la page 10. Mise à jour de votre logiciel iTunes Pour effectuer la mise à jour à l’aide de la version la plus récente d’iTunes,  Sur un Mac, vous pouvez utiliser l’application « Mise à jour de logiciels ». Pour utiliser « Mise à jour de logiciels », choisissez le menu Pomme () > « Mise à jour de logiciels ».  Sur un ordinateur Windows, vous pouvez également accéder à l’Aide iTunes pour effectuer la mise à jour avec la version la plus récente du logiciel. Ouvrez iTunes, puis choisissez Aide > « Rechercher les mises à jour ». 18 Chapitre 2 Configurez. Configuration du partage à domicile Après avoir configuré votre connexion au réseau, il vous faut configurer iTunes et l’Apple TV pour partager le contenu de votre bibliothèque iTunes. Utilisez le partage à domicile dans iTunes et sur votre Apple TV pour partager la bibliothèque iTunes de tous les ordinateurs de votre réseau ayant l’option de partage à domicile activée. Pour configurer le partage à domicile dans iTunes : 1 Ouvrez iTunes sur votre ordinateur. 2 Choisissez Avancé > « Activer le partage à domicile ». 3 Saisissez votre identifiant Apple et votre mot de passe, puis cliquez sur « Créer un partage à domicile ». 4 Répétez les étapes 1 à 3 sur chaque ordinateur dont vous voulez partager le contenu. Pour en savoir plus sur iTunes, ouvrez iTunes puis choisissez Aide > Aide iTunes. Pour configurer le partage à domicile sur l’Apple TV : 1 Sur l’Apple TV, choisissez Réglages > Général > Ordinateurs. 2 Sélectionnez « Activer le partage à domicile », puis saisissez le même identifiant Apple et mot de passe que sur l’ordinateur. www.apple.com/fr/support/appletv Regardez. 3 20 Chapitre 3 Regardez. La lecture de ce chapitre vous permettra d’en savoir plus sur le jumelage et l’utilisation de votre télécommande Apple Remote avec l’Apple TV. Utilisation de votre télécommande Apple Remote Utilisez la télécommande Apple Remote pour contrôler les réglages de l’Apple TV et parcourir votre contenu. Assurez-vous que rien ne se trouve entre la télécommande et l’Apple TV. MENU Haut Bas Menu Lecture/Pause Gauche Droite Sélectionner Chapitre 3 Regardez. 21 Fonctions élémentaires de la télécommande Votre télécommande Apple Remote possède les fonctions élémentaires décrites ci-dessous. Pour procédez ainsi se déplacer parmi les options du menu utilisez les touches Haut, Bas, Gauche, Droite sélectionner une option de menu appuyez sur Sélectionner revenir au menu précédent appuyez sur Menu revenir au menu principal maintenez la touche Menu enfoncée réinitialiser l’Apple TV maintenez appuyés les boutons Menu et Flèche vers le bas jusqu’à ce que le témoin lumineux d’Apple TV clignote rapidement. jumeler l’Apple TV et une télécommande maintenez simultanément enfoncées les touches Menu et Droite pendant environ six secondes Les touches Haut et Bas de la télécommande Apple Remote ne permettent pas de contrôler le volume de votre téléviseur ou de votre récepteur. Utilisez la télécommande livrée avec votre téléviseur ou votre récepteur pour régler le volume. Jumelage de l’Apple TV et d’une télécommande La télécommande Apple Remote est compatible avec le récepteur à infrarouge intégré à l’Apple TV. Vous pouvez configurer l’Apple TV afin qu’il fonctionne exclusivement avec la télécommande fournie, en jumelant l’Apple TV et cette télécommande. 22 Chapitre 3 Regardez. Pour jumeler l’Apple TV avec la télécommande, procédez comme suit : 1 Choisissez Réglages dans le menu principal de l’Apple TV. 2 Choisissez Général > Télécommandes > Jumeler la télécommande Apple Remote. Vous pouvez également maintenir simultanément enfoncées les touches Menu et Droite pendant six secondes pour jumeler l’Apple TV et la télécommande. Une fois que vous avez jumelé votre télécommande Apple Remote, l’Apple TV affiche un symbole en forme de chaîne ( ) au-dessus de l’image représentant une télécommande. L’Apple TV fonctionne désormais exclusivement avec la télécommande jumelée. Désactivation du jumelage de l’Apple TV et de la télécommande Si vous égarez la télécommande Apple Remote que vous avez jumelée avec l’Apple TV, vous pouvez utiliser n’importe quelle télécommande Apple Remote pour désactiver le jumelage entre l’Apple TV et la télécommande égarée, en maintenant simultanément enfoncées les touches Menu et Gauche pendant six secondes. Vous pouvez également suivre les étapes décrites ci-dessous. Chapitre 3 Regardez. 23 Pour désactiver le jumelage de l’Apple TV et d’une télécommande, procédez comme suit : 1 Choisissez Réglages dans le menu principal de l’Apple TV. 2 Choisissez Général > Télécommandes > Désactiver le jumelage de la télécommande Apple Remote. Une fois que vous avez désactivé le jumelage de votre télécommande Apple Remote, l’Apple TV affiche un symbole en forme de chaîne brisée ( ) au-dessus de l’image représentant une télécommande. Vous pouvez dès lors jumeler l’Apple TV avec une autre télécommande. 24 Chapitre 3 Regardez. Remplacement de la pile de la télécommande Si la pile de votre télécommande Apple Remote arrive en fin d’usage, l’Apple TV affiche l’image d’une télécommande et le symbole d’avertissement (·). Il vous faut alors remplacer la pile par une nouvelle pile de type CR2032. Compartiment des piles Pour remplacer la pile, procédez comme suit : 1 Utilisez une pièce de monnaie pour enlever le cache du compartiment des piles. 2 Retirez la pile. 3 Insérez une nouvelle pile CR2032, le signe plus (∂) tourné vers le haut. 4 Replacez le cache du compartiment des piles et utilisez une pièce de monnaie pour le visser. Important : débarrassez-vous de la pile usagée conformément aux lois et directives relatives à la protection de l’environnement de votre pays. Chapitre 3 Regardez. 25 Location de films et de séries TV Vous pouvez louer des films et des séries TV haute définition ou standard directement depuis l’Apple TV (si disponible). Suivez les instructions à l’écran pour voir quand un film ou une série TV arrive à expiration. Lorsque la période de location est terminée, le film ou la série TV ne peut plus être visionné. Pour le regarder une nouvelle fois, il vous faut le louer à nouveau dans iTunes. Remarque : les films et les séries TV en location ne sont pas disponibles dans toutes les régions. www.apple.com/fr/support/appletv Un problème ? Pas de problème. 4 28 Chapitre 4 Un problème ? Pas de problème. Vous pourrez résoudre la plupart des problèmes de l’Apple TV si vous suivez les conseils de ce chapitre. Pour retrouver des astuces complémentaires et de plus amples informations sur le dépannage, consultez la page d’assistance Apple TV à l’adresse www.apple.com/fr/support/appletv. Dépannage Il existe généralement une solution simple et rapide à tout problème rencontré avec l’Apple TV. Vous devez tout d’abord vous assurer que :  les câbles reliant l’Apple TV et votre téléviseur sont fermement connectés ;  les câbles d’alimentation de l’Apple TV et de votre téléviseur sont correctement branchés sur une source électrique en état de fonctionnement ;  votre téléviseur est allumé et réglé sur la bonne entrée ;  l’Apple TV est connecté à votre réseau. Allez dans le menu Réglages sur l’Apple TV, sélectionnez Réseau, puis vérifiez que l’Apple TV possède une adresse IP ;  et que vos connexions au réseau et à Internet sont activées et fonctionnent correctement. Si les problèmes persistent, vous pouvez essayer de réinitialiser votre matériel en débranchant l’Apple TV, votre téléviseur, votre matériel de réseau sans fil ou votre borne d’accès AirPort et votre routeur de leur alimentation électrique. Attendez 30 secondes, puis branchez à nouveau le matériel. Chapitre 4 Un problème ? Pas de problème. 29 Si la télécommande ne fonctionne pas :  Dirigez bien la télécommande vers l’Apple TV.  Si vous avez jumelé une télécommande Apple Remote avec l’Apple TV, assurez-vous que vous utilisez bien cette même télécommande.  Si le voyant d’état de l’Apple TV émet une lumière blanche clignotante lorsque vous appuyez sur les touches de la télécommande avec laquelle il est jumelé, le problème ne provient alors pas de la télécommande. Reportez-vous à la section « Si vous obtenez une image, mais que l’Apple TV ne répond pas : » à la page 30.  Si vous utilisez une télécommande qui n’a pas été jumelée, le voyant d’état de l’Apple TV émet une lumière jaune ambre clignotante.  Si vous avez jumelé l’Apple TV avec une télécommande Apple Remote et que vous ne retrouvez plus cette dernière, réglez l’Apple TV pour fonctionner avec n’importe quelle télécommande en maintenant simultanément enfoncées les touches Menu et Gauche pendant six secondes sur une autre télécommande.  Assurez-vous que l’avant de l’Apple TV n’est pas obstrué par un objet quelconque.  Si l’Apple TV affiche l’image d’une télécommande et le symbole d’avertissement (·), vous devez remplacer la pile de la télécommande. Reportez-vous à la section « Remplacement de la pile de la télécommande » à la page 24. Si l’Apple TV n’arrive pas à accéder au réseau :  Vérifiez l’adresse IP utilisée par l’Apple TV. Si elle commence par 169.x.x.x, il se peut que la borne d’accès ou le routeur ne soit pas configuré correctement. Vérifiez que l’accès DHCP est fonctionnel ou configurez l’Apple TV de façon à utiliser une adresse IP manuelle. 30 Chapitre 4 Un problème ? Pas de problème.  Vérifiez que rien n’obstrue la réception de la borne d’accès ou de l’Apple TV et changez son emplacement au besoin.  Si le réseau est sécurisé, désactivez temporairement la sécurité sur la borne d’accès et tentez de vous reconnecter.  L’Apple TV ne peut pas se connecter à un réseau sans fil dont le nom ou le mot de passe contient des caractères de valeur élevée (étendus) ASCII ou codés sur deux octets (Unicode), comme c’est le cas pour le japonais, le coréen ou le chinois.  Si votre réseau est sécurisé, assurez-vous d’avoir saisi le bon mot de passe. Si vous constatez que l’écran de votre téléviseur est noir ou brouillé :  Assurez-vous d’utiliser le bon câble HDMI et vérifiez qu’il est correctement branché sur l’Apple TV et sur votre téléviseur.  Assurez-vous que le réglage d’entrée choisi sur le téléviseur correspond à l’entrée sur laquelle le câble HDMI est branché. Pour plus d’informations, consultez la documentation livrée avec votre téléviseur.  Assurez-vous que votre téléviseur haute définition prend en charge les vidéos 720 p. Si vous obtenez une image, mais que l’Apple TV ne répond pas :  Essayez de maintenir enfoncée la touche Menu de la télécommande Apple Remote pour revenir au menu principal de l’Apple TV.  Vérifiez que votre téléviseur est allumé et qu’il fonctionne correctement. Pour plus d’informations, consultez la documentation livrée avec votre téléviseur. Chapitre 4 Un problème ? Pas de problème. 31  Si vous avez jumelé une télécommande Apple Remote avec l’Apple TV, assurezvous que vous utilisez bien la télécommande jumelée. Reportez-vous à la section « Jumelage de l’Apple TV et d’une télécommande » à la page 21.  Réinitialisez votre Apple TV en procédant de l’une des manières suivantes :  maintenez appuyés les boutons Menu et Flèche vers le bas de la télécommande Apple Remote jusqu’à ce que le témoin lumineux d’Apple TV clignote rapidement. ;  débranchez l’alimentation électrique, attendez environ cinq secondes, puis rebranchez-la ;  choisissez Général > Réinitialiser les réglages dans le menu principal de l’Apple TV. Si l’Apple TV ne répond pas, essayez de le restaurer :  Sur l’Apple TV, choisissez Réglages > Général > Réinitialiser, puis sélectionnez Restaurer. La restauration de l’Apple TV peut nécessiter un certain temps, soyez donc patient.  Si votre réseau n’exploite pas DHCP, choisissez Configurer TCP/IP puis saisissez la configuration TCP/IP.  Si l’Apple TV ne répond toujours pas :  débranchez l’alimentation de l’Apple TV et les câbles HDMI ;  branchez une extrémité d’un câble micro USB (vendu séparément) à l’arrière de votre Apple TV et l’autre sur votre ordinateur ;  ouvrez iTunes sur votre ordinateur, sélectionnez Apple TV dans la liste des sources, puis cliquez sur Restaurer. 32 Chapitre 4 Un problème ? Pas de problème. Si vous n’obtenez aucun son :  Si l’Apple TV est connecté à un récepteur home-cinéma, assurez-vous que ce dernier est allumé.  Assurez-vous que le réglage d’entrée choisi sur le téléviseur ou le récepteur correspond à l’entrée sur laquelle le câble audio est branché. Pour plus d’informations, consultez la documentation livrée avec votre récepteur.  Assurez-vous que le volume de votre téléviseur ou de votre récepteur est suffisamment élevé et qu’il n’est pas désactivé.  Assurez-vous d’utiliser le bon câble audio et vérifiez qu’il est correctement branché sur l’Apple TV et sur votre téléviseur ou récepteur.  Si vous utilisez le port HDMI du téléviseur et de l’Apple TV pour l’audio, assurezvous que le téléviseur accepte l’audio à travers son port HDMI. Les ports HDMI de certains modèles de téléviseurs anciens ne prennent en charge que la vidéo. Si l’Apple TV n’affiche pas vos albums photo ou vos diaporamas :  Assurez-vous qu’il existe des photos dans votre photothèque ou dans un dossier de votre ordinateur.  Vérifiez que l’Apple TV et l’ordinateur que vous utilisez sont configurés pour le partage à domicile. Reportez-vous à la section « Configuration du partage à domicile » à la page 18.  Assurez-vous que les photos que vous souhaitez partager sont sélectionnées. Dans iTunes, choisissez Avancé > « Choisir des photos à partager », puis sélectionnez les photos que vous souhaitez partager. Chapitre 4 Un problème ? Pas de problème. 33  Vérifiez que l’Apple TV et l’ordinateur que vous utilisez sont sur le même réseau local.  Vérifiez que l’Apple TV et l’ordinateur utilisent le même compte de partage à domicile. Si les hauts-parleurs de votre téléviseurs émettent des bruits :  Si votre téléviseur ou vos hauts-parleurs prennent en charge l’audio Dolby Digital, vérifiez que le réglage de sortie Dolby Digital est correct pour votre téléviseur ou vos hauts-parleurs. Sur l’Apple TV, choisissez Réglages > Audio et vidéo > Sortie Dolby Digital, puis sélectionnez Activé ou Désactivé. Si vous ne voyez pas votre bibliothèque iTunes sous Ordinateurs sur votre Apple TV :  Vérifiez que l’Apple TV et l’ordinateur que vous utilisez sont sur le même réseau local.  Vérifiez que l’Apple TV et l’ordinateur que vous utilisez sont configurés pour le partage à domicile. 34 Chapitre 4 Un problème ? Pas de problème. Voyant d’état L’Apple TV possède, à l’avant, un voyant d’état qui fournit des indications sur l’état de l’appareil. Si l’Apple TV est Le voyant d’état allumé brille éteint ou en veille est éteint en cours de démarrage clignote lentement accepte une commande provenant de la télécommande clignote une seule fois refuse une commande provenant de la télécommande (vous avez jumelé une télécommande avec l’Apple TV, mais vous utilisez une télécommande qui n’est pas jumelée) clignote trois fois rencontre des problèmes clignote rapidement Chapitre 4 Un problème ? Pas de problème. 35 Service et assistance Vous trouverez plus d’informations sur l’utilisation de l’Apple TV dans l’aide à l’écran iTunes et sur le web. Le tableau suivant décrit où trouver de plus amples informations sur les services et les logiciels. Pour en savoir plus sur : procédez ainsi le service et l’assistance, les forums de discussions, les guides d’initiation (didacticiels) et les téléchargements de logiciels Apple accédez à www.apple.com/fr/support/appletv l’utilisation d’iTunes ouvrez iTunes et choisissez Aide > Aide iTunes Pour obtenir le guide d’initiation iTunes à l’écran (uniquement disponible dans certains pays), consultez la page www.apple.com/fr/support/itunes l’utilisation d’iPhoto (sous Mac OS X) ouvrez iPhoto et sélectionnez Aide > Aide iPhoto les informations sur la sécurité et les normes à appliquer Reportez-vous au Guide d’informations importantes sur le produit fourni avec l’Apple TV Numéro de série Le numéro de série est imprimé en dessous de l’Apple TV. Il est également mentionné dans le menu des réglages de l’Apple TV. Sur l’Apple TV, choisissez Réglages > Général > À propos de. 36 Chapitre 4 Un problème ? Pas de problème. Précautions d’emploi et entretien AVIS : tout manquement aux présentes instructions concernant l’entretien et les mesures de précaution peut endommager l’Apple TV ou d’autres éléments en relation. Utilisation des connecteurs et des ports Ne forcez jamais un connecteur dans un port. Vérifiez que rien ne bloque l’entrée au port. Si le connecteur et le port ne s’assemblent pas facilement, c’est probablement parce qu’ils ne sont pas compatibles. Assurez-vous que le connecteur est compatible avec le port et que vous l’avez positionné correctement par rapport à ce dernier. Maintien de l’Apple TV à des températures normales Utilisez l’Apple TV dans un endroit où la température est toujours comprise entre 0º et 40º C. Entretien de l’extérieur de l’Apple TV Pour nettoyer l’Apple TV, débranchez le câble d’alimentation et tous les autres câbles. Utilisez ensuite un chiffon doux non pelucheux. Évitez toute pénétration d’humidité dans les orifices de l’appareil. N’utilisez pas de produits pour le nettoyage des vitres, de produits d’entretien ménager, d’aérosols, de solvants, d’alcool, d’ammoniac ou d’abrasifs pour nettoyer l’Apple TV. Chapitre 4 Un problème ? Pas de problème. 37 Respect des consignes en matière d’élimination pour l’Apple TV Pour obtenir des informations sur la mise au rebut de l’Apple TV, y compris d’importantes informations sur le respect des normes en vigueur, reportez-vous au Guide d’informations importantes sur le produit. iPhoto Premiers contacts Découvrez iPhoto et apprenez à importer et organiser vos photos et à créer un diaporama ou un livre. 2 1 Table des matières Chapitre 1 3 Bienvenue dans iPhoto 3 Ce que vous apprendrez 4 Avant de commencer 4 Éléments nécessaires 5 L’interface iPhoto Chapitre 2 6 Découvrir iPhoto 6 Étape 1 : importez vos photos 9 Étape 2 : organisez et visualisez vos photos 10 Utilisation des mots-clés 11 Organisation de vos photos 12 Étape 3 : créez un diaporama 13 Réglage des options du diaporama 15 Lecture d’un diaporama 16 Étape 4 : créez un livre 17 Effectuer des changements dans votre livre 19 Modification de texte dans votre livre 20 Suite de l’exploration d’iPhoto 22 Plus d’aide 1 3 1 Bienvenue dans iPhoto Créez des trésors inestimables avec vos photos numériques. Ce document vous permettra de vous familiariser avec les fonctionnalités de base d’iPhoto et vous présente les nouvelles fonctionnalités d’iPhoto ‘08. iPhoto vous offre de multiples manières d’améliorer et de partager vos photos numériques, que vous disposiez de 100 images ou bien 100 000. Avec iPhoto, vous pouvez importer et organiser rapidement vos photos, les améliorer et commander ou réaliser vos propres impressions. Vous pouvez utiliser iPhoto pour créer des diaporamas, des livres, des calendriers et des cartes. Depuis iPhoto, vous pouvez également envoyer vos photos par courrier électronique, les utiliser comme économiseur d’écran et publier vos albums photos sur votre galerie MobileMe pour permettre aux autres de les voir et de les télécharger. Ce que vous apprendrez Suivez toutes les étapes de ce guide d’initiation et vous saurez :  connecter votre appareil photo à l’ordinateur,  importer vos photos dans iPhoto à partir de votre appareil photo,  trier vos photos de plusieurs façons,  utiliser ou ajouter des mots-clés pour retrouver et organiser vos photos,  regrouper vos photos dans un ou plusieurs albums photo,  créer et lire un diaporama,  créer un portfolio. 4 Chapitre 1 Bienvenue dans iPhoto Avant de commencer Pour vous faciliter l’utilisation de ce guide d’initiation, il est recommandé d’imprimer ce document avant de commencer. Pour la plupart des tâches de ce guide d’initiation et de l’Aide iPhoto, vous devez choisir des commandes de menu, dont voici un exemple : Choisissez Fichier > Nouvel album Le premier terme se trouvant après Choisissez fait référence au nom d’un menu dans la barre de menus iPhoto en haut de votre écran d’ordinateur. Le terme suivant est l’objet à sélectionner dans ce menu. Éléments nécessaires Voici les éléments dont vous avez besoin pour mettre en pratique toutes les instructions de ce guide d’initiation :  un appareil photo numérique compatible avec iPhoto (la plupart des appareils photo numériques fonctionnent avec iPhoto mais contactez le fabricant de l’appareil afin d’obtenir des renseignements spécifiques concernant la compatibilité) ;  des photos enregistrées sur votre appareil photo numérique ;  un ordinateur équipé de Mac OS X et d’iPhoto ;  des ports Bus série universel (USB) intégrés sur l’appareil photo comme sur l’ordinateur ;  un câble USB A/B connectant votre appareil photo à votre ordinateur. Chapitre 1 Bienvenue dans iPhoto 5 L’interface iPhoto Lorsque vous ouvrez iPhoto, vous arrivez dans la zone d’affichage qui vous permet de choisir votre prochaine action, telle qu’organiser ou afficher des photos, les modifier ou les utiliser pour créer des diaporamas, des portfolios, des calendriers ou des cartes. Zone d’affichage Visualisez les photos dans votre photothèque, vos livres, vos diaporamas et autres. La fenêtre iPhoto bascule d’un affichage à l’autre, comme organiser, modifier, diaporama ou portfolio, selon l’action que vous effectuez. Barre d’outils Utilisez des boutons et commandes pour organiser, modifier, consulter et partager vos photos. Liste Source Accédez à votre bibliothèque, où toutes les photos et tous les clips vidéo apparaissent ainsi que les dossiers, les albums, les diaporamas, les livres, les calendriers et les cartes que vous créez. Sous-fenêtre d’informations Trouvez des informations importantes concernant la photo telles que la date, la taille, les mots-clés associés et le classement par étoiles. 2 6 2 Découvrir iPhoto Vous avez pris de magnifiques photos avec votre appareil photo numérique. Il est temps maintenant de les importer dans iPhoto et de les organiser pour pouvoir les partager facilement, en créant des diaporamas, des livres ou autres. Étape 1 : importez vos photos Pour modifier et partager vos photos, vous devez tout d’abord les transférer vers votre ordinateur. Cette opération de transfert, appelée importation, permet de copier les fichiers photos depuis leur source originale vers iPhoto, où vous pouvez alors les utiliser de diverses façons. L’importation depuis un appareil photo numérique est la méthode de transfert vers iPhoto la plus commune. Pour connecter votre appareil photo à un ordinateur : 1 Ouvrez iPhoto, situé dans le dossier Applications de votre ordinateur. 2 Éteignez votre appareil photo. 3 Reliez le connecteur A (représenté ci-dessous) du câble USB au port USB de votre ordinateur. Chapitre 2 Découvrir iPhoto 7 4 Reliez le connecteur B (représenté ci-dessous) du câble USB au port USB de votre appareil photo. 5 Allumez votre appareil photo. Celui-ci doit s’afficher sous Appareils dans la liste Source d’iPhoto, située du côté gauche de la fenêtre iPhoto. Les photos de votre appareil apparaissent dans la zone d’affichage. Si vous ne constatez aucune réaction lorsque vous connectez votre appareil photo, vérifiez qu’il est bien allumé et qu’il est réglé sur le bon mode d’importation de photos. Pour en savoir plus sur le mode le plus approprié, consultez les instructions fournies avec votre appareil photo. Vous pouvez également régler les préférences de façon à ouvrir automatiquement iPhoto lorsque vous branchez l’appareil photo. Pour cela, choisissez iPhoto > Préférences et cliquez sur Général en haut de la zone de dialogue. Choisissez iPhoto dans le menu local intitulé « Le fait de connecter la caméra ouvre ». Pour importer vos photos depuis un appareil photo numérique : 1 Dans le champ Événement, saisissez un nom décrivant le groupe de photos à importer (par exemple « Mariage de Michaël, pellicule 4 »). Vos photos sont importées dans un groupe d’événement de ce nom. Elles sont organisées en événements dans la photothèque iPhoto pour pouvoir les retrouver et afficher facilement. 2 Saisissez une description pour le groupe de photos concerné (par exemple, « Photos de la deuxième partie de la réception de Michaël ») dans le champ Description. 3 Si vous le souhaitez, vous pouvez cocher la case « Diviser automatiquement les événements après l’importation ». Cette option s’avère utile si vous importez des photos de jours différents. iPhoto les sépare automatiquement en événements distincts dans la photothèque iPhoto. 4 Si vous avez déjà importé des photos de votre appareil, vous pouvez cocher la case « Masquer les photos déjà importées » pour n’afficher que les nouvelles photos dans la fenêtre Importation. 5 Vous pouvez également choisir de n’importer que certaines photos. Pour ce faire, maintenez la touche commande enfoncée (x ) tout en cliquant sur les photos que vous désirez. 6 Pour importer toutes vos photos, cliquez sur le bouton Tout importer. Si vous avez sélectionné des photos spécifiques à importer, cliquez sur le bouton Importation sélectionnée. 8 Chapitre 2 Découvrir iPhoto Pour cesser l’importation des photos à n’importe quel moment du processus, cliquez sur Arrêter l’importation. Avant de déconnecter votre appareil photo, attendez la fin du transfert de toutes les photos vers iPhoto (ou cliquez sur Arrêter l’importation). Si votre appareil photo dispose d’un mode veille, assurez-vous qu’il est désactivé ou réglé sur un intervalle de temps assez long pour permettre le téléchargement de vos photos. Pour en savoir plus, consultez les instructions fournies avec votre appareil photo. Pour voir vos photos, cliquez sur Dernière importation (dans la liste Source) ou sur Événements et affichez vos photos par événement. Pour déconnecter l’appareil photo de l’ordinateur : 1 Faites glisser l’icône de la caméra vers la corbeille iPhoto. 2 Éteignez votre appareil photo. 3 Débranchez l’appareil photo de l’ordinateur. Vous êtes maintenant prêt à visualiser et organiser vos photos. Importation de photos sans utilisation d’appareil photo En plus d’importer des photos de votre appareil photo numérique, vous pouvez importer des photos :  sauvegardées sur CD (Lorsque vous faites développer vos films 35 mm, demandez au photographe s’il ne peut pas stocker les données sur un CD ou une disquette. De nombreux magasins proposent ce service.),  sauvegardées sur DVD ou lecteur flash,  situées dans un fichier ou un dossier de votre disque dur.  sauvegardées sur une carte mémoire. Si vous n’utilisez pas d’appareil photo numérique, dans un souci de qualité, vérifiez que toutes les photos sont au format JPEG. Pour en savoir plus sur l’importation de photos, consultez les rubriques dans l’Aide iPhoto. Chapitre 2 Découvrir iPhoto 9 Étape 2 : organisez et visualisez vos photos Après avoir importé vos photos dans iPhoto, il est temps de les visualiser et de les trier, de leur ajouter des mots-clés, de les visualiser par mots-clés et de créer un album photo. Pour retrouver vos photos : Dans iPhoto, toutes les photos sont stockées dans la photothèque iPhoto. Vous pouvez les voir en cliquant sur Événements situé en haut de la liste Source du côté gauche de la fenêtre iPhoto. Dans la photothèque, les photos sont regroupées par années et par événement (un événement peut être un rouleau de type 35 mm stockée sur CD, ou un groupe de photos importées depuis un appareil photo numérique). iPhoto affiche vos photos en respectant l’ordre dans lequel elles ont été importées. Pour n’afficher rapidement que les photos récentes, cliquez sur l’icône Dernière importation dans la liste Source. Cliquez sur l’icône Mois dernier pour afficher un plus grand choix de photos. Vous pouvez visualiser des photos dans la photothèque en les triant de différentes façons. La photothèque contient toutes les photos et clips vidéo importés, stockés par groupes d’événements en fonction de la date de prise de vue. Les albums intelligents sont automatiquement mis à jour en fonction des critères choisis. Les albums publiés peuvent être consultés sur Internet et mis à jour régulièrement. Les albums vous aident à organiser vos photos par sujet. Les diaporamas de vos photos sont agrémentés d’effets de transitions et de musique Les cartes de voeux comprennent vos photos et messages. Les portfolios incluent des photos et du texte. Les calendriers permettent d’afficher vos jours importants et photos. Les dossiers vous permettent de regrouper les albums par thème ou par sujet. La Corbeille iPhoto contient des photos supprimées de la photothèque. 10 Chapitre 2 Découvrir iPhoto Pour trier vos photos : 1 Cliquez pour sélectionner des photos dans la liste Source. 2 Choisissez Présentation > Trier les photos puis choisissez l’option dans le sous-menu :  Par date : organise les photos en fonction de la date de prise de vue.  Par mot-clé : organise les photos par ordre alphabétique en fonction des mots-clés que vous leur avez attribués (voir la rubrique suivante « Utilisation des mots-clés »).  Par titre : organise les photos par ordre alphabétique en fonction de leur titre.  Par classement : organise les photos du meilleur au moins bon classement. (Vous pouvez classer vos photos pour identifier vos préférées. Consultez la rubrique « Classement des photos préférées » à la page 11.) Vous pouvez également trier vos événements. Pour en savoir plus, consultez les rubriques dans l’Aide iPhoto. Utilisation des mots-clés Les mots-clés sont de brèves étiquettes que vous pouvez ajouter à vos photos, par exemple « Anniversaire » ou « Sport », afin de retrouver facilement toutes les photos d’une même catégorie. iPhoto propose des mots-clés simples à attribuer à vos photos, mais vous pouvez également créer vos propres mots-clés en modifiant la liste Mots-clés. Lorsque vous en avez ajouté un dans la liste, vous pouvez alors l’attribuer à n’importe quelle photo. Pour attribuer des mots-clés à vos photos : 1 Sélectionnez les photos auxquelles vous voulez ajouter des mots-clés. Pour cela, sélectionnez Événements dans la liste Source, double-cliquez sur un événement pour l’ouvrir puis cliquez sur une photo pour la sélectionner. 2 Choisissez Fenêtre > Afficher les mots-clés pour ouvrir la fenêtre du même nom. 3 Cliquez pour sélectionner le mot-clé que vous voulez ajouter à la photo. Vous pouvez sélectionner un ou plusieurs mots-clé(s). Pour désélectionner un mot-clé, recliquez dessus. Pour ajouter vos propres mots-clés à la liste Mots-clés : 1 Choisissez Fenêtre > Afficher les mots-clés. 2 Cliquez sur le bouton Modifier les mots-clés. 3 Cliquez sur le bouton Ajouter (+). 4 Saisissez votre nouveau mot-clé. 5 Cliquez sur OK. Vous pouvez également supprimer des mots clés, en renommer ou ajouter des raccourcis pour les mots-clés longs. Chapitre 2 Découvrir iPhoto 11 Important : la modification d’un mot-clé se répercute sur toutes les photos auxquelles vous l’aviez attribué. Pour rechercher une photo en fonction d’un mot-clé : 1 Cliquez sur l’icône Rechercher (du côté gauche du champ de recherche). 2 Choisissez Mot-clé dans le menu local. 3 Cliquez pour sélectionner un ou plusieurs mots. Les photos comportant ces mots-clés apparaissent dans zone d’affichage. Organisation de vos photos Vous pouvez grouper vos photos en albums pour mieux organiser votre photothèque, regrouper les photos que vous voulez graver sur CD ou DVD ou choisir celles que vous souhaitez publier sur une page web, par exemple. De plus, vous pouvez utiliser un album comme lieu de stockage temporaire pour un groupe de photos jusqu’à ce que vous ayez défini ce que vous vouliez en faire, que ce soit un diaporama, un livre, un calendrier ou une carte de voeux ou pour publier un album sur votre galerie MobileMe. Les photos dans la photothèque ne sont pas affectées par les déplacements d’un album à l’autre. Pour créer un album photo : 1 Cliquez sur le bouton Ajouter (+) dans le coin inférieur gauche de la fenêtre iPhoto. 2 Cliquez sur le bouton Album dans la zone de dialogue. 3 Saisissez un nom d’album et cliquez sur Créer. Votre nouvel album apparaît dans la liste Source. 4 Cliquez sur Événement dans la liste puis double-cliquez sur un événement pour l’ouvrir. Classement des photos préférées Vous pouvez attribuer à vos photos une note allant d’une à cinq étoiles pour indiquer vos préférences. Ce classement facilite également le tri des photos et permet de les retrouver facilement. Pour noter les photos : 1 Cliquez pour sélectionner la ou les photos à noter. 2 Choisissez Photos > Mon classement puis choisissez dans le sous-menu le nombre d’étoiles que vous souhaitez affecter. Bouton Ajouter 12 Chapitre 2 Découvrir iPhoto 5 Faites glisser les photos de l’événement vers votre nouvel album dans la liste. Vous pouvez faire glisser des photos dans votre album à partir de plusieurs événements. Vous pouvez également faire glisser une photo vers un album directement depuis un autre album, un CD ou un DVD ou encore depuis un autre emplacement de votre disque dur. Lorsque vous ajoutez une photo à un album de cette façon, iPhoto l’importe automatiquement dans votre photothèque. Vous avez par ailleurs la possibilité de créer des albums intelligents automatiquement mis à jour à mesure que le contenu de votre photothèque change. Pour en savoir plus sur la création d’albums intelligents, consultez les rubriques de l’Aide iPhoto. Maintenant que vous savez utiliser iPhoto sans problème, vous êtes prêt à créer votre premier diaporama avec vos photos préférées. Étape 3 : créez un diaporama Dans un diaporama, les photos apparaissent les unes après les autres, dans un certain ordre. Vous pouvez utiliser autant de photos que vous le souhaitez et les organiser dans n’importe quel ordre. Lorsque vous enregistrez un diaporama, celui-ci s’affiche dans votre liste Source sous Diaporamas. Pour créer un diaporama : 1 Sélectionnez les photos que vous voulez inclure dans votre diaporama :  Pour utiliser un album entier, cliquez dessus dans la liste Source du côté gauche de la fenêtre iPhoto.  Pour utiliser un événement en particulier, cliquez sur Événements dans la liste Source puis sélectionnez l’événement désiré dans la zone d’affichage.  Pour sélectionner plusieurs photos dans un album ou votre photothèque, ouvrez l’album ou la photothèque et maintenez la touche Commande (x) enfoncée tout en cliquant sur chacune des photos souhaitées. 2 Cliquez sur le bouton Ajouter (+) dans le coin inférieur gauche de la fenêtre iPhoto. 3 Cliquez sur le bouton Diaporama dans la zone de dialogue. 4 Saisissez un nom pour votre diaporama et cliquez sur Créer. Votre nouveau diaporama apparaît dans la liste Source. Création d’un album à partir d’un dossier de photos Vous pouvez également créer un album en faisant glisser un dossier de photos du Finder dans la liste Source. iPhoto crée alors un album portant le nom du dossier déplacé et importe toutes les photos qu’il contient dans votre photothèque. Chapitre 2 Découvrir iPhoto 13 5 Dans le navigateur de photos situé en haut de la fenêtre iPhoto, faites glisser les photos du diaporama dans l’ordre d’apparition souhaité. 6 Pour commencer votre diaporama, cliquez sur le bouton Lire. Pour l’interrompre, cliquez n’importe où dans l’écran. Réglage des options du diaporama Avant de lancer un diaporama, vous pouvez ajouter votre propre musique de fond, spécifier la durée d’affichage de chaque diapositive, choisir l’aspect des transitions entre chaque diapo, afficher les commandes du diaporama et régler d’autres options. Pour spécifier la durée de l’affichage : 1 Cliquez pour sélectionner votre diaporama dans la liste Source. La fenêtre iPhoto passe en mode diaporama. 2 Cliquez sur le bouton Réglages situé dans l’angle inférieur droit de la fenêtre de diaporama. 3 Dans la zone de dialogue Réglages, cliquez sur les flèches en regard de « secondes » pour spécifier pendant combien de secondes chaque photo reste affichée à l’écran. Navigateur de photos 14 Chapitre 2 Découvrir iPhoto Pour choisir les effets de transition : 1 Cliquez pour sélectionner votre diaporama dans la liste Source. La fenêtre iPhoto passe en mode diaporama. 2 Cliquez sur le bouton Réglages situé dans l’angle inférieur droit de la fenêtre de diaporama. 3 Choisissez une transition dans le menu local Transition. La transition par défaut pour tout nouveau diaporama est la transition Fondu. Vos photos peuvent s’afficher sur les faces d’un cube, s’enchaîner par effet de fondu noir, etc. 4 Spécifiez la durée des transitions en utilisant le curseur de vitesse. Dans cette zone de dialogue, vous pouvez également régler d’autres options pour la totalité du diaporama, notamment la taille des photos, l’effet Ken Burns et la répétition automatique du diaporama. Vous pouvez par ailleurs choisir de la musique de fond dans le dossier Musique d’échantillon ou dans votre bibliothèque iTunes et l’ajouter à votre diaporama. Pour ajouter de la musique de fond à votre diaporama : 1 Cliquez pour sélectionner votre diaporama dans la liste Source. La fenêtre iPhoto passe en mode diaporama. 2 Cliquez sur le bouton Musique situé dans l’angle inférieur droit de la fenêtre de diaporama. 3 Cliquez pour sélectionner un morceau ou une liste de lecture que vous souhaitez ajouter à votre diaporama. Vous pouvez rechercher un morceau en saisissant son interprète ou son titre dans le champ Rechercher. 4 Cliquez sur OK. Chapitre 2 Découvrir iPhoto 15 Lecture d’un diaporama Une fois votre diaporama créé, vous pouvez le lire sur votre ordinateur. Le diaporama, en mode lecture, remplit la totalité de l’écran. Pour lire un diaporama : 1 Cliquez dans la liste Source pour sélectionner le diaporama que vous souhaitez lire. 2 Pour le lancer, cliquez sur le bouton Lire situé dans l’angle inférieur gauche de la fenêtre diaporama. Pour interrompre le diaporama, cliquez n’importe où dans l’écran. Pour mettre un diaporama en pause ou reprendre sa lecture, appuyez sur la barre d’espace. Tout en visualisant votre diaporama, vous pouvez :  utiliser les touches Flèche vers le haut et Flèche vers le bas pour régler la vitesse de votre diaporama,  utiliser les touches Flèche droite et Flèche gauche pour vous déplacer manuellement dans votre diaporama,  appuyer sur Supprimer pour supprimer la photo actuellement affichée dans le diaporama,  appuyer sur Commande + R pour faire pivoter la photo actuellement affichée (la touche Commande comporte un symbole x dessus). Votre premier diaporama est terminé. Autre méthode d’affichage des photos dans un diaporama Il est possible de visualiser n’importe quelle combinaison d’albums photo ou de photos individuelles dans un diaporama temporaire. Il vous suffit de cliquer pour sélectionner les photos ou albums que vous voulez voir puis de cliquer sur le bouton Lire dans l’angle inférieur gauche de la fenêtre iPhoto. Bouton Lire 16 Chapitre 2 Découvrir iPhoto Étape 4 : créez un livre Il est plus facile de créer un livre dans iPhoto que d’imprimer toutes vos photos et de les coller dans un album. Après avoir créé votre chef-d’oeuvre, plusieurs options de partage sont à votre disposition : vous pouvez l’imprimer sur une imprimante couleur, le commander sous forme de livre relié ou bien même l’utiliser pour créer un diaporama plus créatif. Pour créer un portfolio : 1 Sélectionnez les photos que vous voulez inclure dans votre livre :  Pour utiliser un album entier, cliquez sur un album de la liste Source.  Pour utiliser un événement en particulier, cliquez sur Événements dans la liste Source puis cliquez sur l’événement à sélectionner dans la zone d’affichage.  Pour sélectionner plusieurs photos dans un album ou des événements de votre photothèque, ouvrez l’album ou la photothèque et maintenez la touche Commande (x) enfoncée tout en cliquant sur chacune des photos souhaitées. 2 Cliquez sur le bouton Ajouter (+) dans le coin inférieur gauche de la fenêtre iPhoto. 3 Cliquez sur le bouton Livre dans la zone de dialogue. 4 Saisissez un nom pour votre livre. 5 Choisissez une taille de livre relié, broché ou broché à spirale dans le menu local Type de livre. 6 Sélectionnez un thème pour votre livre dans la liste déroulante des thèmes. Lorsque vous sélectionnez un thème de livre, un exemple s’en affiche à droite de la liste des thèmes (pour obtenir une description et des tarifs plus détaillés, cliquez sur le bouton Options + Prix pour vous rendre sur le site web d’iPhoto). 7 Cliquez sur Choisir. iPhoto passe en aperçu livre. Votre nouveau livre s’affiche dans la liste Source et les photos que vous avez choisies apparaissent sous forme de vignettes dans le navigateur de photos situé en haut de l’écran. Si vous optez pour un livre relié et que vous ne souhaitez imprimer des pages que sur une face, cliquez sur le bouton Réglages et décochez la case Pages recto-verso dans la zone de dialogue. 8 Faites glisser vos photos du navigateur de photos vers les cadres photo des pages de votre livre. Chapitre 2 Découvrir iPhoto 17 Une vignette par photo utilisée, marquée d’une coche, est stockée dans le navigateur de photos pour montrer que la photo est utilisée. Si vous avez plus de photos que nécessaire pour remplir toutes les pages de votre livre, vous pouvez en laisser dans le navigateur de photos. Si vous avez besoin de plus de photos, consultez la rubrique « Effectuer des changements dans votre livre » ci-après. Effectuer des changements dans votre livre Vous pouvez changer le thème de votre livre, ajouter des photos, les réorganiser et modifier du texte. Pour découvrir comment faire encore plus de changements dans votre livre, consultez les rubriques de l’Aide iPhoto. Pour changer le thème de votre livre : 1 Cliquez pour sélectionner le livre dont vous voulez modifier le thème. 2 Cliquez sur le bouton Thèmes dans la barre d’outils. 3 Sélectionnez un thème pour votre livre dans la liste déroulante des thèmes. Dans cette zone de dialogue, vous pouvez également modifier le type de livre. Choisissez une option (reliure, brochure ou brochure spirale) dans le menu local Type de livre. 4 Cliquez sur Choisir. Il est recommandé de décider d’un thème avant d’ajouter du texte au modèle de livre. Si vous ajoutez du texte personnalisé au modèle de livre avant de changer de thème, vous pouvez perdre votre texte. Si vous optez pour un livre relié et que vous ne souhaitez imprimer des pages que sur une face, cliquez sur le bouton Réglages et décochez la case Pages recto-verso dans la zone de dialogue. Élaboration de votre livre par iPhoto iPhoto peut concevoir votre livre automatiquement. Pour placer toutes vos photos sélectionnées sur des pages du livre dans l’ordre de votre album ou photothèque, cliquez sur le bouton Formatage automatique. 18 Chapitre 2 Découvrir iPhoto Pour ajouter des photos à votre livre : 1 Cliquez pour sélectionner un événement de votre photothèque ou un album dans la liste Source. 2 Faites glisser les photos de la photothèque ou de l’album vers votre livre dans la liste Source. 3 Cliquez pour sélectionner votre livre dans la liste Source. iPhoto passe alors en mode livre. 4 Cliquez sur le bouton du navigateur Photo pour voir toutes les photos de votre livre et notamment les derniers ajouts. Il s’agit d’une zone de suspension, un peu comme une salle d’attente, pour les photos que vous souhaitez placer dans votre livre. 5 Effectuez l’une des opérations suivantes pour placer les photos dans votre livre :  Pour ajouter une photo à un cadre photo vide, faites-la glisser du navigateur vers le cadre vide.  Pour remplacer une photo de votre livre par une nouvelle, faites glisser cette dernière depuis le navigateur sur la photo à remplacer. La nouvelle photo remplace alors l’ancienne.  Pour ajouter une photo à une page, modifiez d’abord le nombre de photos autorisées sur celle-ci en cliquant sur Disposition dans la barre d’outils et en choisissant une option dans le menu local, puis faites glisser les photos vers les nouveaux emplacements vides.  Pour ajouter toutes les photos non utilisées dans le livre, cliquez sur le bouton Formatage automatique. De nouvelles pages sont alors ajoutées en fonction des besoins. Il est possible de modifier l’ordre des photos sur une page ou d’une page à l’autre. Bouton du navigateur Photo Chapitre 2 Découvrir iPhoto 19 Pour réorganiser les photos de votre livre : 1 Cliquez sur le bouton Affichage page pour afficher les pages du livre dans le navigateur de photos. 2 Effectuez l’une des opérations suivantes :  Pour permuter des photos affichées sur une même page, cliquez pour sélectionner la page dans le navigateur puis faites glisser l’une des photos à permuter sur l’autre photo dans la zone d’affichage.  Pour permuter des photos affichées sur la même double page, cliquez sur le bouton Affichage page double, sélectionnez d’un clic la page dans le navigateur de photos et faites glisser l’une des photos à permuter sur l’autre photo.  Pour déplacer une photo d’une page à l’autre, cliquez pour sélectionner la page sur laquelle la photo apparaît dans le navigateur et faites glisser la photo de la zone d’affichage vers une nouvelle page du navigateur. Modification de texte dans votre livre La plupart des thèmes d’un livre comprennent des pages contenant du texte modifiable. Si une page ne contient pas de texte et que vous souhaitez en ajouter, vous devez choisir un modèle de page contenant du texte. Pour en savoir plus sur le choix et les modifications de thème, reportez-vous aux rubriques correspondantes de l’Aide iPhoto. Pour modifier du texte dans votre livre : 1 Cliquez sur le bouton Affichage page pour afficher les pages du livre dans le navigateur de photos. 2 Cliquez pour sélectionner la page contenant le texte à modifier. 3 Dans la zone d’affichage, cliquez sur le texte que vous souhaitez modifier puis ajoutez du texte ou modifiez le texte existant. Bouton Affichage page Bouton Affichage page double 20 Chapitre 2 Découvrir iPhoto Lorsque vous modifiez du texte, il est recommandé d’effectuer en premier lieu un zoom avant sur la zone de texte. Pour cela, faites glisser le curseur de taille vers la droite. Si vous ne voulez pas de texte dans un champ existant, ne saisissez rien. Le texte de paramètre fictif tel que « Insérer un titre » n’apparaît pas dans le livre si le champ correspondant n’a pas été pas modifié. Vous avez créé un livre et donc terminé votre découverte du guide d’initiation iPhoto. Si vous voulez imprimer ou commander un exemplaire de votre livre, consultez la rubrique correspondante de l’Aide iPhoto. Suite de l’exploration d’iPhoto iPhoto ‘08 offre une gamme d’options créatives pour utiliser et améliorer vos photos. Découvrez une ou plusieurs fonctionnalités complémentaires :  Publication web rapide : utilisez votre galerie MobileMe pour partager vos albums photos en ligne, d’un simple clic. Votre famille et vos amis pourront les visualiser et les télécharger afin d’imprimer de grandes photos, de haute qualité et pourront même, eux aussi, publier les photos qu’ils veulent vous faire partager. Vous pouvez également envoyer des photos par courrier électronique à partir de votre téléphone portable ou un autre appareil mobile vers vos albums publiés.  Mode Plein écran : affichez vos photos sur la totalité de l’écran de votre ordinateur. L’affichage plein écran haute résolution facilite l’édition et la rend plus précise. Il est également possible d’afficher deux ou plusieurs photos à la fois pour pouvoir les comparer ou les modifier en même temps. Curseur de taille Visualisation d’un livre dans un diaporama Vous pouvez utiliser un livre iPhoto comme point de départ pour un diaporama plus élaboré à partager avec vos amis et famille. Choisissez un thème de livre dans la gamme proposée, ajoutez-y vos photos et votre texte puis cliquez sur le bouton Lire pour visualiser la séquence. Vous pouvez la modifier comme un diaporama en adaptant les transitions, en ajoutant de la musique d’arrière-plan et plus. Bouton Lire Chapitre 2 Découvrir iPhoto 21  Modification minutieuse et effets spéciaux : du rognage à la correction des couleurs en passant par la retouche, iPhoto vous offre un contrôle précis des améliorations à apporter à vos photos. Pour des corrections rapides, vous pouvez en un seul clic redonner de la couleur à une photo fade, abaisser la luminosité d’une photo surexposée ou utiliser des améliorations spéciales comme le floutage ou l’adoucissement des bords.  Personnalisation des mots-clés et recherche rapide : ajoutez des mots-clés standards ou personnalisés à vos photos pour pouvoir les organiser en fonction de vos besoins et créer des raccourcis pour vos mots-clés les plus utilisés. Faites une recherche sur le texte, les mots-clés, la date ou le classement pour retrouver aussi rapidement que facilement les photos que vous cherchez.  Impression sur place : réglez la taille, le rognage ou la couleur de vos photos sans affecter l’image originale, choisissez des cadres à texture créés par Apple et imprimez des photos prêtes à être encadrées sur votre imprimante personnelle.  Calendriers sympathiques : n’oubliez pas les personnes et les moments qui comptent avec un calendrier 10 x 13 créé à partir de vos propres photos. Personnalisez vos vacances grâce à une gamme de thèmes. Faites ressortir les jours spéciaux comme les anniversaires avec des photos et du texte.  Cartes de voeux personnalisées : envoyez vos meilleures photos à vos amis et à vos proches sur des cartes de voeux recto-verso 4 x 6 ou en double 5 x 7. Faites votre choix parmi des thèmes tels que les anniversaires, les invitations, les cartes postales ou les cartes vierges, ajoutez-y des messages personnels et recevez une série de cartes chez vous.  Des sites web grandeur nature : créez votre propre site web ou blog en envoyant votre album photo d’iPhoto vers iWeb, l’application de publication web d’Apple. Choisissez le thème qui met le mieux en valeur vos photos, décidez de la disposition, ajoutez des liens et des publicités. Les visiteurs peuvent visualiser et commenter vos photos ou entrées de blog. 22 Chapitre 2 Découvrir iPhoto Plus d’aide Pour obtenir de l’aide lorsque vous utilisez iPhoto, consultez l’Aide iPhoto disponible depuis le menu Aide lorsque iPhoto est ouvert. Vous y trouverez plus d’informations sur les rubriques de ce document ainsi que des informations et des instructions sur bien d’autres rubriques. Vous pouvez également visionner des vidéos explicatives des rubriques les plus populaires d’iPhoto à l’adresse www.apple.com/fr/ilife/tutorials/iphoto. Pour obtenir des informations techniques, en savoir plus sur les groupes de discussions et la configuration requise, visitez www.apple.com/fr/support/iphoto. Pour obtenir des informations complètes et à jour sur iPhoto, notamment les astuces, les actualités sur les nouvelles fonctionnalités et la liste des appareils photo compatibles, rendez-vous sur le site web d’iPhoto à l’adresse www.apple.com/fr/ilife/iphoto. www.apple.com/ilife/iphoto © 2008 Apple Inc. Tous droits réservés. Apple, le logo Apple, iLife, iPhoto, iTunes et Mac OS sont des marques d’Apple Inc. déposées aux États-Unis et dans d’autres pays. Finder et iWeb sont des marques d’Apple Inc. MobileMe est une marque de service d’Apple Inc. F019-1280 06/2008 iWork Formulas and Functions User Guide KKApple Inc. © 2009 Apple Inc. All rights reserved. Under the copyright laws, this manual may not be copied, in whole or in part, without the written consent of Apple. Your rights to the software are governed by the accompanying software license agreement. The Apple logo is a trademark of Apple Inc., registered in the U.S. and other countries. Use of the “keyboard” Apple logo (Option-Shift-K) for commercial purposes without the prior written consent of Apple may constitute trademark infringement and unfair competition in violation of federal and state laws. Every effort has been made to ensure that the information in this manual is accurate. Apple is not responsible for printing or clerical errors. Apple 1 Infinite Loop Cupertino, CA 95014-2084 408-996-1010 www.apple.com Apple, the Apple logo, iWork, Keynote, Mac, Mac OS, Numbers, and Pages are trademarks of Apple Inc., registered in the U.S. and other countries. Adobe and Acrobat are trademarks or registered trademarks of Adobe Systems Incorporated in the U.S. and/or other countries. Other company and product names mentioned herein are trademarks of their respective companies. Mention of third-party products is for informational purposes only and constitutes neither an endorsement nor a recommendation. Apple assumes no responsibility with regard to the performance or use of these products. 019-1588 09/2009 13 Preface: Welcome to iWork Formulas & Functions 15 Chapter 1:  Using Formulas in Tables 15 The Elements of Formulas 17 Performing Instant Calculations in Numbers 18 Using Predefined Quick Formulas 19 Creating Your Own Formulas 19 Adding and Editing Formulas Using the Formula Editor 20 Adding and Editing Formulas Using the Formula Bar 21 Adding Functions to Formulas 23 Handling Errors and Warnings in Formulas 24 Removing Formulas 24 Referring to Cells in Formulas 26 Using the Keyboard and Mouse to Create and Edit Formulas 27 Distinguishing Absolute and Relative Cell References 28 Using Operators in Formulas 28 The Arithmetic Operators 29 The Comparison Operators 30 The String Operator and the Wildcards 30 Copying or Moving Formulas and Their Computed Values 31 Viewing All Formulas in a Spreadsheet 32 Finding and Replacing Formula Elements 33 Chapter 2:  Overview of the iWork Functions 33 An Introduction to Functions 34 Information About Functions 34 Syntax Elements and Terms Used In Function Definitions 36 Value Types 40 Listing of Function Categories 41 Pasting from Examples in Help 42 Chapter 3:  Date and Time Functions 42 Listing of Date and Time Functions 44 DATE 3 Contents 4 Contents 45 DATEDIF 47 DATEVALUE 47 DAY 48 DAYNAME 49 DAYS360 50 EDATE 51 EOMONTH 51 HOUR 52 MINUTE 53 MONTH 54 MONTHNAME 54 NETWORKDAYS 55 NOW 56 SECOND 56 TIME 57 TIMEVALUE 58 TODAY 59 WEEKDAY 60 WEEKNUM 61 WORKDAY 62 YEAR 63 YEARFRAC 64 Chapter 4:  Duration Functions 64 Listing of Duration Functions 65 DUR2DAYS 65 DUR2HOURS 66 DUR2MILLISECONDS 67 DUR2MINUTES 68 DUR2SECONDS 69 DUR2WEEKS 70 DURATION 71 STRIPDURATION 72 Chapter 5:  Engineering Functions 72 Listing of Engineering Functions 73 BASETONUM 74 BESSELJ 75 BESSELY 76 BIN2DEC 77 BIN2HEX 78 BIN2OCT 79 CONVERT Contents 5 80 Supported Conversion Units 80 Weight and mass 80 Distance 80 Duration 81 Speed 81 Pressure 81 Force 81 Energy 82 Power 82 Magnetism 82 Temperature 82 Liquid 83 Metric prefixes 83 DEC2BIN 84 DEC2HEX 85 DEC2OCT 86 DELTA 87 ERF 87 ERFC 88 GESTEP 89 HEX2BIN 90 HEX2DEC 91 HEX2OCT 92 NUMTOBASE 93 OCT2BIN 94 OCT2DEC 95 OCT2HEX 96 Chapter 6:  Financial Functions 96 Listing of Financial Functions 99 ACCRINT 101 ACCRINTM 103 BONDDURATION 104 BONDMDURATION 105 COUPDAYBS 107 COUPDAYS 108 COUPDAYSNC 109 COUPNUM 110 CUMIPMT 112 CUMPRINC 114 DB 116 DDB 117 DISC 6 Contents 119 EFFECT 120 FV 122 INTRATE 123 IPMT 125 IRR 126 ISPMT 128 MIRR 129 NOMINAL 130 NPER 132 NPV 134 PMT 135 PPMT 137 PRICE 138 PRICEDISC 140 PRICEMAT 141 PV 144 RATE 146 RECEIVED 147 SLN 148 SYD 149 VDB 150 YIELD 152 YIELDDISC 153 YIELDMAT 155 Chapter 7:  Logical and Information Functions 155 Listing of Logical and Information Functions 156 AND 157 FALSE 158 IF 159 IFERROR 160 ISBLANK 161 ISERROR 162 ISEVEN 163 ISODD 164 NOT 165 OR 166 TRUE 167 Chapter 8:  Numeric Functions 167 Listing of Numeric Functions 170 ABS 170 CEILING Contents 7 172 COMBIN 173 EVEN 174 EXP 174 FACT 175 FACTDOUBLE 176 FLOOR 177 GCD 178 INT 179 LCM 179 LN 180 LOG 181 LOG10 182 MOD 183 MROUND 184 MULTINOMIAL 185 ODD 186 PI 186 POWER 187 PRODUCT 188 QUOTIENT 189 RAND 189 RANDBETWEEN 190 ROMAN 191 ROUND 192 ROUNDDOWN 193 ROUNDUP 195 SIGN 195 SQRT 196 SQRTPI 196 SUM 197 SUMIF 198 SUMIFS 200 SUMPRODUCT 201 SUMSQ 202 SUMX2MY2 203 SUMX2PY2 204 SUMXMY2 204 TRUNC 206 Chapter 9:  Reference Functions 206 Listing of Reference Functions 207 ADDRESS 209 AREAS 8 Contents 209 CHOOSE 210 COLUMN 211 COLUMNS 211 HLOOKUP 213 HYPERLINK 214 INDEX 216 INDIRECT 217 LOOKUP 218 MATCH 219 OFFSET 221 ROW 221 ROWS 222 TRANSPOSE 223 VLOOKUP 225 Chapter 10:  Statistical Functions 225 Listing of Statistical Functions 230 AVEDEV 231 AVERAGE 232 AVERAGEA 233 AVERAGEIF 234 AVERAGEIFS 236 BETADIST 237 BETAINV 238 BINOMDIST 239 CHIDIST 239 CHIINV 240 CHITEST 242 CONFIDENCE 242 CORREL 244 COUNT 245 COUNTA 246 COUNTBLANK 247 COUNTIF 248 COUNTIFS 250 COVAR 252 CRITBINOM 253 DEVSQ 253 EXPONDIST 254 FDIST 255 FINV 256 FORECAST 257 FREQUENCY Contents 9 259 GAMMADIST 260 GAMMAINV 260 GAMMALN 261 GEOMEAN 262 HARMEAN 262 INTERCEPT 264 LARGE 265 LINEST 267 Additional Statistics 268 LOGINV 269 LOGNORMDIST 270 MAX 270 MAXA 271 MEDIAN 272 MIN 273 MINA 274 MODE 275 NEGBINOMDIST 276 NORMDIST 277 NORMINV 277 NORMSDIST 278 NORMSINV 279 PERCENTILE 280 PERCENTRANK 281 PERMUT 282 POISSON 282 PROB 284 QUARTILE 285 RANK 287 SLOPE 288 SMALL 289 STANDARDIZE 290 STDEV 291 STDEVA 293 STDEVP 294 STDEVPA 296 TDIST 297 TINV 297 TTEST 298 VAR 300 VARA 302 VARP 303 VARPA 10 Contents 305 ZTEST 306 Chapter 11:  Text Functions 306 Listing of Text Functions 308 CHAR 308 CLEAN 309 CODE 310 CONCATENATE 311 DOLLAR 312 EXACT 312 FIND 313 FIXED 314 LEFT 315 LEN 316 LOWER 316 MID 317 PROPER 318 REPLACE 319 REPT 319 RIGHT 320 SEARCH 322 SUBSTITUTE 323 T 323 TRIM 324 UPPER 325 VALUE 326 Chapter 12:  Trigonometric Functions 326 Listing of Trigonometric Functions 327 ACOS 328 ACOSH 329 ASIN 329 ASINH 330 ATAN 331 ATAN2 332 ATANH 333 COS 334 COSH 334 DEGREES 335 RADIANS 336 SIN 337 SINH 338 TAN Contents 11 339 TANH 340 Chapter 13:  Additional Examples and Topics 340 Additional Examples and Topics Included 341 Common Arguments Used in Financial Functions 348 Choosing Which Time Value of Money Function to Use 348 Regular Cash Flows and Time Intervals 350 Irregular Cash Flows and Time Intervals 351 Which Function Should You Use to Solve Common Financial Questions? 353 Example of a Loan Amortization Table 355 More on Rounding 358 Using Logical and Information Functions Together 358 Adding Comments Based on Cell Contents 360 Trapping Division by Zero 360 Specifying Conditions and Using Wildcards 362 Survey Results Example 365 Index 13 iWork comes with more than 250 functions you can use to simplify statistical, financial, engineering, and other computations. The built-in Function Browser gives you a quick way to learn about functions and add them to a formula. To get started, just type the equal sign in an empty table cell to open the Formula Editor. Then choose Insert > Function > Show Function Browser. This user guide provides detailed instructions to help you write formulas and use functions. In addition to this book, other resources are available to help you. Onscreen help Onscreen help contains all of the information in this book in an easy-to-search format that’s always available on your computer. You can open iWork Formulas & Functions Help from the Help menu in any iWork application. With Numbers, Pages, or Keynote open, choose Help > “iWork Formulas & Functions Help.” Preface Welcome to iWork Formulas & Functions 14 Preface Welcome to iWork Formulas & Functions iWork website Read the latest news and information about iWork at www.apple.com/iwork. Support website Find detailed information about solving problems at www.apple.com/support/iwork. Help tags iWork applications provide help tags—brief text descriptions—for most onscreen items. To see a help tag, hold the pointer over an item for a few seconds. Online video tutorials Online video tutorials at www.apple.com/iwork/tutorials provide how-to videos about performing common tasks in Keynote, Numbers, and Pages. The first time you open an iWork application, a message appears with a link to these tutorials on the web. You can view these video tutorials anytime by choosing Help > Video Tutorials in Keynote, Numbers, and Pages. 15 This chapter explains how to perform calculations in table cells by using formulas. The Elements of Formulas A formula performs a calculation and displays the result in the cell where you place the formula. A cell containing a formula is referred to as a formula cell. For example, in the bottom cell of a column you can insert a formula that sums the numbers in all the cells above it. If any of the values in the cells above the formula cell change, the sum displayed in the formula cell updates automatically. A formula performs calculations using specific values you provide. The values can be numbers or text (constants) you type into the formula. Or they can be values that reside in table cells you identify in the formula by using cell references. Formulas use operators and functions to perform calculations using the values you provide:  Operators are symbols that initiate arithmetic, comparison, or string operations. You use the symbols in formulas to indicate the operation you want to use. For example, the symbol + adds values, and the symbol = compares two values to determine whether they’re equal. =A2 + 16:  A formula that uses an operator to add two values. =:  Always precedes a formula. A2:  A cell reference. A2 refers to the second cell in the first column. +:  An arithmetic operator that adds the value that precedes it with the value that follows it. 16:  A numeric constant.  Functions are predefined, named operations, such as SUM and AVERAGE. To use a function, you enter its name and, in parentheses following the name, you provide the arguments the function needs. Arguments specify the values the function will use when it performs its operations. Using Formulas in Tables 1 =SUM(A2:A10):  A formula that uses the function SUM to add the values in a range of cells (nine cells in the first column). A2:A10:  A cell reference that refers to the values in cells A2 through A10. To learn how to Go to Instantly display the sum, average, minimum value, maximum value, and count of values in selected cells and optionally save the formula used to derive these values in Numbers “Performing Instant Calculations in Numbers” (page 17) Quickly add a formula that displays the sum, average, minimum value, maximum value, count, or product of values in selected cells “Using Predefined Quick Formulas” (page 18) Use tools and techniques to create and modify your formulas in Numbers “Adding and Editing Formulas Using the Formula Editor” (page 19) “Adding and Editing Formulas Using the Formula Bar” (page 20) “Adding Functions to Formulas” (page 21) “Removing Formulas” (page 24) Use tools and techniques to create and modify your formulas in Pages and Keynote “Adding and Editing Formulas Using the Formula Editor” (page 19) Use the hundreds of iWork functions and review examples illustrating ways to apply the functions in financial, engineering, statistical, and other contexts Help > “iWork Formulas and Functions Help” Help > “iWork Formulas and Functions User Guide” Add cell references of different kinds to a formula in Numbers “Referring to Cells in Formulas” (page 24) “Using the Keyboard and Mouse to Create and Edit Formulas” (page 26) “Distinguishing Absolute and Relative Cell References” (page 27) Use operators in formulas “The Arithmetic Operators” (page 28) “The Comparison Operators” (page 29) “The String Operator and the Wildcards” (page 30) Copy or move formulas or the value they compute among table cells “Copying or Moving Formulas and Their Computed Values” (page 30) Find formulas and formula elements in Numbers “Viewing All Formulas in a Spreadsheet” (page 31) “Finding and Replacing Formula Elements” (page 32) 16 Chapter 1 Using Formulas in Tables Chapter 1 Using Formulas in Tables 17 Performing Instant Calculations in Numbers In the lower left of the Numbers window, you can view the results of common calculations using values in two or more selected table cells. To perform instant calculations: 1 Select two or more cells in a table. They don’t have to be adjacent. The results of calculations using the values in those cells are instantly displayed in the lower left corner of the window. The results in the lower left are based on values in these two selected cells. sum:  Shows the sum of numeric values in selected cells. avg:  Shows the average of numeric values in selected cells. min:  Shows the smallest numeric value in selected cells. max:  Shows the largest numeric value in selected cells. count:  Shows the number of numeric values and date/time values in selected cells. Empty cells and cells that contain types of values not listed above aren’t used in the calculations. 2 To perform another set of instant calculations, select different cells. If you find a particular calculation very useful and you want to incorporate it into a table, you can add it as a formula to an empty table cell. Simply drag sum, avg, or one of the other items in the lower left to an empty cell. The cell doesn’t have to be in the same table as the cells used in the calculations. Using Predefined Quick Formulas An easy way to perform a basic calculation using values in a range of adjacent table cells is to select the cells and then add a quick formula. In Numbers, this is accomplished using the Function pop-up menu in the toolbar. In Keynote and Pages, use the Function pop-up menu in the Format pane of the Table inspector. Sum:  Calculates the sum of numeric values in selected cells. Average:  Calculates the average of numeric values in selected cells. Minimum:  Determines the smallest numeric value in selected cells. Maximum:  Determines the largest numeric value in selected cells Count:  Determines the number of numeric values and date/time values in selected cells. Product:  Multiplies all the numeric values in selected cells. You can also choose Insert > Function and use the submenu that appears. Empty cells and cells containing types of values not listed are ignored. Here are ways to add a quick formula: To use selec mm ted values in a column or a row, select the cells. In Numbers, click Function in the toolbar, and choose a calculation from the pop-up menu. In Keynote or Pages, choose Insert > Function and use the submenu that appears. If the cells are in the same column, the result is placed in the first empty cell beneath the selected cells. If there is no empty cell, a row is added to hold the result. Clicking on the cell will display the formula. If the cells are in the same row, the result is placed in the first empty cell to the right of the selected cells. If there is no empty cell, a column is added to hold the result. Clicking on the cell will display the formula. mm To use all the values in a column’s body cells, first click the column’s header cell or reference tab. Then, in Numbers, click Function in the toolbar, and choose a calculation from the pop-up menu. In Keynote or Pages, choose Insert > Function and use the submenu that appears. The result is placed in a footer row. If a footer row doesn’t exist, one is added. Clicking on the cell will display the formula. 18 Chapter 1 Using Formulas in Tables Chapter 1 Using Formulas in Tables 19 mm To use all the values in a row, first click the row’s header cell or reference tab. Then, in Numbers, click Function in the toolbar, and choose a calculation from the popup menu. In Keynote or Pages, choose Insert > Function and use the submenu that appears. The result is placed in a new column. Clicking on the cell will display the formula. Creating Your Own Formulas Although you can use several shortcut techniques to add formulas that perform simple calculations (see “Performing Instant Calculations in Numbers” on page 17 and “Using Predefined Quick Formulas” on page 18), when you want more control you use the formula tools to add formulas. To learn how to Go to Use the Formula Editor to work with a formula “Adding and Editing Formulas Using the Formula Editor” (page 19) Use the resizable formula bar to work with a formula in Numbers “Adding and Editing Formulas Using the Formula Bar” (page 20) Use the Function Browser to quickly add functions to formulas when using the Formula Editor or the formula bar “Adding Functions to Formulas” (page 21) Detect an erroneous formula “Handling Errors and Warnings in Formulas” (page 23) Adding and Editing Formulas Using the Formula Editor The Formula Editor may be used as an alternative to editing a formula directly in the formula bar (see “Adding and Editing Formulas Using the Formula Bar” on page 20). The Formula Editor has a text field that holds your formula. As you add cell references, operators, functions, or constants to a formula, they look like this in the Formula Editor. All formulas must begin with the equal sign. The Sum function. References to cells using their names. A reference to a range of three cells. The Subtraction operator. Here are ways to work with the Formula Editor: mm To open the Formula Editor, do one of the following:  Select a table cell and then type the equal sign (=).  In Numbers, double-click a table cell that contains a formula. In Keynote and Pages, select the table, and then double-click a table cell that contains a formula.  In Numbers only, select a table cell, click Function in the toolbar, and then choose Formula Editor from the pop-up menu.  In Numbers only, select a table cell and then choose Insert > Function > Formula Editor. In Keynote and Pages, choose Formula Editor from the Function pop-up menu in the Format pane of the Table inspector.  Select a cell that contains a formula, and then press Option-Return. The Formula Editor opens over the selected cell, but you can move it. mm To move the Formula Editor, hold the pointer over the left side of the Formula Editor until it changes into a hand, and then drag. mm To build your formula, do the following:  To add an operator or a constant to the text field, place the insertion point and type. You can use the arrow keys to move the insertion point around in the text field. See “Using Operators in Formulas” on page 28 to learn about operators you can use. Note: When your formula requires an operator and you haven’t added one, the + operator is inserted automatically. Select the + operator and type a different operator if needed.  To add cell references to the text field, place the insertion point and follow the instructions in “Referring to Cells in Formulas” on page 24.  To add functions to the text field, place the insertion point and follow the instructions in “Adding Functions to Formulas” on page 21. mm To remove an element from the text field, select the element and press Delete. mm To accept changes, press Return, press Enter, or click the Accept button in the Formula Editor. You can also click outside the table. To close the Formula Editor and not accept any changes you made, press Esc or click the Cancel button in the Formula Editor. Adding and Editing Formulas Using the Formula Bar In Numbers, the formula bar, located beneath the format bar, lets you create and modify formulas for a selected cell. As you add cell references, operators, functions, or constants to a formula, they appear like this. The Subtraction operator. References to cells The Sum function. using their names. All formulas must begin with the equal sign. A reference to a range of three cells. Here are ways to work with the formula bar: mm To add or edit a formula, select the cell and add or change formula elements in the formula bar. mm To add elements to your formula, do the following: 20 Chapter 1 Using Formulas in Tables Chapter 1 Using Formulas in Tables 21  To add an operator or a constant, place the insertion point in the formula bar and type. You can use the arrow keys to move the insertion point around. See “Using Operators in Formulas” on page 28 to learn about operators you can use. When your formula requires an operator and you haven’t added one, the + operator is inserted automatically. Select the + operator and type a different operator if needed.  To add cell references to the formula, place the insertion point and follow the instructions in “Referring to Cells in Formulas” on page 24.  To add functions to the formula, place the insertion point and follow the instructions in “Adding Functions to Formulas” on page 21. mm To increase or decrease the display size of formula elements in the formula bar, choose an option from the Formula Text Size pop-up menu above the formula bar. To increase or decrease the height of the formula bar, drag the resize control at the far right of the formula bar down or up, or double-click the resize control to auto-fit the formula. mm To remove an element from the formula, select the element and press Delete. mm To save changes, press Return, press Enter, or click the Accept button above the formula bar. You can also click outside the formula bar. To avoid saving any changes you made, click the Cancel button above the formula bar. Adding Functions to Formulas A function is a predefined, named operation (such as SUM and AVERAGE) that you can use to perform a calculation. A function can be one of several elements in a formula, or it can be the only element in a formula. There are several categories of functions, ranging from financial functions that calculate interest rates, investment values, and other information to statistical functions that calculate averages, probabilities, standard deviations, and so on. To learn about all the iWork function categories and their functions, and to review numerous examples that illustrate how to use them, choose Help > “iWork Formulas and Functions Help” or Help > “iWork Formulas and Functions User Guide”. Although you can type a function into the text field of the Formula Editor or into the formula bar (Numbers only), the Function Browser offers a convenient way to add a function to a formula. Select a function to view information about it. Search for a function. Insert the selected function. Select a category to view functions in that category. Left pane:  Lists categories of functions. Select a category to view functions in that category. Most categories represent families of related functions. The All category lists all the functions in alphabetical order. The Recent category lists the ten functions most recently inserted using the Function Browser. Right pane:  Lists individual functions. Select a function to view information about it and to optionally add it to a formula. Lower pane:  Displays detailed information about the selected function. To use the Function Browser to add a function: 1 In the Formula Editor or the formula bar (Numbers only), place the insertion point where you want the function added. Note: When your formula requires an operator before or after a function and you haven’t added one, the + operator is inserted automatically. Select the + operator and type a different operator if needed. 22 Chapter 1 Using Formulas in Tables Chapter 1 Using Formulas in Tables 23 2 In Pages or Keynote, choose Insert > Function > Show Function Browser to open the Function Browser. In Numbers, open the Function Browser by doing one of the following:  Click the Function Browser button in the formula bar.  Click the Function button in the toolbar and choose Show Function Browser.  Choose Insert > Function > Show Function Browser.  Choose View > Show Function Browser. 3 Select a function category. 4 Choose a function by double-clicking it or by selecting it and clicking Insert Function. 5 In the Formula Editor or formula bar (Numbers only), replace each argument placeholder in the inserted function with a value. Help for the “issue” argument appears when the pointer is over the placeholder. Placeholders for optional arguments are light gray. Click to see a list of valid values. To review a brief description of an argument’s value:  Hold the pointer over the argument placeholder. You can also refer to information about the argument in the Function Browser window. To specify a value to replace any argument placeholder:  Click the argument placeholder and type a constant or insert a cell reference (see “Referring to Cells in Formulas” on page 24 for instructions). If the argument placeholder is light gray, providing a value is optional. To specify a value to replace an argument placeholder that has a disclosure triangle:  Click the disclosure triangle and then choose a value from the pop-up menu. To review information about a value in the pop-up menu, hold the pointer over the value. To review help for the function, select Function Help. Handling Errors and Warnings in Formulas When a formula in a table cell is incomplete, contains invalid cell references, or is otherwise incorrect, or when an import operation creates an error condition in a cell, Number or Pages displays an icon in the cell. A blue triangle in the upper left of a cell indicates one or more warnings. A red triangle in the middle of a cell means that a formula error occurred. To view error and warning messages: mm Click the icon. A message window summarizes each error and warning condition associated with "the cell. To have Numbers issue a warning when a cell referenced in a formula is empty, choose Numbers > Preferences and in the General pane select “Show warnings when formulas reference empty cells.” This option is not available in Keynote or Pages. Removing Formulas If you no longer want to use a formula that’s associated with a cell, you can quickly remove the formula. To remove a formula from a cell: 1 Select the cell. 2 Press the Delete key. In Numbers, if you need to review formulas in a spreadsheet before deciding what to delete, choose View > Show Formula List. Referring to Cells in Formulas All tables have reference tabs. These are the row numbers and column headings. In Numbers, the reference tabs are visible anytime the table has focus; for example, a cell in the table is currently selected. In Keynote and Pages, reference tabs appear only when a formula within a table cell is selected. In Numbers, the reference tabs look like this: The reference tabs are the gray box at the top of each column or at the left of each row containing the column letters (for example, “A”) or row numbers (for example, “3”). The look of the reference tabs in Keynote and Pages is similar to the look in Numbers. You use cell references to identify cells whose values you want to use in formulas. In Numbers, the cells can be in the same table as the formula cell, or they can be in another table on the same or a different sheet. 24 Chapter 1 Using Formulas in Tables Chapter 1 Using Formulas in Tables 25 Cell references have different formats, depending on such factors as whether the cell’s table has headers, whether you want to refer to a single cell or a range of cells, and so on. Here’s a summary of the formats that you can use for cell references. To refer to Use this format Example Any cell in the table containing the formula The reference tab letter followed by the reference tab number for the cell C55 refers to the 55th row in the third column. A cell in a table that has a header row and a header column The column name followed by the row name 2006 Revenue refers to a cell whose header row contains 2006 and header column contains Revenue. A cell in a table that has multiple header rows or columns The name of the header whose columns or rows you want to refer to If 2006 is a header that spans two columns (Revenue and Expenses), 2006 refers to all the cells in the Revenue and Expenses columns. A range of cells A colon (:) between the first and last cell in the range, using reference tab notation to identify the cells B2:B5 refers to four cells in the second column. All the cells in a row The row name or rownumber: row-number 1:1 refers to all the cells in the first row. All the cells in a column The column letter or name C refers to all the cells in the third column. All the cells in a range of rows A colon (:) between the row number or name of the first and last row in the range 2:6 refers to all the cells in five rows. All the cells in a range of columns A colon (:) between the column letter or name of the first and last column in the range B:C refers to all the cells in the second and third columns. In Numbers, a cell in another table on the same sheet If the cell name is unique in the spreadsheet then only the cell name is required; otherwise, the table name followed by two colons (::) and then the cell identifier Table 2::B5 refers to cell B5 in a table named Table 2. Table 2::2006 Class Enrollment refers to a cell by name. In Numbers, a cell in a table on another sheet If the cell name is unique in the spreadsheet then only the cell name is required; otherwise, the sheet name followed by two colons (::), the table name, two more colons, then the cell identifier Sheet 2::Table 2::2006 Class Enrollment refers to a cell in a table named Table 2 on a sheet named Sheet 2. In Numbers, you can omit a table or sheet name if the cell or cells referenced have names unique in the spreadsheet. In Numbers, when you reference a cell in a multirow or multicolumn header, you’ll notice the following behavior:  The name in the header cell closest to the cell referring to it is used. For example, if a table has two header rows, and B1 contains “Dog” and B2 contains “Cat,” when you save a formula that uses “Dog,” “Cat” is saved instead.  However, if “Cat” appears in another header cell in the spreadsheet, “Dog” is retained. To learn how to insert cell references into a formula, see “Using the Keyboard and Mouse to Create and Edit Formulas” below. See “Distinguishing Absolute and Relative Cell References” on page 27 to learn about absolute and relative forms of cell references, which are important when you need to copy or move a formula. Using the Keyboard and Mouse to Create and Edit Formulas You can type cell references into a formula, or you can insert cell references using mouse or keyboard shortcuts. Here are ways to insert cell references: mm To use a keyboard shortcut to enter a cell reference, place the insertion point in the Formula Editor or formula bar (Numbers only) and do one of the following:  To refer to a single cell, press Option and then use the arrow keys to select the cell.  To refer to a range of cells, press and hold Shift-Option after selecting the first cell in the range until the last cell in the range is selected.  In Numbers, to refer to cells in another table on the same or a different sheet, select the table by pressing Option-Command–Page Down to move downward through tables or Option-Command–Page Up to move upward through tables. Once the desired table is selected, continue holding down Option, but release Command, and use the arrow keys to select the desired cell or range (using Shift-Option) of cells.  To specify absolute and relative attributes of a cell reference after inserting one, click the inserted reference and press Command-K to cycle through the options. See “Distinguishing Absolute and Relative Cell References” on page 27 for more information. mm To use the mouse to enter a cell reference, place the insertion point in the Formula Editor or the formula bar (Numbers only) and do one of the following in the same table as the formula cell or, for Numbers only, in a different table on the same or a different sheet:  To refer to a single cell, click the cell.  To refer to all the cells in a column or a row, click the reference tab for the column or row. 26 Chapter 1 Using Formulas in Tables Chapter 1 Using Formulas in Tables 27 To r  efer to a range of cells, click a cell in the range and drag up, down, left, or right to select or resize the cell range.  To specify absolute and relative attributes of a cell reference, click the disclosure triangle of the inserted reference and choose an option from the pop-up menu. See “Distinguishing Absolute and Relative Cell References” on page 27 for more information. In Numbers, the cell reference inserted uses names instead of reference tab notation unless the “Use header cell names as references” is deselected in the General pane of Numbers preferences. In Keynote and Pages, the cell reference inserted uses names instead of reference tab notation if referenced cells have headers. mm To type a cell reference, place the insertion point in the Formula Editor or the formula bar (Numbers only), and enter the cell reference using one of the formats listed in “Referring to Cells in Formulas” on page 24. When you type a cell reference that includes the name of a header cell (all applications), table (Numbers only), or sheet (Numbers only), after typing 3 characters a list of suggestions pops up if the characters you typed match one or more names in your spreadsheet. You can select from the list or continue typing. To disable name suggestions in Numbers, choose Numbers > Preferences and deselect “Use header cell names as references” in the General pane. Distinguishing Absolute and Relative Cell References Use absolute and relative forms of a cell reference to indicate the cell to which you want the reference to point if you copy or move its formula. If a cell reference is relative (A1):  When its formula moves, it stays the same. However, when the formula is cut or copied and then pasted, the cell reference changes so that it retains the same position relative to the formula cell. For example, if a formula containing A1 appears in C4 and you copy the formula and paste it in C5, the cell reference in C5 becomes A2. If the row and column components of a cell reference are absolute ($A$1):  When its formula is copied, the cell reference doesn’t change. You use the dollar sign ($) to designate a row or column component absolute. For example, if a formula containing $A$1 appears in C4 and you copy the formula and paste it in C5 or in D5, the cell reference in C5 or D5 remains $A$1. If the row component of a cell reference is absolute (A$1):  The column component is relative and may change to retain its position relative to the formula cell. For example, if a formula containing A$1 appears in C4 and you copy the formula and paste it in D5, the cell reference in D5 becomes B$1. If the column component of a cell reference is absolute ($A1):  The row component is relative and may change to retain its position relative to the formula cell. For example, if a formula containing $A1 appears in C4 and you copy the formula and paste it in C5 or in D5, the cell reference in C5 and D5 becomes $A2. Here are ways to specify the absoluteness of cell reference components: mm Type the cell reference using one of the conventions described above. mm Click the disclosure triangle of a cell reference and choose an option from the pop-up menu. mm Select a cell reference and press Command-K to cycle through options. Using Operators in Formulas Use operators in formulas to perform arithmetic operations and to compare values:  Arithmetic operators perform arithmetic operations, such as addition and subtraction, and return numerical results. See “The Arithmetic Operators” on page 28 to learn more.  Comparison operators compare two values and return TRUE or FALSE. See “The Comparison Operators” on page 29 to learn more. The Arithmetic Operators You can use arithmetic operators to perform arithmetic operations in formulas. When you want to Use this arithmetic operator For example, if A2 contains 20 and B2 contains 2, the formula Add two values + (plus sign) A2 + B2 returns 22. Subtract one value from another value – (minus sign) A2 – B2 returns 18. Multiply two values * (asterisk) A2 * B2 returns 40. Divide one value by another value / (forward slash) A2 / B2 returns 10. Raise one value to the power of another value ^ (caret) A2 ^ B2 returns 400. Calculate a percentage % (percent sign) A2% returns 0.2, formatted for display as 20%. Using a string with an arithmetic operator returns an error. For example, 3 + “hello” is not a correct arithmetic operation. 28 Chapter 1 Using Formulas in Tables Chapter 1 Using Formulas in Tables 29 The Comparison Operators You can use comparison operators to compare two values in formulas. Comparison operations always return the values TRUE or FALSE. Comparison operators can also used to build the conditions used by some functions. See “condition” in the table “Syntax Elements and Terms Used In Function Definitions” on page 34 When you want to determine whether Use this comparison operator For example, if A2 contains 20 and B2 contains 2, the formula Two values are equal = A2 = B2 returns FALSE. Two values aren’t equal <> A2 <> B2 returns TRUE. The first value is greater than the second value > A2 > B2 returns TRUE. The first value is less than the second value < A2 < B2 returns FALSE. The first value is greater than or equal to the second value >= A2 >= B2 returns TRUE. The first value is less than or equal to the second value <= A2 <= B2 returns FALSE. Strings are larger than numbers. For example, “hello” > 5 returns TRUE. TRUE and FALSE can be compared with each other, but not with numbers or strings. TRUE > FALSE, and FALSE < TRUE, because TRUE is interpreted as 1 and FALSE is interpreted as 0. TRUE = 1 returns FALSE, and TRUE = “SomeText” returns FALSE. Comparison operations are used primarily in functions, such as IF, which compare two values and then perform other operations depending on whether the comparison returns TRUE or FALSE. For more information about this topic, choose Help > “iWork Formulas and Functions Help” or Help > “iWork Formulas and Functions User Guide.” The String Operator and the Wildcards The string operator can be used in formulas and wildcards can be used in conditions. When you want to Use this string operator or wildcard For example Concatenate strings or the contents of cells & “abc”&”def” returns “abcdef” “abc”&A1 returns “abc2” if cell A1 contains 2. A1&A2 returns “12” if cell A1 contains 1 and cell A2 contains 2. Match a single character ? “ea?” will match any string beginning with “ea” and containing exactly one additional character. Match any number of characters * “*ed” will match a string of any length ending with “ed”. Literally match a wildcard character ~ “~?” will match the question mark, instead of using the question mark to match any single character. For more information on the use of wildcards in conditions, see “Specifying Conditions and Using Wildcards” on page 360. Copying or Moving Formulas and Their Computed Values Here are techniques for copying and moving cells related to a formula: mm To copy the computed value in a formula cell but not the formula, select the cell, choose Edit > Copy, select the cell you want to hold the value, and then choose Edit > Paste Values. mm To copy or move a formula cell or a cell that a formula refers to, follow the instructions in “Copying and Moving Cells” in Numbers Help or the Numbers User Guide. In Numbers, if the table is large and you want to move the formula to a cell that’s out of view, select the cell, choose Edit > “Mark for Move,” select the other cell, and then choose Edit > Move. For example, if the formula =A1 is in cell D1 and you want to move the same formula to cell X1, select D1, choose Edit > “Mark for Move,” select X1, and then choose Edit > Move. The formula =A1 appears in cell X1. If you copy or move a formula cell:  Change cell references as “Distinguishing Absolute and Relative Cell References” on page 27 describes if needed. If you move a cell that a formula refers to:  The cell reference in the formula is automatically updated. For example, if a reference to A1 appears in a formula and you move A1 to D95, the cell reference in the formula becomes D95. 30 Chapter 1 Using Formulas in Tables Chapter 1 Using Formulas in Tables 31 Viewing All Formulas in a Spreadsheet In Numbers, to view a list of all the formulas in a spreadsheet, choose View > Show Formula List or click on the formula list button in the toolbar. Location: Identifies the sheet and table in which the formula is located. Results:  Displays the current value computed by the formula. Formula:  Shows the formula. Here are ways to use the formula list window: mm To identify the cell containing a formula, click the formula. The table is shown above the formula list window with the formula cell selected. mm To edit the formula, double-click it. mm To change the size of the formula list window, drag the selection handle in its upper right corner up or down. mm To find formulas that contain a particular element, type the element in the search field and press Return. Finding and Replacing Formula Elements In Numbers, using the Find & Replace window, you can search through all of a spreadsheet’s formulas to find and optionally change elements. Here are ways to open the Find & Replace window: mm Choose Edit > Find > Show Search, and then click Find & Replace. mm Choose View > Show Formula List, and then click Find & Replace. Find: Type the formula element (cell reference, operator, function, and so on) you want to find. In:  Choose Formulas Only from this pop-up menu. Match case:  Select to find only elements whose uppercase and lowercase letters match exactly what’s in the Find field. Whole words:  Select to find only elements whose entire contents match what’s in the Find field. Replace:  Optionally type what you want to use to replace what’s in the Find field. Repeat search (loop):  Select to continue looking for what’s in the Find field even after the entire spreadsheet has been searched. Next or Previous:  Click to search for the next or previous instance of what’s in the Find field. When an element is found, the Formula Editor opens and displays the formula containing the instance of the element. Replace All:  Click to replace all instances of what’s in the Find field with what’s in the Replace field. Replace:  Click to replace the current instance of what’s in the Find field with what’s in the Replace field. Replace & Find:  Click to replace the current instance of what’s in the Find field and to locate the next instance. 32 Chapter 1 Using Formulas in Tables 33 This chapter introduces the functions available in iWork. An Introduction to Functions A function is a named operation that you can include in a formula to perform a calculation or to manipulate data in a table cell. iWork provides functions that do things such as perform mathematical or financial operations, retrieve cell values based on a search, manipulate strings of text, or get the current date and time. Each function has a name followed by one or more arguments enclosed in parentheses. You use arguments to provide the values that the function needs to perform its work. For example, the following formula contains a function named SUM with a single argument (a range of cells) that adds the values in column A, rows 2 through 10: =SUM(A2:A10) The number and types of arguments vary for each function. The number and description of the arguments are included with the function in the alphabetical “Listing of Function Categories” on page 40. The descriptions also include additional information and examples for each function. Overview of the iWork Functions 2 Information About Functions For further information on Go to Syntax used in function definitions “Syntax Elements and Terms Used In Function Definitions” on page 34 Types of arguments that are used by functions “Value Types” on page 36 Categories of functions, such as duration and statistical “Listing of Function Categories” on page 40. Functions are listed alphabetically within each category. Arguments common to several financial functions “Common Arguments Used in Financial Functions” on page 341 Supplemental examples and topics “Additional Examples and Topics Included” on page 340 Syntax Elements and Terms Used In Function Definitions Functions are described using specific syntax elements and terms. Term or symbol Meaning uppercase text Function names are shown in all uppercase text. However, a function name can be entered using any combination of uppercase or lowercase letters. parentheses Function arguments are enclosed in parentheses. Parentheses are required, although in limited circumstances iWork can automatically insert the final closing parenthesis for you. italic text Italic text indicates that you must replace the argument name with a value the function will use to calculate a result. Arguments have a value type, such as “number,” “date/time,” or “string.” Value types are discussed in “Value Types” on page 36. commas and semicolons The syntax descriptions for functions use commas to separate arguments. If your Language and Text preferences (Mac OS X version 10.6 or higher) or International preferences (earlier versions of Max OS X) are set up to use the comma as a decimal separator, separate arguments using a semicolon instead of a comma. 34 Chapter 2 Overview of the iWork Functions Chapter 2 Overview of the iWork Functions 35 Term or symbol Meaning ellipsis (…) An argument followed by an ellipsis can be repeated as many times as necessary. Any limitations are described in the argument definition. array An array is a sequence of values used by a function, or returned by a function. array constant An array constant is a set of values enclosed within braces ({}) and is typed directly into the function. For example, {1, 2, 5, 7} or {“12/31/2008”, “3/15/2009”, “8/20/2010”}. array function A small number of functions are described as “array function,” meaning the function returns an array of values rather than a single value. These functions are commonly used to provide values to another function. Boolean expression A Boolean expression is an expression that evaluates to the Boolean value TRUE or FALSE. constant A constant is a value specified directly within the formula that contains no function calls or references. For example, in the formula =CONCATENATE(”cat”, “s”), “cat” and “s” are constants. modal argument A modal argument is one that can have one of several possible specified values. Usually, modal arguments specify something about the type of calculation the function should perform or about the type of data the function should return. If a modal argument has a default value, it is specified in the argument description. condition A condition is an expression that can include comparison operators, constants, the ampersand string operator, and references. The contents of the condition must be such that the result of comparing the condition to another value results in the Boolean value TRUE or FALSE. Further information and examples are included in “Specifying Conditions and Using Wildcards” on page 360. Value Types A function argument has a type, which specifies what type of information the argument can contain. Functions also return a value of a particular type. Value Type Description any If an argument is specified as “any,” it can be a Boolean value, date/time value, duration value, number value, or string value. Boolean A Boolean value is a logical TRUE (1) or FALSE (0) value or a reference to a cell containing or resulting in a logical TRUE or FALSE value. It is generally the result of evaluating a Boolean expression, but a Boolean value can be specified directly as an argument to a function or as the content of a cell. A common use of a Boolean value is to determine which expression is to be returned by the IF function. collection An argument that is specified as a collection can be a reference to a single table cell range, an array constant, or an array returned by an array function. An argument specified as collection will have an additional attribute defining the type of values it can contain. date/time This is a date/time value or a reference to a cell containing a date/time value in any of the formats supported by iWork. If a date/time value is typed into the function, it should be enclosed in quotation marks. You can choose to display only a date or time in a cell, but all date/time values contain both a date and a time. Although dates can usually be entered directly as strings (for example, “12/31/2010”), using the DATE function insures the date will be interpreted consistently regardless of the date format selected in System Preferences (search for “date format” in the System Preferences window). 36 Chapter 2 Overview of the iWork Functions Chapter 2 Overview of the iWork Functions 37 Value Type Description duration A duration is a length of time or a reference to a cell containing a length of time. Duration values consist of weeks (w or weeks), days (d or days), hours (h or hours), minutes (m or minutes), seconds (s or seconds), and milliseconds (ms or milliseconds). A duration value can be entered in one of two formats. The first format consists of a number, followed by a time period (such as h for hours), optionally followed by a space, and is repeated for other time periods. You can use either the abbreviation for specifying the period, such as “h”, or the full name, such as “hours.” For example, 12h 5d 3m represents a duration of 12 hours, 5 days, and 3 minutes. TIme periods do not have to be entered in order and spaces are not required. 5d 5h is the same as 5h5d. If typed directly into a formula, the string should be enclosed in quotation marks, as in “12h 5d 3m”. A duration can also be entered as a series of numbers delimited by colons. If this format is used, the seconds argument should be included and end with a decimal followed by the number of milliseconds, which can be 0, if the duration value could be confused with a date/time value. For example, 12:15:30.0 would represent a duration of 12 hours, 15 minutes, and 30 seconds, whereas 12:15:30 would be 12:15:30 a.m. 5:00.0 would represent a duration of exactly 5 minutes. If typed directly into a function, the string should be enclosed in quotation marks, as in “12:15:30.0” or “5:00.0”. If the cell is formatted to a particular duration display, the duration units are applied relative to that duration display and the milliseconds need not be specified. Value Type Description list A list is a comma-separated sequence of other values. For example, =CHOOSE(3, “1st”, “second”, 7, “last”). In some cases, the list is enclosed in an additional set of parentheses. For example, =AREAS((B1:B5, C10:C12)). modal A modal value is a single value, often a number, representing a specific mode for a modal argument. “Modal argument” is defined in “Syntax Elements and Terms Used In Function Definitions” on page 34. number A number value is a number, a numeric expression, or a reference to a cell containing a numeric expression. If the acceptable values of a number are limited (for example, the number must be greater than 0), this is included within the argument description. range value A range value is a reference to a single range of cells (can be a single cell). A range value will have an additional attribute defining the type of values it should contain. This will be included within the argument description. 38 Chapter 2 Overview of the iWork Functions Chapter 2 Overview of the iWork Functions 39 Value Type Description reference This is a reference to a single cell or a range of cells. If the range is more than one cell, the starting and ending cell are separated by a single colon. For example, =COUNT(A3:D7). Unless the cell name is unique within all tables, the reference must contain the name of the table if the reference is to a cell on another table. For example, =Table 2::B2. Note that the table name and cell reference are separated by a double colon (::). If the table is on another sheet, the sheet name must also be included, unless the cell name is unique within all the the sheets. For example, =SUM(Sheet 2::Table 1::C2:G2). The sheet name, table name and cell reference are separated by double colons. Some functions that accept ranges can operate on ranges that span multiple tables. Assume that you have a file open that has one sheet containing three tables (Table 1, Table 2, Table 3). Assume further that cell C2 in each table contains the number 1. The table-spanning formula =SUM(Table 1:Table 2 :: C2) would sum cell C2 in all tables between Table 1 and Table 2. So the result would be 2. If you drag Table 3 so that it appears between Table 1 and Table 2 in the sidebar, the function will return 3, since it is now summing cell C2 in all three tables (Table 3 is between Table 1 and Table 2). string A string is zero or more characters, or a reference to a cell containing one or more characters. The characters can consist of any printable characters, including numbers. If a string value is typed into the formula, it must be enclosed in quotation marks. If the string value is somehow limited (for example, the string must represent a date), this is included within the argument description. Listing of Function Categories There are several categories of functions. For example, some functions perform calculations on date/time values, logical functions give a Boolean (TRUE or FALSE) result, and other functions perform financial calculations. Each of the categories of functions is discussed in a separate chapter. “Listing of Date and Time Functions” on page 42 “Listing of Duration Functions” on page 64 “Listing of Engineering Functions” on page 72 “Listing of Financial Functions” on page 96 “Listing of Logical and Information Functions” on page 155 “Listing of Numeric Functions” on page 167 “Listing of Reference Functions” on page 206 “Listing of Statistical Functions” on page 225 “Listing of Text Functions” on page 306 “Listing of Trigonometric Functions” on page 326 40 Chapter 2 Overview of the iWork Functions Chapter 2 Overview of the iWork Functions 41 Pasting from Examples in Help Many of the examples in help can be copied and pasted directly into a table or, in Numbers, onto a blank canvas. There are two groups of examples which can be copied from help and pasted into a table. The first are individual examples included within help. All such examples begin with an equal sign (=). In the help for the HOUR function, there are two such examples. To use one of these examples, select the text beginning with the equal sign through the end of the example. Once this text is highlighted, you can copy it and then paste it into any cell in a table. An alternative to copy and paste is to drag the selection from the example and drop it onto any cell in a table. The second kind of example that can be copied are example tables included within help. This is the help example table for ACCRINT. To use an example table, select all the cells in the example table, including the first row. Once this text is highlighted, you can copy it and then paste it into any cell in a table or onto a blank canvas in a Numbers sheet. Drag and drop cannot be used for this type of example. 42 The date and time functions help you work with dates and times to solve problems such as finding the number of working days between two dates or finding the name of the day of the week a date will fall on. Listing of Date and Time Functions iWork includes these date and time functions for use with tables. Function Description “DATE” (page 44) The DATE function combines separate values for year, month, and day and returns a date/time value. Although dates can usually be entered directly as strings (for example, “12/31/2010”), using the DATE function ensures the date will be interpreted consistently regardless of the date format specified in System Preferences (search for “date format” in the System Preferences window). “DATEDIF” (page 45) The DATEDIF function returns the number of days, months, or years between two dates. “DATEVALUE” (page 47) The DATEVALUE function converts a date text string and returns a date/time value. This function is provided for compatibility with other spreadsheet programs. “DAY” (page 47) The DAY function returns the day of the month for a given date/time value. “DAYNAME” (page 48) The DAYNAME function returns the name of the day of the week from a date/time value or a number. Day 1 is Sunday. “DAYS360” (page 49) The DAYS360 function returns the number of days between two dates based on twelve 30-day months and a 360-day year. Date and Time Functions 3 Chapter 3 Date and Time Functions 43 Function Description “EDATE” (page 50) The EDATE function returns a date that is some number of months before or after a given date. “EOMONTH” (page 51) The EOMONTH function returns a date that is the last day of the month some number of months before or after a given date. “HOUR” (page 51) The HOUR function returns the hour for a given date/time value. “MINUTE” (page 52) The MINUTE function returns the minutes for a given date/time value. “MONTH” (page 53) The MONTH function returns the month for a given date/time value. “MONTHNAME” (page 54) The MONTHNAME function returns the name of the month from a number. Month 1 is January. “NETWORKDAYS” (page 54) The NETWORKDAYS function returns the number of working days between two dates. Working days exclude weekends and any other specified dates. “NOW” (page 55) The NOW function returns the current date/time value from the system clock. “SECOND” (page 56) The SECOND function returns the seconds for a given date/time value. “TIME” (page 56) The TIME function converts separate values for hours, minutes, and seconds into a date/time value. “TIMEVALUE” (page 57) The TIMEVALUE function returns the time as a decimal fraction of a 24-hour day from a given date/time value or from a text string. “TODAY” (page 58) The TODAY function returns the current system date. The time is set to 12:00 a.m. Function Description “WEEKDAY” (page 59) The WEEKDAY function returns a number that is the day of the week for a given date. “WEEKNUM” (page 60) The WEEKNUM function returns the number of the week within the year for a given date. “WORKDAY” (page 61) The WORKDAY function returns the date that is the given number of working days before or after a given date. Working days exclude weekends and any other dates specifically excluded. “YEAR” (page 62) The YEAR function returns the year for a given date/time value. “YEARFRAC” (page 63) The YEARFRAC function finds the fraction of a year represented by the number of whole days between two dates. DATE The DATE function combines separate values for year, month, and day and returns a date/time value. Although dates can usually be entered directly as strings (for example, “12/31/2010”), using the DATE function ensures the date will be interpreted consistently regardless of the date format specified in System Preferences (search for “date format” in the System Preferences window). DATE(year, month, day)  year:  The year to include in the value returned. year is a number value. The value isn’t converted. If you specify 10, the year 10 is used, not the year 1910 or 2010.  month:  The month to include in the value returned. month is a number and should be in the range 1 to 12.  day:  The day to include in the value returned. day is a number value and should be in the range 1 to the number of days in month. Examples If A1 contains 2014, A2 contains 11, and A3 contains 10: =DATE(A1, A2, A3) returns Nov 10, 2014, which is displayed according to the cell’s current format. =DATE(A1, A3, A2) returns Oct 11, 2014. =DATE(2012, 2, 14) returns Feb 14, 2012. Related Topics For related functions and additional information, see: “DURATION” on page 70 44 Chapter 3 Date and Time Functions Chapter 3 Date and Time Functions 45 “TIME” on page 56 “Listing of Date and Time Functions” on page 42 “Value Types” on page 36 “The Elements of Formulas” on page 15 “Using the Keyboard and Mouse to Create and Edit Formulas” on page 26 “Pasting from Examples in Help” on page 41 DATEDIF The DATEDIF function returns the number of days, months, or years between two dates. DATEDIF(start-date, end-date, calc-method)  start-date:  The starting date. start-date is a date/time value.  end-date:  The ending date. end-date is a date/time value.  calc-method:  Specifies how to express the time difference and how dates in different years or months are handled. “D”:  Count the number of days between the start and end dates. “M”:  Count the number of months between the start and end dates. “Y”:  Count the number of years between the start and end dates. “MD”:  Count the days between the start and end dates, ignoring months and years. The month in end-date is considered to be the month in start-date. If the starting day is after the ending day, the count starts from the ending day as if it were in the preceding month. The year of the end-date is used to check for a leap year. “YM”:  Count the number of whole months between the start and end dates, ignoring the year. If the starting month/day is before the ending month/day, the dates are treated as though they are in the same year. If the starting month/day is after the ending month/day, the dates are treated as though they are in consecutive years. “YD”:  Count the number of days between the start and end dates, ignoring the year. If the starting month/day is before the ending month/day, the dates are treated as though they are in the same year. If the starting month/day is after the ending month/day, the dates are treated as though they are in consecutive years. Examples If A1 contains the date/time value 4/6/88 and A2 contains the date/time value 10/30/06: =DATEDIF(A1, A2, “D”) returns 6781, the number of days between April 6, 1988, and October 30, 2006. =DATEDIF(A1, A2, “M”) returns 222, the number of whole months between April 6, 1988, and October 30, 2006. =DATEDIF(A1, A2, “Y”) returns 18, the number of whole years between April 6, 1988, and October 30, 2006. =DATEDIF(A1, A2, “MD”) returns 24, the number of days between the sixth day of a month and the thirtieth day of the same month. =DATEDIF(A1, A2, “YM”) returns 6, the number of months between April and the following October in any year. =DATEDIF(A1, A2, “YD”) returns 207, the number of days between April 6 and the following October 30 in any year. =DATEDIF(”04/06/1988”, NOW(), “Y”) & “ years, “ & DATEDIF(”04/06/1988”, NOW(), “YM”) & “ months, and “ & DATEDIF(”04/06/1988”, NOW(), “MD”) & “ days” returns the current age of someone born on April 6, 1988. Related Topics For related functions and additional information, see: “DAYS360” on page 49 “NETWORKDAYS” on page 54 “NOW” on page 55 “YEARFRAC” on page 63 “Listing of Date and Time Functions” on page 42 “Value Types” on page 36 “The Elements of Formulas” on page 15 “Using the Keyboard and Mouse to Create and Edit Formulas” on page 26 “Pasting from Examples in Help” on page 41 46 Chapter 3 Date and Time Functions Chapter 3 Date and Time Functions 47 DATEVALUE The DATEVALUE function converts a date text string and returns a date/time value. This function is provided for compatibility with other spreadsheet programs. DATEVALUE(date-text)  date-text:  The date string to be converted. date-text is a string value. It must be a date specified within quotations or a date/time value. If date-text is not a valid date, an error is returned. Examples If cell B1 contains the date/time value August 2, 1979 06:30:00 and cell C1 contains the string 10/16/2008: =DATEVALUE(B1) returns Aug 2, 1979, and is treated as a date value if referenced in other formulas. The value returned is formatted according to the current cell format. A cell formatted as Automatic uses the date format specified in System Preferences (search for “date format” in the System Preferences window). =DATEVALUE(C1) returns Oct 16, 2008. =DATEVALUE(“12/29/1974”) returns Dec 29, 1979. Related Topics For related functions and additional information, see: “DATE” on page 44 “TIME” on page 56 “Listing of Date and Time Functions” on page 42 “Value Types” on page 36 “The Elements of Formulas” on page 15 “Using the Keyboard and Mouse to Create and Edit Formulas” on page 26 “Pasting from Examples in Help” on page 41 DAY The DAY function returns the day of the month for a given date/time value. DAY(date)  date:  The date the function should use. date is a date/time value. The time portion is ignored by this function. Examples =DAY(”4/6/88 11:59:22 PM”) returns 6. =DAY(“5/12/2009”) returns 12. Related Topics For related functions and additional information, see: “DAYNAME” on page 48 “HOUR” on page 51 “MINUTE” on page 52 “MONTH” on page 53 “SECOND” on page 56 “YEAR” on page 62 “Listing of Date and Time Functions” on page 42 “Value Types” on page 36 “The Elements of Formulas” on page 15 “Using the Keyboard and Mouse to Create and Edit Formulas” on page 26 “Pasting from Examples in Help” on page 41 DAYNAME The DAYNAME function returns the name of the day of the week from a date/time value or a number. Day 1 is Sunday. DAYNAME(day-num)  day-num:  The desired day of the week. day-num is a date/time value, or number value in the range 1 to 7. If day-num has a decimal portion, it is ignored. Examples If B1 contains the date/time value August 2, 1979 06:30:00, C1 contains the string 10/16/2008, and D1 contains 6: =DAYNAME(B1) returns Thursday. =DAYNAME(C1) returns Thursday. =DAYNAME(D1) returns Friday. =DAYNAME(“12/29/1974”) returns Sunday. 48 Chapter 3 Date and Time Functions Chapter 3 Date and Time Functions 49 Related Topics For related functions and additional information, see: “DAY” on page 47 “MONTHNAME” on page 54 “WEEKDAY” on page 59 “Listing of Date and Time Functions” on page 42 “Value Types” on page 36 “The Elements of Formulas” on page 15 “Using the Keyboard and Mouse to Create and Edit Formulas” on page 26 “Pasting from Examples in Help” on page 41 DAYS360 The DAYS360 function returns the number of days between two dates based on twelve 30-day months and a 360-day year. DAYS360(start-date, end-date, use-euro-method)  start-date:  The starting date. start-date is a date/time value.  end-date:  The ending date. end-date is a date/time value.  use-euro-method:  An optional value that specifies whether to use the NASD or European method for dates falling on the 31st of a month. NASD method (0, FALSE, or omitted):  Use the NASD method for dates falling on the 31st of a month. EURO method (1 or TRUE):  Use the European method for dates falling on the 31st of a month. Examples =DAYS360(”12/20/2008”, “3/31/2009”) returns 101d. =DAYS360(”2/27/2008”, “3/31/2009”,0) returns 394d. =DAYS360(”2/27/2008”, “3/31/2009”,1) returns 393d, as the European calculation method is used. Related Topics For related functions and additional information, see: “DATEDIF” on page 45 “NETWORKDAYS” on page 54 “YEARFRAC” on page 63 “Listing of Date and Time Functions” on page 42 “Value Types” on page 36 “The Elements of Formulas” on page 15 “Using the Keyboard and Mouse to Create and Edit Formulas” on page 26 “Pasting from Examples in Help” on page 41 EDATE The EDATE function returns a date that is some number of months before or after a given date. EDATE(start-date, month-offset)  start-date:  The starting date. start-date is a date/time value.  month-offset: The number of months before or after the starting date. month-offset is a number value. A negative month-offset is used to specify a number of months before the starting date and a positive month-offset is used to specify a number of months after the starting date. Examples =EDATE(”1/15/2000”, 1) returns 2/15/2000, the date one month later. =EDATE(”1/15/2000”, -24) returns 1/15/1998, the date 24 months earlier. Related Topics For related functions and additional information, see: “EOMONTH” on page 51 “Listing of Date and Time Functions” on page 42 “Value Types” on page 36 “The Elements of Formulas” on page 15 “Using the Keyboard and Mouse to Create and Edit Formulas” on page 26 “Pasting from Examples in Help” on page 41 50 Chapter 3 Date and Time Functions Chapter 3 Date and Time Functions 51 EOMONTH The EOMONTH function returns a date that is the last day of the month some number of months before or after a given date. EOMONTH(start-date, month-offset)  start-date:  The starting date. start-date is a date/time value.  month-offset: The number of months before or after the starting date. month-offset is a number value. A negative month-offset is used to specify a number of months before the starting date and a positive month-offset is used to specify a number of months after the starting date. Examples =EOMONTH(”5/15/2010”, 5) returns Oct 31, 2010, the last day of the month five months after May 2010. =EOMONTH(”5/15/2010”, -5) returns Dec 31, 2009, the last day of the month five months before May 2010. Related Topics For related functions and additional information, see: “EDATE” on page 50 “Listing of Date and Time Functions” on page 42 “Value Types” on page 36 “The Elements of Formulas” on page 15 “Using the Keyboard and Mouse to Create and Edit Formulas” on page 26 “Pasting from Examples in Help” on page 41 HOUR The HOUR function returns the hour for a given date/time value. HOUR(time)  time:  The time the function should use. time is a date/time value. The date portion is ignored by this function. Usage Notes  The hour returned is in 24-hour format (0 is midnight, 23 is 11:00 p.m.). Examples =HOUR(NOW()) returns the current hour of the day. =HOUR(”4/6/88 11:59:22 AM”) returns 11. Related Topics For related functions and additional information, see: “DAY” on page 47 “MINUTE” on page 52 “MONTH” on page 53 “SECOND” on page 56 “YEAR” on page 62 “Listing of Date and Time Functions” on page 42 “Value Types” on page 36 “The Elements of Formulas” on page 15 “Using the Keyboard and Mouse to Create and Edit Formulas” on page 26 “Pasting from Examples in Help” on page 41 MINUTE The MINUTE function returns the minutes for a given date/time value. MINUTE(time)  time:  The time the function should use. time is a date/time value. The date portion is ignored by this function. Example =MINUTE(”4/6/88 11:59:22 AM”) returns 59. Related Topics For related functions and additional information, see: “DAY” on page 47 “HOUR” on page 51 “MONTH” on page 53 “SECOND” on page 56 “YEAR” on page 62 “Listing of Date and Time Functions” on page 42 52 Chapter 3 Date and Time Functions Chapter 3 Date and Time Functions 53 “Value Types” on page 36 “The Elements of Formulas” on page 15 “Using the Keyboard and Mouse to Create and Edit Formulas” on page 26 “Pasting from Examples in Help” on page 41 MONTH The MONTH function returns the month for a given date/time value. MONTH(date)  date:  The date the function should use. date is a date/time value. The time portion is ignored by this function. Example =MONTH(”April 6, 1988 11:59:22 AM”) returns 4. Related Topics For related functions and additional information, see: “DAY” on page 47 “HOUR” on page 51 “MINUTE” on page 52 “MONTHNAME” on page 54 “SECOND” on page 56 “YEAR” on page 62 “Listing of Date and Time Functions” on page 42 “Value Types” on page 36 “The Elements of Formulas” on page 15 “Using the Keyboard and Mouse to Create and Edit Formulas” on page 26 “Pasting from Examples in Help” on page 41 MONTHNAME The MONTHNAME function returns the name of the month from a number. Month 1 is January. MONTHNAME(month-num)  month-num:  The desired month. month-num is a number value and must be in the range 1 to 12. If month-num has a decimal portion, it is ignored. Examples =MONTHNAME(9) returns September. =MONTHNAME(6) returns June. Related Topics For related functions and additional information, see: “DAYNAME” on page 48 “MONTH” on page 53 “WEEKDAY” on page 59 “Listing of Date and Time Functions” on page 42 “Value Types” on page 36 “The Elements of Formulas” on page 15 “Using the Keyboard and Mouse to Create and Edit Formulas” on page 26 “Pasting from Examples in Help” on page 41 NETWORKDAYS The NETWORKDAYS function returns the number of working days between two dates. Working days exclude weekends and any other specified dates. NETWORKDAYS(start-date, end-date, exclude-dates)  start-date:  The starting date. start-date is a date/time value.  end-date:  The ending date. end-date is a date/time value.  exclude-dates:  An optional collection of dates that should be excluded from the count. exclude-dates is a collection containing date/time values. Example =NETWORKDAYS(”11/01/2009”, “11/30/2009”, {”11/11/2009”,”11/26/2009”}) returns 19d, the number of working days in November 2009 excluding weekends and the two holidays specifically excluded. 54 Chapter 3 Date and Time Functions Chapter 3 Date and Time Functions 55 Related Topics For related functions and additional information, see: “DATEDIF” on page 45 “DAYS360” on page 49 “WORKDAY” on page 61 “YEARFRAC” on page 63 “Listing of Date and Time Functions” on page 42 “Value Types” on page 36 “The Elements of Formulas” on page 15 “Using the Keyboard and Mouse to Create and Edit Formulas” on page 26 “Pasting from Examples in Help” on page 41 NOW The NOW function returns the current date/time value from the system clock. NOW() Usage Notes The NO  W function does not have any arguments. However, you must include the parentheses: =NOW(). Example =NOW() returns October 4, 2008 10:47 am, if your file is updated on October 4, 2008, at 10:47 a.m. Related Topics For related functions and additional information, see: “TODAY” on page 58 “Listing of Date and Time Functions” on page 42 “Value Types” on page 36 “The Elements of Formulas” on page 15 “Using the Keyboard and Mouse to Create and Edit Formulas” on page 26 “Pasting from Examples in Help” on page 41 SECOND The SECOND function returns the seconds for a given date/time value. SECOND(time)  time:  The time the function should use. time is a date/time value. The date portion is ignored by this function. Example =SECOND(”4/6/88 11:59:22 am”) returns 22. Related Topics For related functions and additional information, see: “DAY” on page 47 “HOUR” on page 51 “MINUTE” on page 52 “Listing of Date and Time Functions” on page 42 “Value Types” on page 36 “The Elements of Formulas” on page 15 “Using the Keyboard and Mouse to Create and Edit Formulas” on page 26 “Pasting from Examples in Help” on page 41 TIME The TIME function converts separate values for hours, minutes, and seconds into a date/time value. TIME(hours, minutes, seconds)  hours:  The number of hours to include in the value returned. hours is a number value. If hours has a decimal portion, it is ignored.  minutes:  The number of minutes to include in the value returned. minutes is a number value. If minutes has a decimal portion, it is ignored.  seconds:  The number of seconds to include in the value returned. seconds is a number value. If seconds has a decimal portion, it is ignored. Usage Notes  You can specify hour, minute, and second values greater than 24, 60, and 60, respectively. If the hours, minutes, and seconds add up to more than 24 hours, 24 hours are repeatedly subtracted until the value is less than 24 hours. 56 Chapter 3 Date and Time Functions Chapter 3 Date and Time Functions 57 Examples =TIME(12, 0, 0) returns 12:00 pm. =TIME(16, 45, 30) returns 4:45 pm. =TIME(0, 900, 0) returns 3:00 pm. =TIME(60, 0, 0) returns 12:00 pm. =TIME(4.25, 0, 0) returns 4:00 am. Related Topics For related functions and additional information, see: “DATE” on page 44 “DATEVALUE” on page 47 “DURATION” on page 70 “Listing of Date and Time Functions” on page 42 “Value Types” on page 36 “The Elements of Formulas” on page 15 “Using the Keyboard and Mouse to Create and Edit Formulas” on page 26 “Pasting from Examples in Help” on page 41 TIMEVALUE The TIMEVALUE function returns the time as a decimal fraction of a 24-hour day from a given date/time value or from a text string. TIMEVALUE(time)  time:  The time the function should use. time is a date/time value. The date portion is ignored by this function. Examples =TIMEVALUE(”4/6/88 12:00”) returns 0.5 (noon represents one-half of the day). =TIMEVALUE(”12:00:59”) returns 0.5007 (rounded to four decimal places of accuracy). =TIMEVALUE(”9:00 pm”) returns 0.875 (21 hours, or 9:00 p.m., divided by 24). Related Topics For related functions and additional information, see: “Listing of Date and Time Functions” on page 42 “Value Types” on page 36 “The Elements of Formulas” on page 15 “Using the Keyboard and Mouse to Create and Edit Formulas” on page 26 “Pasting from Examples in Help” on page 41 TODAY The TODAY function returns the current system date. The time is set to 12:00 a.m. TODAY() Usage Notes The TODAY func  tion does not have any arguments. However, you must include the parentheses: =TODAY().  The displayed date is updated every time you open or modify your file.  You can use the NOW function to get the current date and time and to format the cell to display both. Example =TODAY() returns Apr 6, 2008, when calculated on April 6, 2008. Related Topics For related functions and additional information, see: “NOW” on page 55 “Listing of Date and Time Functions” on page 42 “Value Types” on page 36 “The Elements of Formulas” on page 15 “Using the Keyboard and Mouse to Create and Edit Formulas” on page 26 “Pasting from Examples in Help” on page 41 58 Chapter 3 Date and Time Functions Chapter 3 Date and Time Functions 59 WEEKDAY The WEEKDAY function returns a number that is the day of the week for a given date. WEEKDAY(date, first-day)  date:  The date the function should use. date is a date/time value. The time portion is ignored by this function.  first-day: An optional value that specifies how days are numbered. Sunday is 1 (1 or omitted):  Sunday is the first day (day 1) of the week and Saturday is day 7. Monday is 1 (2):  Monday is the first day (day 1) of the week and Sunday is day 7. Monday is 0 (3):  Monday is the first day (day 0) of the week and Sunday is day 6. Examples =WEEKDAY(”Apr 6, 1988”, 1) returns 4 (Wednesday, the fourth day if you start counting Sunday as day 1). =WEEKDAY(”Apr 6, 1988”) returns the same value as the preceding example (numbering scheme 1 is used if no number-scheme argument is specified). =WEEKDAY(”Apr 6, 1988”, 2) returns 3 (Wednesday, the third day if you start counting Monday as day 1). =WEEKDAY(”Apr 6, 1988”, 3) returns 2 (Wednesday, day number 2 if you start counting Monday as day 0). Related Topics For related functions and additional information, see: “DAYNAME” on page 48 “MONTHNAME” on page 54 “Listing of Date and Time Functions” on page 42 “Value Types” on page 36 “The Elements of Formulas” on page 15 “Using the Keyboard and Mouse to Create and Edit Formulas” on page 26 “Pasting from Examples in Help” on page 41 WEEKNUM The WEEKNUM function returns the number of the week within the year for a given date. WEEKNUM(date, first-day)  date:  The date the function should use. date is a date/time value. The time portion is ignored by this function.  first-day: An optional value that specifies whether weeks should begin on Sunday or Monday. Sunday is 1 (1 or omitted):  Sunday is the first day (day 1) of the week and Saturday is day 7. Monday is 1 (2):  Monday is the first day (day 1) of the week and Sunday is day 7. Example =WEEKNUM(”7/12/2009”,1) returns 29. =WEEKNUM(”7/12/2009”,2) returns 28. Related Topics For related functions and additional information, see: “DAY” on page 47 “HOUR” on page 51 “MINUTE” on page 52 “MONTH” on page 53 “SECOND” on page 56 “YEAR” on page 62 “Listing of Date and Time Functions” on page 42 “Value Types” on page 36 “The Elements of Formulas” on page 15 “Using the Keyboard and Mouse to Create and Edit Formulas” on page 26 “Pasting from Examples in Help” on page 41 60 Chapter 3 Date and Time Functions Chapter 3 Date and Time Functions 61 WORKDAY The WORKDAY function returns the date that is the given number of working days before or after a given date. Working days exclude weekends and any other dates specifically excluded. WORKDAY(date, work-days, exclude-dates)  date:  The date the function should use. date is a date/time value. The time portion is ignored by this function.  work-days:  The number of working days before or after the given date. work-days is a number value. It is positive if the desired date is after date and negative if the desired date is before date.  exclude-dates:  An optional collection of dates that should be excluded from the count. exclude-dates is a collection containing date/time values. Example =WORKDAY(”11/01/2009”, 20, {”11/11/2009”,”11/26/2009”}) returns Dec 1, 2009, the work day 20 days after 11/01/2009 excluding weekends and the two holidays specifically excluded. Related Topics For related functions and additional information, see: “NETWORKDAYS” on page 54 “Listing of Date and Time Functions” on page 42 “Value Types” on page 36 “The Elements of Formulas” on page 15 “Using the Keyboard and Mouse to Create and Edit Formulas” on page 26 “Pasting from Examples in Help” on page 41 YEAR The YEAR function returns the year for a given date/time value. YEAR(date)  date:  The date the function should use. date is a date/time value. The time portion is ignored by this function. Examples =YEAR(”April 6, 2008”) returns 2008. =YEAR(NOW()) returns 2009 when evaluated on June 4, 2009. Related Topics For related functions and additional information, see: “DAY” on page 47 “HOUR” on page 51 “MINUTE” on page 52 “MONTH” on page 53 “SECOND” on page 56 “Listing of Date and Time Functions” on page 42 “Value Types” on page 36 “The Elements of Formulas” on page 15 “Using the Keyboard and Mouse to Create and Edit Formulas” on page 26 “Pasting from Examples in Help” on page 41 62 Chapter 3 Date and Time Functions Chapter 3 Date and Time Functions 63 YEARFRAC The YEARFRAC function finds the fraction of a year represented by the number of whole days between two dates. YEARFRAC(start-date, end-date, days-basis)  start-date:  The starting date. start-date is a date/time value.  end-date:  The ending date. end-date is a date/time value.  days-basis:  An optional argument specifying the number of days per month and days per year used in the calculations. 30/360 (0 or omitted):  30 days in a month, 360 days in a year, using the NASD method for dates falling on the 31st of a month. actual/actual (1):  Actual days in each month, actual days in each year. actual/360 (2):  Actual days in each month, 360 days in a year. actual/365 (3):  Actual days in each month, 365 days in a year. 30E/360 (4):  30 days in a month, 360 days in a year, using the European method for dates falling on the 31st of a month (European 30/360). Examples =YEARFRAC(”12/15/2009”, “6/30/2010”,0) returns 0.541666667. =YEARFRAC(”12/15/2009”, “6/30/2010”,1) returns 0.539726027. =YEARFRAC(”12/15/2009”, “6/30/2010”,2) returns 0.547222222. =YEARFRAC(”12/15/2009”, “6/30/2010”,3) returns 0.539726027. =YEARFRAC(”12/15/2009”, “6/30/2010”,4) returns 0.541666667. Related Topics For related functions and additional information, see: “DATEDIF” on page 45 “DAYS360” on page 49 “NETWORKDAYS” on page 54 “Listing of Date and Time Functions” on page 42 “Value Types” on page 36 “The Elements of Formulas” on page 15 “Using the Keyboard and Mouse to Create and Edit Formulas” on page 26 “Pasting from Examples in Help” on page 41 64 The duration functions help you work with periods of time (durations) by converting between different time periods, such as hours, days, and weeks. Listing of Duration Functions iWork provides these duration functions for use with tables. Function Description “DUR2DAYS” (page 65) The DUR2DAYS function converts a duration value to a number of days. “DUR2HOURS” (page 65) The DUR2HOURS function converts a duration value to a number of hours. “DUR2MILLISECONDS” (page 66) The DUR2MILLISECONDS function converts a duration value to a number of milliseconds. “DUR2MINUTES” (page 67) The DUR2MINUTES function converts a duration value to a number of minutes. “DUR2SECONDS” (page 68) The DUR2SECONDS function converts a duration value to a number of seconds. “DUR2WEEKS” (page 69) The DUR2WEEKS function converts a duration value to a number of weeks. “DURATION” (page 70) The DURATION function combines separate values for weeks, days, hours, minutes, seconds, and milliseconds and returns a duration value. “STRIPDURATION” (page 71) The STRIPDURATION function evaluates a given value and returns either the number of days represented, if a duration value, or the given value. This function is included for compatibility with other spreadsheet applications. Duration Functions 4 Chapter 4 Duration Functions 65 DUR2DAYS The DUR2DAYS function converts a duration value to a number of days. DUR2DAYS(duration)  duration:  The length of time to be converted. duration is a duration value. Examples =DUR2DAYS(”2w 3d 2h 10m 0s 5ms”) returns 17.09027784. =DUR2DAYS(”10:0:13:00:05.500”) returns 70.5417302. Related Topics For related functions and additional information, see: “DUR2HOURS” on page 65 “DUR2MILLISECONDS” on page 66 “DUR2MINUTES” on page 67 “DUR2SECONDS” on page 68 “DUR2WEEKS” on page 69 “Listing of Duration Functions” on page 64 “Value Types” on page 36 “The Elements of Formulas” on page 15 “Using the Keyboard and Mouse to Create and Edit Formulas” on page 26 “Pasting from Examples in Help” on page 41 DUR2HOURS The DUR2HOURS function converts a duration value to a number of hours. DUR2HOURS(duration)  duration:  The length of time to be converted. duration is a duration value. Examples =DUR2HOURS(”2w 3d 2h 10m 0s 5ms”) returns 410.1666681. =DUR2HOURS(”10:0:13:00:05.500”) returns 1693.001528. Related Topics For related functions and additional information, see: “DUR2DAYS” on page 65 “DUR2MILLISECONDS” on page 66 “DUR2MINUTES” on page 67 “DUR2SECONDS” on page 68 “DUR2WEEKS” on page 69 “Listing of Duration Functions” on page 64 “Value Types” on page 36 “The Elements of Formulas” on page 15 “Using the Keyboard and Mouse to Create and Edit Formulas” on page 26 “Pasting from Examples in Help” on page 41 DUR2MILLISECONDS The DUR2MILLISECONDS function converts a duration value to a number of milliseconds. DUR2MILLISECONDS(duration)  duration:  The length of time to be converted. duration is a duration value. Examples =DUR2MILLISECONDS(”2w 3d 2h 10m 0s 5ms”) returns 1476600005. =DUR2MILLISECONDS(”10:0:13:00:05.500”) returns 6094805500. Related Topics For related functions and additional information, see: “DUR2DAYS” on page 65 “DUR2HOURS” on page 65 “DUR2MINUTES” on page 67 “DUR2SECONDS” on page 68 “DUR2WEEKS” on page 69 “Listing of Duration Functions” on page 64 66 Chapter 4 Duration Functions Chapter 4 Duration Functions 67 “Value Types” on page 36 “The Elements of Formulas” on page 15 “Using the Keyboard and Mouse to Create and Edit Formulas” on page 26 “Pasting from Examples in Help” on page 41 DUR2MINUTES The DUR2MINUTES function converts a duration value to a number of minutes. DUR2MINUTES(duration)  duration:  The length of time to be converted. duration is a duration value. Examples =DUR2MINUTES(”2w 3d 2h 10m 0s 5ms”) returns 24610.0000833333. =DUR2MINUTES(”10:0:13:00:05.500”) returns 101580.091666667. Related Topics For related functions and additional information, see: “DUR2DAYS” on page 65 “DUR2HOURS” on page 65 “DUR2MILLISECONDS” on page 66 “DUR2SECONDS” on page 68 “DUR2WEEKS” on page 69 “Listing of Duration Functions” on page 64 “Value Types” on page 36 “The Elements of Formulas” on page 15 “Using the Keyboard and Mouse to Create and Edit Formulas” on page 26 “Pasting from Examples in Help” on page 41 DUR2SECONDS The DUR2SECONDS function converts a duration value to a number of seconds. DUR2SECONDS(duration)  duration:  The length of time to be converted. duration is a duration value. Examples =DUR2SECONDS(”2w 3d 2h 10m 0s 5ms”) returns 1476600.005. =DUR2SECONDS(”10:0:13:00:05.500”) returns 6094805.5. Related Topics For related functions and additional information, see: “DUR2DAYS” on page 65 “DUR2HOURS” on page 65 “DUR2MILLISECONDS” on page 66 “DUR2MINUTES” on page 67 “DUR2WEEKS” on page 69 “Listing of Duration Functions” on page 64 “Value Types” on page 36 “The Elements of Formulas” on page 15 “Using the Keyboard and Mouse to Create and Edit Formulas” on page 26 “Pasting from Examples in Help” on page 41 68 Chapter 4 Duration Functions Chapter 4 Duration Functions 69 DUR2WEEKS The DUR2WEEKS function converts a duration value to a number of weeks. DUR2WEEKS(duration)  duration:  The length of time to be converted. duration is a duration value. Examples =DUR2WEEKS(”2w 3d 2h 10m 0s 5ms”) returns 2.44146826223545. =DUR2WEEKS(”10:0:13:00:05.500”) returns 10.0773900462963. Related Topics For related functions and additional information, see: “DUR2DAYS” on page 65 “DUR2HOURS” on page 65 “DUR2MILLISECONDS” on page 66 “DUR2MINUTES” on page 67 “DUR2SECONDS” on page 68 “Listing of Duration Functions” on page 64 “Value Types” on page 36 “The Elements of Formulas” on page 15 “Using the Keyboard and Mouse to Create and Edit Formulas” on page 26 “Pasting from Examples in Help” on page 41 DURATION The DURATION function combines separate values for weeks, days, hours, minutes, seconds, and milliseconds and returns a duration value. DURATION(weeks, days, hours, minutes, seconds, milliseconds)  weeks:  A value representing the number of weeks. weeks is a number value.  days:  An optional value representing the number of days. days is a number value.  hours:  An optional value representing the number of hours. hours is a number value.  minutes:  An optional value representing the number of minutes. minutes is a number value.  seconds:  An optional value representing the number of seconds. seconds is a number value.  milliseconds:  An optional value representing the number of milliseconds. milliseconds is a number value. Usage Notes  An argument that is 0 can be omitted, but the comma must be included if later values are included. For example, =DURATION(, ,12, 3) would return a duration value of 12h 3m (12 hours and 3 minutes).  Negative values are permitted. For example, =DURATION(0, 2, -24) would return a duration of 1 day (2 days minus 24 hours). Examples =DURATION(1) returns 1w (1 week). =DURATION(,,1) returns 1h (1 hour). =DURATION(1.5) returns 1w 3d 12h (1 week, 3 days, 12 hours or 1.5 weeks). =DURATION(3, 2, 7, 10, 15.3505) returns 3w 2d 7h 10m 15s 350ms (3 weeks, 2 days, 7 hours, 10 minutes, 15 seconds, 350 milliseconds). Related Topics For related functions and additional information, see: “DATE” on page 44 “TIME” on page 56 “Listing of Duration Functions” on page 64 “Value Types” on page 36 “The Elements of Formulas” on page 15 “Using the Keyboard and Mouse to Create and Edit Formulas” on page 26 “Pasting from Examples in Help” on page 41 70 Chapter 4 Duration Functions Chapter 4 Duration Functions 71 STRIPDURATION The STRIPDURATION function evaluates a given value and returns either the number of days represented, if a duration value, or the given value. This function is included for compatibility with other spreadsheet applications. STRIPDURATION(any-value)  any-value:  A value. any-value can contain any value type. Usage Notes  If any-value is a duration value, the result is the same as for DUR2DAYS; otherwise any-value is returned.  This function may be automatically inserted when a Numbers ’08 document is upgraded, or an Excel or Appleworks document is imported. It is removed in any copy of the file saved as a Numbers ’08 or Excel document. Examples =STRIPDURATION(”1w”) returns 7, the equivalent of one week in days. =STRIPDURATION(12) returns 12; since it was not a duration value it is returned. =STRIPDURATION (”abc”) returns “abc”. Related Topics For related functions and additional information, see: “Listing of Duration Functions” on page 64 “Value Types” on page 36 “The Elements of Formulas” on page 15 “Using the Keyboard and Mouse to Create and Edit Formulas” on page 26 “Pasting from Examples in Help” on page 41 72 The engineering functions help you calculate some common engineering values and convert between different numeric bases. Listing of Engineering Functions iWork provides these engineering functions for use with tables. Function Description “BASETONUM” (page 73) The BASETONUM function converts a number of the specified base into a number in base 10. “BESSELJ” (page 74) The BESSELJ function returns the integer Bessel function Jn(x). “BESSELY” (page 75) The BESSELY function returns the integer Bessel function Yn(x). “BIN2DEC” (page 76) The BIN2DEC function converts a binary number to the corresponding decimal number. “BIN2HEX” (page 77) The BIN2HEX function converts a binary number to the corresponding hexadecimal number. “BIN2OCT” (page 78) The BIN2OCT function converts a binary number to the corresponding octal number. “CONVERT” (page 79) The CONVERT function converts a number from one measurement system to its corresponding value in another measurement system. “DEC2BIN” (page 83) The DEC2BIN function converts a decimal number to the corresponding binary number. “DEC2HEX” (page 84) The DEC2HEX function converts a decimal number to the corresponding hexadecimal number. Engineering Functions 5 Chapter 5 Engineering Functions 73 Function Description “DEC2OCT” (page 85) The DEC2OCT function converts a decimal number to the corresponding octal number. “DELTA” (page 86) The DELTA function determines whether two values are exactly equal. “ERF” (page 87) The ERF function returns the error function integrated between two values. “ERFC” (page 87) The ERFC function returns the complementary ERF function integrated between a given lower bound and infinity. “GESTEP” (page 88) The GESTEP function determines if one value is greater than or exactly equal to another value. “HEX2BIN” (page 89) The HEX2BIN function converts a hexadecimal number to the corresponding binary number. “HEX2DEC” (page 90) The HEX2DEC function converts a hexadecimal number to the corresponding decimal number. “HEX2OCT” (page 91) The HEX2OCT function converts a hexadecimal number to the corresponding octal number. “NUMTOBASE” (page 92) The NUMTOBASE function converts a number from base 10 into a number in the specified base. “OCT2BIN” (page 93) The OCT2BIN function converts an octal number to the corresponding binary number. “OCT2DEC” (page 94) The OCT2DEC function converts an octal number to the corresponding decimal number. “OCT2HEX” (page 95) The OCT2HEX function converts an octal number to the corresponding hexadecimal number. BASETONUM The BASETONUM function converts a number of the specified base into a number in base 10. BASETONUM(convert-string, base)  convert-string:  The string representing the number to be converted. convert-string is a string value. It must contain only numbers and letters that apply in the base of the number being converted.  base:  The current base of the number to be converted. base is a number value and must be in the range 1 to 36. Usage Notes  This function returns a number value and can properly be used in a formula containing other number values. Some other spreadsheet applications return a string value. Examples =BASETONUM(”3f”, 16) returns 63. =BASETONUM(1000100, 2) returns 68. =BASETONUM(”7279”, 8) returns an error, since the digit “9” is not valid in base 8. Related Topics For related functions and additional information, see: “BIN2DEC” on page 76 “HEX2DEC” on page 90 “NUMTOBASE” on page 92 “OCT2DEC” on page 94 “Listing of Engineering Functions” on page 72 “Value Types” on page 36 “The Elements of Formulas” on page 15 “Using the Keyboard and Mouse to Create and Edit Formulas” on page 26 “Pasting from Examples in Help” on page 41 BESSELJ The BESSELJ function returns the integer Bessel function Jn(x). BESSELJ(any-x-value, n-value)  any-x-value:  The x value at which you want to evaluate the function. any-x-value is a number value.  n-value:  The order of the function. n-value is a number value and must be greater than or equal to 0. If n-value has a decimal portion, it is ignored. Examples =BESSELJ(25, 3) returns 0.108343081061509. =BESSELJ(25, 3.9) also returns 0.108343081061509, since any decimal portion of n-value is ignored. =BESSELJ(-25, 3) returns -0.108343081061509. 74 Chapter 5 Engineering Functions Chapter 5 Engineering Functions 75 Related Topics For related functions and additional information, see: “BESSELY” on page 75 “Listing of Engineering Functions” on page 72 “Value Types” on page 36 “The Elements of Formulas” on page 15 “Using the Keyboard and Mouse to Create and Edit Formulas” on page 26 “Pasting from Examples in Help” on page 41 BESSELY The BESSELY function returns the integer Bessel function Yn(x). BESSELY(pos-x-value, n-value)  pos-x-value:  The positive x value at which you want to evaluate the function. pos-x-value is a number value and must be greater than 0.  n-value:  The order of the function. n-value is a number value and must be greater than or equal to 0. If n-value has a decimal portion, it is ignored. Usage Notes  This form of the Bessel function is also known as the Neumann function. Examples =BESSELY(25, 3) returns 0.117924850396893. =BESSELY(25, 3.9) also returns 0.117924850396893, since any decimal portion of n-value is ignored. =BESSELY(-25, 3) returns an error, since negative or zero values are not permitted. Related Topics For related functions and additional information, see: “BESSELJ” on page 74 “Listing of Engineering Functions” on page 72 “Value Types” on page 36 “The Elements of Formulas” on page 15 “Using the Keyboard and Mouse to Create and Edit Formulas” on page 26 “Pasting from Examples in Help” on page 41 BIN2DEC The BIN2DEC function converts a binary number to the corresponding decimal number. BIN2DEC(binary-string, convert-length)  binary-string:  The string representing the number to be converted. binary-string is a string value. It must contain only 0s and 1s.  convert-length:  An optional value specifying minimum length of the number returned. convert-length is a number value and must be in the range 1 to 32. If omitted, it is assumed to be 1. If included, convert-string is padded with leading zeros, if necessary, so that it is at least the length specified by convert-length. Examples =BIN2DEC(”1001”) returns 9. =BIN2DEC(”100111”, 3) returns 039. =BIN2DEC(101101) returns 45. Related Topics For related functions and additional information, see: “BIN2HEX” on page 77 “BIN2OCT” on page 78 “DEC2BIN” on page 83 “HEX2DEC” on page 90 “OCT2DEC” on page 94 “Listing of Engineering Functions” on page 72 “Value Types” on page 36 “The Elements of Formulas” on page 15 “Using the Keyboard and Mouse to Create and Edit Formulas” on page 26 “Pasting from Examples in Help” on page 41 76 Chapter 5 Engineering Functions Chapter 5 Engineering Functions 77 BIN2HEX The BIN2HEX function converts a binary number to the corresponding hexadecimal number. BIN2HEX(binary-string, convert-length)  binary-string:  The string representing the number to be converted. binary-string is a string value. It must contain only 0s and 1s.  convert-length:  An optional value specifying minimum length of the number returned. convert-length is a number value and must be in the range 1 to 32. If omitted, it is assumed to be 1. If included, convert-string is padded with leading zeros, if necessary, so that it is at least the length specified by convert-length. Usage Notes  This function uses two’s complement notation, based on 32 bits. Therefore, negative numbers will always be 8 digits in length. Examples =BIN2HEX(”100101”) returns 25. =BIN2HEX(”100111”, 3) returns 027. =BIN2HEX(101101) returns 2D. Related Topics For related functions and additional information, see: “BIN2DEC” on page 76 “BIN2OCT” on page 78 “DEC2HEX” on page 84 “HEX2BIN” on page 89 “OCT2HEX” on page 95 “Listing of Engineering Functions” on page 72 “Value Types” on page 36 “The Elements of Formulas” on page 15 “Using the Keyboard and Mouse to Create and Edit Formulas” on page 26 “Pasting from Examples in Help” on page 41 BIN2OCT The BIN2OCT function converts a binary number to the corresponding octal number. BIN2OCT(binary-string, convert-length)  binary-string:  The string representing the number to be converted. binary-string is a string value. It must contain only 0s and 1s.  convert-length:  An optional value specifying minimum length of the number returned. convert-length is a number value and must be in the range 1 to 32. If omitted, it is assumed to be 1. If included, convert-string is padded with leading zeros, if necessary, so that it is at least the length specified by convert-length. Usage Notes  This function uses two’s complement notation, based on 32 bits. Therefore, negative numbers will always be 11 digits in length. Examples =BIN2OCT(”10011”) returns 23. =BIN2OCT(”100111”, 3) returns 047. Related Topics For related functions and additional information, see: “BIN2HEX” on page 77 “DEC2OCT” on page 85 “HEX2OCT” on page 91 “OCT2BIN” on page 93 “BIN2DEC” on page 76 “Listing of Engineering Functions” on page 72 “Value Types” on page 36 “The Elements of Formulas” on page 15 “Using the Keyboard and Mouse to Create and Edit Formulas” on page 26 “Pasting from Examples in Help” on page 41 78 Chapter 5 Engineering Functions Chapter 5 Engineering Functions 79 CONVERT The CONVERT function converts a number from one measurement system to its corresponding value in another measurement system. CONVERT(convert-num, from-unit, to-unit)  convert-num:  The number to be converted. convert-num is a number value.  from-unit:  The current unit of the number to be converted. from-unit is a string value. It must be one of the specified constants.  to-unit:  The new unit of the number to be converted. to-unit is a string value. It must be one of the specified constants. Usage Notes  The possible values for from-unit and to-unit are contained in tables that follow the examples (“Supported Conversion Units” on page 80). The tables are organized by category. If the value is entered into a referenced cell, instead of being typed directly into the function, the quotes included in the tables are not required. Case is important and must be strictly followed. Examples =CONVERT(9, “lbm”, “kg”) returns 4.08233133 (9 pounds is approximately 4.08 kilograms). =CONVERT (26.2, “mi”, “m”) returns 42164.8128 (26.2 miles is approximately 42,164.8 meters). =CONVERT(1, “tsp”, “ml”) returns 4.92892159375 (1 teaspoon is approximately 4.9 milliliters). Related Topics For related functions and additional information, see: “Listing of Engineering Functions” on page 72 “Value Types” on page 36 “The Elements of Formulas” on page 15 “Using the Keyboard and Mouse to Create and Edit Formulas” on page 26 “Pasting from Examples in Help” on page 41 Supported Conversion Units Weight and mass Measure Constant Gram “g” (can be used with metric prefixes) Slug “sg” Pound mass (avoirdupois) “lbm” U (atomic mass unit) “u” (can be used with metric prefixes) Ounce mass (avoirdupois) “ozm” Distance Measure Constant Meter “m” (can be used with metric prefixes) Statute mile “mi” Nautical mile “Nmi” Inch “in” Foot “ft” Yard “yd” Angstrom “ang” (can be used with metric prefixes) Pica (1/6 in., Postscript Pica) “Pica” Duration Measure Constant Year “yr” Week “wk” Day “day” Hour “hr” Minute “mn” Second “sec” (can be used with metric prefixes) 80 Chapter 5 Engineering Functions Chapter 5 Engineering Functions 81 Speed Measure Constant Miles per hour “mi/h” Miles per minute “mi/mn” Meters per hour “m/h” (can be used with metric prefixes) Meters per minute “m/mn” (can be used with metric prefixes) Meters per second “m/s” (can be used with metric prefixes) Feet per minute “ft/mn” Feet per second “ft/s” Knot “kt” Pressure Measure Constant Pascal “Pa” (can be used with metric prefixes) Atmosphere “atm” (can be used with metric prefixes) Millimeters of mercury “mmHg” (can be used with metric prefixes) Force Measure Constant Newton “N” (can be used with metric prefixes) Dyne “dyn” (can be used with metric prefixes) Pound force “lbf” Energy Measure Constant Joule “J” (can be used with metric prefixes) Erg “e” (can be used with metric prefixes) Thermodynamic calorie “c” (can be used with metric prefixes) IT calorie “cal” (can be used with metric prefixes) Electron volt “eV” (can be used with metric prefixes) Horsepower-hour “HPh” Measure Constant Watt-hour “Wh” (can be used with metric prefixes) Foot-pound “flb” BTU “BTU” Power Measure Constant Horsepower “HP” Watt “W” (can be used with metric prefixes) Magnetism Measure Constant Tesla “T” (can be used with metric prefixes) Gauss “ga” (can be used with metric prefixes) Temperature Measure Constant Degrees Celsius “C” Degrees Fahrenheit “F” Kelvins “K” (can be used with metric prefixes) Liquid Measure Constant Teaspoon “tsp” Tablespoon “tbs” Fluid ounce “oz” Cup “cup” U.S. pint “pt” U.K. pint “uk_pt” Quart “qt” Gallon “gal” Liter “l” (can be used with metric prefixes) 82 Chapter 5 Engineering Functions Chapter 5 Engineering Functions 83 Metric prefixes Measure Constant Multiplier exa “E” 1E+18 peta “P” 1E+15 tera “T” 1E+12 giga “G” 1E+09 mega “M” 1E+06 kilo “k” 1E+03 hecto “h” 1E+02 deca “e” 1E+01 deci “d” 1E-01 centi “c” 1E-02 milli “m” 1E-03 micro “u” or “μ” 1E-06 nano “n” 1E-09 pico “p” 1E-12 femto “f” 1E-15 atto “a” 1E-18 Usage Notes These prefixes can only be used with the metric constants “g”, “u”, “ m”, “ang”, “sec”, “m/h”, “m/mn”, “m/s”, “Pa”, “atm”, “mmHg”, “N”, “dyn”, “J”, “e”, “c”, “cal”, “eV”, “Wh”, “W”, “T”, “ga”, “K”, and “l”. DEC2BIN The DEC2BIN function converts a decimal number to the corresponding binary number. DEC2BIN(decimal-string, convert-length)  decimal-string:  The string representing the number to be converted. decimal-string is a string value. It must contain only the numbers 0 through 9.  convert-length:  An optional value specifying minimum length of the number returned. convert-length is a number value and must be in the range 1 to 32. If omitted, it is assumed to be 1. If included, convert-string is padded with leading zeros, if necessary, so that it is at least the length specified by convert-length. Examples =DEC2BIN(100) returns 01100100. =DEC2BIN(”1001”, 12) returns 001111101001. Related Topics For related functions and additional information, see: “BIN2DEC” on page 76 “DEC2HEX” on page 84 “DEC2OCT” on page 85 “HEX2BIN” on page 89 “OCT2BIN” on page 93 “Listing of Engineering Functions” on page 72 “Value Types” on page 36 “The Elements of Formulas” on page 15 “Using the Keyboard and Mouse to Create and Edit Formulas” on page 26 “Pasting from Examples in Help” on page 41 DEC2HEX The DEC2HEX function converts a decimal number to the corresponding hexadecimal number. DEC2HEX(decimal-string, convert-length)  decimal-string:  The string representing the number to be converted. decimal-string is a string value. It must contain only the numbers 0 through 9.  convert-length:  An optional value specifying minimum length of the number returned. convert-length is a number value and must be in the range 1 to 32. If omitted, it is assumed to be 1. If included, convert-string is padded with leading zeros, if necessary, so that it is at least the length specified by convert-length. Examples =DEC2HEX(100) returns 64. =DEC2HEX(”1001”, 4) returns 03E9. 84 Chapter 5 Engineering Functions Chapter 5 Engineering Functions 85 Related Topics For related functions and additional information, see: “BIN2HEX” on page 77 “DEC2BIN” on page 83 “DEC2OCT” on page 85 “HEX2DEC” on page 90 “OCT2HEX” on page 95 “Listing of Engineering Functions” on page 72 “Value Types” on page 36 “The Elements of Formulas” on page 15 “Using the Keyboard and Mouse to Create and Edit Formulas” on page 26 “Pasting from Examples in Help” on page 41 DEC2OCT The DEC2OCT function converts a decimal number to the corresponding octal number. DEC2OCT(decimal-string, convert-length)  decimal-string:  The string representing the number to be converted. decimal-string is a string value. It must contain only the numbers 0 through 9.  convert-length:  An optional value specifying minimum length of the number returned. convert-length is a number value and must be in the range 1 to 32. If omitted, it is assumed to be 1. If included, convert-string is padded with leading zeros, if necessary, so that it is at least the length specified by convert-length. Examples =DEC2OCT(100) returns 144. =DEC2OCT(”1001”, 4) returns 1751. Related Topics For related functions and additional information, see: “BIN2OCT” on page 78 “DEC2BIN” on page 83 “DEC2HEX” on page 84 “HEX2OCT” on page 91 “OCT2DEC” on page 94 “Listing of Engineering Functions” on page 72 “Value Types” on page 36 “The Elements of Formulas” on page 15 “Using the Keyboard and Mouse to Create and Edit Formulas” on page 26 “Pasting from Examples in Help” on page 41 DELTA The DELTA function determines whether two values are exactly equal. This function uses exact equality. By comparison, the = operator uses string-based equality. DELTA(compare-from, compare-to)  compare-from:  A number. compare-from is a number value.  compare-to:  A number. compare-to is a number value. Usage Notes  DELTA returns 1 (TRUE) if compare-from is exactly equal to compare-to; otherwise 0 (FALSE) is returned. Examples =DELTA(5, 5) returns 1 (TRUE). =DELTA(5, -5) returns 0 (FALSE). =DELTA(5, 5.000) returns 1 (TRUE). Related Topics For related functions and additional information, see: “GESTEP” on page 88 “Listing of Engineering Functions” on page 72 “Value Types” on page 36 “The Elements of Formulas” on page 15 “Using the Keyboard and Mouse to Create and Edit Formulas” on page 26 “Pasting from Examples in Help” on page 41 86 Chapter 5 Engineering Functions Chapter 5 Engineering Functions 87 ERF The ERF function returns the error function integrated between two values. ERF(lower, upper)  lower:  The lower limit or bound. lower is a number value.  upper:  An optional argument specifying the upper limit or bound. upper is a number value. If upper is omitted it is assumed to be 0. Usage Notes  This function is also known as the Gauss error function. Examples =ERF(0, 1) returns 0.842700792949715. =ERF(-1, 1) returns 1.68540158589943. =ERF(1, 8) returns 0.157299207050285. Related Topics For related functions and additional information, see: “ERFC” on page 87 “Listing of Engineering Functions” on page 72 “Value Types” on page 36 “The Elements of Formulas” on page 15 “Using the Keyboard and Mouse to Create and Edit Formulas” on page 26 “Pasting from Examples in Help” on page 41 ERFC The ERFC function returns the complementary ERF function integrated between a given lower bound and infinity. ERFC(lower)  lower:  The lower limit or bound. lower is a number value. Examples =ERFC(-1) returns 1.84270079294971. =ERFC(1) returns 0.157299207050285. =ERFC(12) returns 1.3562611692059E-64. Related Topics For related functions and additional information, see: “ERF” on page 87 “Listing of Engineering Functions” on page 72 “Value Types” on page 36 “The Elements of Formulas” on page 15 “Using the Keyboard and Mouse to Create and Edit Formulas” on page 26 “Pasting from Examples in Help” on page 41 GESTEP The GESTEP function determines if one value is greater than or exactly equal to another value. This function uses exact equality. By comparison, the = operator uses string-based equality. GESTEP(compare-num, step-number)  compare-num:  The number to compare. compare-num is a number value.  step-number:  The size of the step. step-number is a number value. Usage Notes  GESTEP returns 1 (TRUE) if compare-num is greater than or exactly equal to stepnumber; otherwise 0 (FALSE) is returned. Examples =GESTEP(-4, -5) returns 1 (TRUE), since -4 is greater than -5. =GESTEP(4, 5) returns 0 (FALSE), since 4 is less than 5. =GESTEP(5, 4) returns 1 (TRUE), since 5 is greater than 4. =GESTEP(20, 20) returns 1 (TRUE), since 20 is exactly equal to 20. Related Topics For related functions and additional information, see: “DELTA” on page 86 “Listing of Engineering Functions” on page 72 “Value Types” on page 36 “The Elements of Formulas” on page 15 88 Chapter 5 Engineering Functions Chapter 5 Engineering Functions 89 “Using the Keyboard and Mouse to Create and Edit Formulas” on page 26 “Pasting from Examples in Help” on page 41 HEX2BIN The HEX2BIN function converts a hexadecimal number to the corresponding binary number. HEX2BIN(hex-string, convert-length)  hex-string:  The string representing the number to be converted. hex-string is a string value. It must contain only the numbers 0 through 9 and the letters A through F.  convert-length:  An optional value specifying minimum length of the number returned. convert-length is a number value and must be in the range 1 to 32. If omitted, it is assumed to be 1. If included, convert-string is padded with leading zeros, if necessary, so that it is at least the length specified by convert-length. Usage Notes  This function uses two’s complement notation, based on 32 bits. Therefore, negative numbers will always be 32 digits in length. Examples =HEX2BIN(”F”, 8) returns 00001111. =HEX2BIN(“3F”) returns 0111111. Related Topics For related functions and additional information, see: “BIN2HEX” on page 77 “HEX2DEC” on page 90 “HEX2OCT” on page 91 “OCT2BIN” on page 93 “DEC2BIN” on page 83 “Listing of Engineering Functions” on page 72 “Value Types” on page 36 “The Elements of Formulas” on page 15 “Using the Keyboard and Mouse to Create and Edit Formulas” on page 26 “Pasting from Examples in Help” on page 41 HEX2DEC The HEX2DEC function converts a hexadecimal number to the corresponding decimal number. HEX2DEC(hex-string, convert-length)  hex-string:  The string representing the number to be converted. hex-string is a string value. It must contain only the numbers 0 through 9 and the letters A through F.  convert-length:  An optional value specifying minimum length of the number returned. convert-length is a number value and must be in the range 1 to 32. If omitted, it is assumed to be 1. If included, convert-string is padded with leading zeros, if necessary, so that it is at least the length specified by convert-length. Examples =HEX2DEC(”F”, 3) returns 015. =HEX2DEC(“3F”) returns 63. Related Topics For related functions and additional information, see: “BIN2DEC” on page 76 “DEC2HEX” on page 84 “HEX2BIN” on page 89 “HEX2OCT” on page 91 “OCT2DEC” on page 94 “Listing of Engineering Functions” on page 72 “Value Types” on page 36 “The Elements of Formulas” on page 15 “Using the Keyboard and Mouse to Create and Edit Formulas” on page 26 “Pasting from Examples in Help” on page 41 90 Chapter 5 Engineering Functions Chapter 5 Engineering Functions 91 HEX2OCT The HEX2OCT function converts a hexadecimal number to the corresponding octal number. HEX2OCT(hex-string, convert-length)  hex-string:  The string representing the number to be converted. hex-string is a string value. It must contain only the numbers 0 through 9 and the letters A through F.  convert-length:  An optional value specifying minimum length of the number returned. convert-length is a number value and must be in the range 1 to 32. If omitted, it is assumed to be 1. If included, convert-string is padded with leading zeros, if necessary, so that it is at least the length specified by convert-length. Usage Notes  This function uses two’s complement notation, based on 32 bits. Therefore, negative numbers will always be 11 digits in length. Examples =HEX2OCT(”F”, 3) returns 017. =HEX2OCT(“4E”) returns 116. Related Topics For related functions and additional information, see: “BIN2OCT” on page 78 “DEC2OCT” on page 85 “HEX2BIN” on page 89 “HEX2DEC” on page 90 “OCT2HEX” on page 95 “Listing of Engineering Functions” on page 72 “Value Types” on page 36 “The Elements of Formulas” on page 15 “Using the Keyboard and Mouse to Create and Edit Formulas” on page 26 “Pasting from Examples in Help” on page 41 NUMTOBASE The NUMTOBASE function converts a number from base 10 into a number in the specified base. NUMTOBASE(decimal-string, base, convert-length)  decimal-string:  The string representing the number to be converted. decimal-string is a string value. It must contain only the numbers 0 through 9.  base:  The new base of the number to be converted. base is a number value and must be in the range 1 to 36.  convert-length:  An optional value specifying minimum length of the number returned. convert-length is a number value and must be in the range 1 to 32. If omitted, it is assumed to be 1. If included, convert-string is padded with leading zeros, if necessary, so that it is at least the length specified by convert-length. Examples =NUMTOBASE(16, 16) returns 10. =NUMTOBASE(100, 32, 4) returns 0034. =NUMTOBASE(100,2) returns 1100100. Related Topics For related functions and additional information, see: “BASETONUM” on page 73 “DEC2BIN” on page 83 “DEC2HEX” on page 84 “DEC2OCT” on page 85 “Listing of Engineering Functions” on page 72 “Value Types” on page 36 “The Elements of Formulas” on page 15 “Using the Keyboard and Mouse to Create and Edit Formulas” on page 26 “Pasting from Examples in Help” on page 41 92 Chapter 5 Engineering Functions Chapter 5 Engineering Functions 93 OCT2BIN The OCT2BIN function converts an octal number to the corresponding binary number. OCT2BIN(octal-string, convert-length)  octal-string:  The string representing the number to be converted. octal-string is a string value. It must contain only the numbers 0 through 7.  convert-length:  An optional value specifying minimum length of the number returned. convert-length is a number value and must be in the range 1 to 32. If omitted, it is assumed to be 1. If included, convert-string is padded with leading zeros, if necessary, so that it is at least the length specified by convert-length. Usage Notes  This function uses two’s complement notation, based on 32 bits. Therefore, negative numbers will always be 32 digits in length. Examples =OCT2BIN(127,8) returns 01010111. =OCT2BIN(15) returns 01101. Related Topics For related functions and additional information, see: “BIN2OCT” on page 78 “DEC2BIN” on page 83 “HEX2BIN” on page 89 “OCT2DEC” on page 94 “OCT2HEX” on page 95 “Listing of Engineering Functions” on page 72 “Value Types” on page 36 “The Elements of Formulas” on page 15 “Using the Keyboard and Mouse to Create and Edit Formulas” on page 26 “Pasting from Examples in Help” on page 41 OCT2DEC The OCT2DEC function converts an octal number to the corresponding decimal number. OCT2DEC(octal-string, convert-length)  octal-string:  The string representing the number to be converted. octal-string is a string value. It must contain only the numbers 0 through 7.  convert-length:  An optional value specifying minimum length of the number returned. convert-length is a number value and must be in the range 1 to 32. If omitted, it is assumed to be 1. If included, convert-string is padded with leading zeros, if necessary, so that it is at least the length specified by convert-length. Examples =OCT2DEC(127,4) returns 0087. =OCT2DEC(15) returns 13. Related Topics For related functions and additional information, see: “BIN2DEC” on page 76 “DEC2OCT” on page 85 “OCT2BIN” on page 93 “OCT2HEX” on page 95 “Listing of Engineering Functions” on page 72 “Value Types” on page 36 “The Elements of Formulas” on page 15 “Using the Keyboard and Mouse to Create and Edit Formulas” on page 26 “Pasting from Examples in Help” on page 41 94 Chapter 5 Engineering Functions Chapter 5 Engineering Functions 95 OCT2HEX The OCT2HEX function converts an octal number to the corresponding hexadecimal number. OCT2HEX(octal-string, convert-length)  octal-string:  The string representing the number to be converted. octal-string is a string value. It must contain only the numbers 0 through 7.  convert-length:  An optional value specifying minimum length of the number returned. convert-length is a number value and must be in the range 1 to 32. If omitted, it is assumed to be 1. If included, convert-string is padded with leading zeros, if necessary, so that it is at least the length specified by convert-length. Usage Notes  This function uses two’s complement notation, based on 32 bits. Therefore, negative numbers will always be 8 digits in length. Examples =OCT2HEX(127,4) returns 0057. =OCT2HEX(15) returns 0D. Related Topics For related functions and additional information, see: “BIN2HEX” on page 77 “DEC2HEX” on page 84 “HEX2OCT” on page 91 “OCT2BIN” on page 93 “OCT2DEC” on page 94 “Listing of Engineering Functions” on page 72 “Value Types” on page 36 “The Elements of Formulas” on page 15 “Using the Keyboard and Mouse to Create and Edit Formulas” on page 26 “Pasting from Examples in Help” on page 41 96 The financial functions help you work with cash flows, depreciable assets, annuities, and investments by solving problems such as the amount of annual depreciation of an asset, the interest earned on an investment, and the current market price of a bond. Listing of Financial Functions iWork provides these financial functions for use with tables. Function Description “ACCRINT” (page 99) The ACCRINT function calculates the accrued interest added to the purchase price of a security and paid to the seller when the security pays periodic interest. “ACCRINTM” (page 101) The ACCRINTM function calculates the total accrued interest added to the purchase price of a security and paid to the seller when the security pays interest only at maturity. “BONDDURATION” (page 103) The BONDDURATION function calculates the weighted average of the present value of the cash flows for an assumed par value of $100. “BONDMDURATION” (page 104) The BONDMDURATION function calculates the modified weighted average of the present value of the cash flows for an assumed par value of $100. “COUPDAYBS” (page 105) The COUPDAYBS function returns the number of days between the beginning of the coupon period in which settlement occurs and the settlement date. “COUPDAYS” (page 107) The COUPDAYS function returns the number of days in the coupon period in which settlement occurs. Financial Functions 6 Chapter 6 Financial Functions 97 Function Description “COUPDAYSNC” (page 108) The COUPDAYSNC function returns the number of days between the settlement date and the end of the coupon period in which settlement occurs. “COUPNUM” (page 109) The COUPNUM function returns the number of coupons remaining to be paid between the settlement date and the maturity date. “CUMIPMT” (page 110) The CUMIPMT function returns the total interest included in loan or annuity payments over a chosen time interval based on fixed periodic payments and a fixed interest rate. “CUMPRINC” (page 112) The CUMPRINC function returns the total principal included in loan or annuity payments over a chosen time interval based on fixed periodic payments and a fixed interest rate. “DB” (page 114) The DB function returns the amount of depreciation of an asset for a specified period using the fixed-declining balance method. “DDB” (page 116) The DDB function returns the amount of depreciation of an asset based on a specified depreciation rate. “DISC” (page 117) The DISC function returns the annual discount rate of a security that pays no interest and is sold at a discount to its redemption value. “EFFECT” (page 119) The EFFECT function returns the effective annual interest rate from the nominal annual interest rate based on the number of compounding periods per year. “FV” (page 120) The FV function returns the future value of an investment based on a series of regular periodic cash flows (payments of a constant amount and all cash flows at constant intervals) and a fixed interest rate. “INTRATE” (page 122) The INTRATE function returns the effective annual interest rate for a security that pays interest only at maturity. “IPMT” (page 123) The IPMT function returns the interest portion of a specified loan or annuity payment based on fixed, periodic payments and a fixed interest rate. “IRR” (page 125) The IRR function returns the internal rate of return for an investment that is based on a series of potentially irregular cash flows that occur at regular time intervals. Function Description “ISPMT” (page 126) The ISPMT function returns the interest portion of a specified loan or annuity payment based on fixed, periodic payments and a fixed interest rate. This function is provided for compatibility with tables imported from other spreadsheet applications. “MIRR” (page 128) The MIRR function returns the modified internal rate of return for an investment that is based on a series of potentially irregular cash flows that occur at regular time intervals. The rate earned on positive cash flows and the rate paid to finance negative cash flows can differ. “NOMINAL” (page 129) The NOMINAL function returns the nominal annual interest rate from the effective annual interest rate based on the number of compounding periods per year. “NPER” (page 130) The NPER function returns the number of payment periods for a loan or annuity based on a series of regular periodic cash flows (payments of a constant amount and all cash flows at constant intervals) and a fixed interest rate. “NPV” (page 132) The NPV function returns the net present value of an investment based on a series of potentially irregular cash flows that occur at regular time intervals. “PMT” (page 134) The PMT function returns the fixed periodic payment for a loan or annuity based on a series of regular periodic cash flows (payments of a constant amount and all cash flows at constant intervals) and a fixed interest rate. “PPMT” (page 135) The PPMT function returns the principal portion of a specified loan or annuity payment based on fixed periodic payments and a fixed interest rate. “PRICE” (page 137) The PRICE function returns the price of a security that pays periodic interest per $100 of redemption (par) value. “PRICEDISC” (page 138) The PRICEDISC function returns the price of a security that is sold at a discount to redemption value and does not pay interest per $100 of redemption (par) value. “PRICEMAT” (page 140) The PRICEMAT function returns the price of a security that pays interest only at maturity per $100 of redemption (par) value. 98 Chapter 6 Financial Functions Chapter 6 Financial Functions 99 Function Description “PV” (page 141) The PV function returns the present value of an investment or annuity based on a series of regular periodic cash flows (payments of a constant amount and all cash flows at constant intervals) and a fixed interest rate. “RATE” (page 144) The RATE function returns the interest rate of an investment, loan, or annuity based on a series of regular periodic cash flows (payments of a constant amount and all cash flows at constant intervals) and a fixed interest rate. “RECEIVED” (page 146) The RECEIVED function returns the maturity value for a security that pays interest only at maturity. “SLN” (page 147) The SLN function returns the amount of depreciation of an asset for a single period using the straight-line method. “SYD” (page 148) The SYD function returns the amount of depreciation of an asset for a specified period using the sum-of-the-years-digits method. “VDB” (page 149) The VDB function returns the amount of depreciation of an asset over a chosen time interval, based on a specified depreciation rate. “YIELD” (page 150) The YIELD function returns the effective annual interest rate for a security that pays regular periodic interest. “YIELDDISC” (page 152) The YIELDDISC function returns the effective annual interest rate for a security that is sold at a discount to redemption value and pays no interest. “YIELDMAT” (page 153) The YIELDMAT function returns the effective annual interest rate for a security that pays interest only at maturity. ACCRINT The ACCRINT function calculates the accrued interest added to the purchase price of a security and paid to the seller when the security pays periodic interest. ACCRINT(issue, first, settle, annual-rate, par, frequency, days-basis)  issue:  The date the security was originally issued. issue is a date/time value and must be the earliest date given.  first: The date of the first interest payment. first is a date/time value and must be after issue.  settle:  The trade settlement date. settle is a date/time value. The trade settlement date is usually one or more days after the trade date.  annual-rate:  The annual coupon rate or stated annual interest rate of the security. annual-rate is a number value and is either entered as a decimal (for example, 0.08) or with a percent sign (for example, 8%).  par:  The face (par) or maturity value of the security. par is a number value. If omitted (comma, but no value), par is assumed to be 1000.  frequency:  The number of coupon payments each year. annual (1): One payment per year. semiannual (2): Two payments per year. quarterly (4): Four payments per year.  days-basis:  An optional argument specifying the number of days per month and days per year used in the calculations. 30/360 (0 or omitted):  30 days in a month, 360 days in a year, using the NASD method for dates falling on the 31st of a month. actual/actual (1):  Actual days in each month, actual days in each year. actual/360 (2):  Actual days in each month, 360 days in a year. actual/365 (3):  Actual days in each month, 365 days in a year. 30E/360 (4):  30 days in a month, 360 days in a year, using the European method for dates falling on the 31st of a month (European 30/360). Usage Notes  If settle is before first, the function returns the interest accrued since issue. If settle is after first, the function returns the interest accrued since the coupon payment date that most immediately precedes settle.  Use ACCRINTM for a security that pays interest only at maturity. Example 1 Assume you are considering the purchase of the hypothetical security described by the values listed. The settlement date is assumed to be before the first coupon date. You could use the ACCRINT function to determine the amount of accrued interest that would be added to the purchase/sale price. The function evaluates to $38.06, which represents the interest accrued between the issue date and the settlement date. issue first settle annual-rate par frequency days-basis =ACCRINT (B2, C2, D2, E2, F2, G2, H2) 12/14/2008 07/01/2009 05/01/2009 0.10 1000 2 0 100 Chapter 6 Financial Functions Chapter 6 Financial Functions 101 Example 2 Assume you are considering the purchase of the hypothetical security described by the values listed. The settlement date is assumed to be after the first coupon date. You could use the ACCRINT function to determine the amount of accrued interest that would be added to the purchase/sale price. The function evaluates to approximately $20.56, which represents the interest accrued between the immediately preceding coupon payment date and the settlement date. issue first settle annual-rate par frequency days-basis =ACCRINT (B2, C2, D2, E2, F2, G2, H2) 12/14/2008 07/01/2009 09/15/2009 0.10 1000 2 0 Related Topics For related functions and additional information, see: “ACCRINTM” on page 101 “Common Arguments Used in Financial Functions” on page 341 “Listing of Financial Functions” on page 96 “Value Types” on page 36 “The Elements of Formulas” on page 15 “Using the Keyboard and Mouse to Create and Edit Formulas” on page 26 “Pasting from Examples in Help” on page 41 ACCRINTM The ACCRINTM function calculates the total accrued interest added to the purchase price of a security and paid to the seller when the security pays interest only at maturity. ACCRINTM(issue, settle, annual-rate, par, days-basis)  issue:  The date the security was originally issued. issue is a date/time value and must be the earliest date given.  settle:  The trade settlement date. settle is a date/time value. The trade settlement date is usually one or more days after the trade date.  annual-rate:  The annual coupon rate or stated annual interest rate of the security. annual-rate is a number value and is either entered as a decimal (for example, 0.08) or with a percent sign (for example, 8%).  par:  The face (par) or maturity value of the security. par is a number value. If omitted (comma, but no value), par is assumed to be 1000.  days-basis:  An optional argument specifying the number of days per month and days per year used in the calculations. 30/360 (0 or omitted):  30 days in a month, 360 days in a year, using the NASD method for dates falling on the 31st of a month. actual/actual (1):  Actual days in each month, actual days in each year. actual/360 (2):  Actual days in each month, 360 days in a year. actual/365 (3):  Actual days in each month, 365 days in a year. 30E/360 (4):  30 days in a month, 360 days in a year, using the European method for dates falling on the 31st of a month (European 30/360). Usage Notes  Use ACCRINT for a security that pays periodic interest. Example Assume you are considering the purchase of the hypothetical security described by the values listed. This security pays interest only at maturity. You could use the ACCRINTM function to determine the amount of accrued interest that would be added to the purchase/sale price. The function evaluates to approximately $138.06, which represents the interest accrued between the issue date and the settlement date. issue settle annual-rate par days-basis =ACCRINTM(B2, C2, D2, E2, F2) 12/14/2007 05/01/2009 0.10 1000 0 Related Topics For related functions and additional information, see: “ACCRINT” on page 99 “Common Arguments Used in Financial Functions” on page 341 “Listing of Financial Functions” on page 96 “Value Types” on page 36 “The Elements of Formulas” on page 15 “Using the Keyboard and Mouse to Create and Edit Formulas” on page 26 “Pasting from Examples in Help” on page 41 102 Chapter 6 Financial Functions Chapter 6 Financial Functions 103 BONDDURATION The BONDDURATION function returns the weighted average of the present value of the cash flows for an assumed par value of $100. BONDDURATION(settle, maturity, annual-rate, annual-yield, frequency, days-basis)  settle:  The trade settlement date. settle is a date/time value. The trade settlement date is usually one or more days after the trade date.  maturity:  The date when the security matures. maturity is a date/time value. It must be after settle.  annual-rate:  The annual coupon rate or stated annual interest rate of the security. annual-rate is a number value and is either entered as a decimal (for example, 0.08) or with a percent sign (for example, 8%).  annual-yield:  The annual yield of the security. annual-yield is a number value and is either entered as a decimal (for example, 0.08) or with a percent sign (for example, 8%).  frequency:  The number of coupon payments each year. annual (1): One payment per year. semiannual (2): Two payments per year. quarterly (4): Four payments per year.  days-basis:  An optional argument specifying the number of days per month and days per year used in the calculations. 30/360 (0 or omitted):  30 days in a month, 360 days in a year, using the NASD method for dates falling on the 31st of a month. actual/actual (1):  Actual days in each month, actual days in each year. actual/360 (2):  Actual days in each month, 360 days in a year. actual/365 (3):  Actual days in each month, 365 days in a year. 30E/360 (4):  30 days in a month, 360 days in a year, using the European method for dates falling on the 31st of a month (European 30/360). Usage Notes  This function returns a value known as the Macauley duration. Example Assume you are considering the purchase of a hypothetical security. The purchase will settle April 2, 2010 and the maturity will mature on December 31, 2015. The coupon rate is 5%, resulting in a yield of approximately 5.284% (the yield was calculated using the YIELD function). The bond pays interest quarterly, based on actual days. =BONDDURATION(“4/2/2010”, “12/31/2015”, 0.05, 0.05284, 4, 1) returns approximately 5.0208, the present value of the future cash flows (the bond duration), based on the Macauley duration. The cash flows consist of the price paid, interest received, and principal received at maturity. Related Topics For related functions and additional information, see: “BONDMDURATION” on page 104 “Common Arguments Used in Financial Functions” on page 341 “Listing of Financial Functions” on page 96 “Value Types” on page 36 “The Elements of Formulas” on page 15 “Using the Keyboard and Mouse to Create and Edit Formulas” on page 26 “Pasting from Examples in Help” on page 41 BONDMDURATION The BONDMDURATION function returns the modified weighted average of the present value of the cash flows for an assumed par value of $100. BONDMDURATION(settle, maturity, annual-rate, annual-yield, frequency, days-basis)  settle:  The trade settlement date. settle is a date/time value. The trade settlement date is usually one or more days after the trade date.  maturity:  The date when the security matures. maturity is a date/time value. It must be after settle.  annual-rate:  The annual coupon rate or stated annual interest rate of the security. annual-rate is a number value and is either entered as a decimal (for example, 0.08) or with a percent sign (for example, 8%).  annual-yield:  The annual yield of the security. annual-yield is a number value and is either entered as a decimal (for example, 0.08) or with a percent sign (for example, 8%).  frequency:  The number of coupon payments each year. annual (1): One payment per year. semiannual (2): Two payments per year. quarterly (4): Four payments per year.  days-basis:  An optional argument specifying the number of days per month and days per year used in the calculations. 30/360 (0 or omitted):  30 days in a month, 360 days in a year, using the NASD method for dates falling on the 31st of a month. actual/actual (1):  Actual days in each month, actual days in each year. actual/360 (2):  Actual days in each month, 360 days in a year. 104 Chapter 6 Financial Functions Chapter 6 Financial Functions 105 actual/365 (3):  Actual days in each month, 365 days in a year. 30E/360 (4):  30 days in a month, 360 days in a year, using the European method for dates falling on the 31st of a month (European 30/360). Usage Notes  This function returns a value known as the modified Macauley duration. Example Assume you are considering the purchase of a hypothetical security. The purchase will settle April 2, 2010 and the maturity will mature on December 31, 2015. The coupon rate is 5%, resulting in a yield of approximately 5.284% (the yield was calculated using the YIELD function). The bond pays interest quarterly, based on actual days. =BONDMDURATION(“4/2/2010”, “12/31/2015”, 0.05, 0.05284, 4, 1) returns approximately 4.9554, the present value of the future cash flows (the bond duration), based on the modified Macauley duration. The cash flows consist of the price paid, interest received, and principal received at maturity. Related Topics For related functions and additional information, see: “BONDDURATION” on page 103 “Common Arguments Used in Financial Functions” on page 341 “Listing of Financial Functions” on page 96 “Value Types” on page 36 “The Elements of Formulas” on page 15 “Using the Keyboard and Mouse to Create and Edit Formulas” on page 26 “Pasting from Examples in Help” on page 41 COUPDAYBS The COUPDAYBS function returns the number of days between the beginning of the coupon period in which settlement occurs and the settlement date. COUPDAYBS(settle, maturity, frequency, days-basis)  settle:  The trade settlement date. settle is a date/time value. The trade settlement date is usually one or more days after the trade date.  maturity:  The date when the security matures. maturity is a date/time value. It must be after settle.  frequency:  The number of coupon payments each year. annual (1): One payment per year. semiannual (2): Two payments per year. quarterly (4): Four payments per year.  days-basis:  An optional argument specifying the number of days per month and days per year used in the calculations. 30/360 (0 or omitted):  30 days in a month, 360 days in a year, using the NASD method for dates falling on the 31st of a month. actual/actual (1):  Actual days in each month, actual days in each year. actual/360 (2):  Actual days in each month, 360 days in a year. actual/365 (3):  Actual days in each month, 365 days in a year. 30E/360 (4):  30 days in a month, 360 days in a year, using the European method for dates falling on the 31st of a month (European 30/360). Example Assume you are considering the purchase of the hypothetical security described by the values listed. You could use the COUPDAYBS function to determine the number of days from the last coupon payment date until the settlement date. This would be the number of days included in the computation of the accrued interest that would be added to the bond’s purchase price. The function returns 2, since there are 2 days between the last coupon payment date of March 31, 2010, and the settlement date of April 2, 2010. settle maturity frequency days-basis =COUPDAYBS(B2, C2, D2, E2, F2, G2) 4/2/2010 12/31/2015 4 1 Related Topics For related functions and additional information, see: “COUPDAYS” on page 107 “COUPDAYSNC” on page 108 “Common Arguments Used in Financial Functions” on page 341 “Listing of Financial Functions” on page 96 “Value Types” on page 36 “The Elements of Formulas” on page 15 “Using the Keyboard and Mouse to Create and Edit Formulas” on page 26 “Pasting from Examples in Help” on page 41 106 Chapter 6 Financial Functions Chapter 6 Financial Functions 107 COUPDAYS The COUPDAYS function returns the number of days in the coupon period in which settlement occurs. COUPDAYS(settle, maturity, frequency, days-basis)  settle:  The trade settlement date. settle is a date/time value. The trade settlement date is usually one or more days after the trade date.  maturity:  The date when the security matures. maturity is a date/time value. It must be after settle.  frequency:  The number of coupon payments each year. annual (1): One payment per year. semiannual (2): Two payments per year. quarterly (4): Four payments per year.  days-basis:  An optional argument specifying the number of days per month and days per year used in the calculations. 30/360 (0 or omitted):  30 days in a month, 360 days in a year, using the NASD method for dates falling on the 31st of a month. actual/actual (1):  Actual days in each month, actual days in each year. actual/360 (2):  Actual days in each month, 360 days in a year. actual/365 (3):  Actual days in each month, 365 days in a year. 30E/360 (4):  30 days in a month, 360 days in a year, using the European method for dates falling on the 31st of a month (European 30/360). Example Assume you are considering the purchase of the hypothetical security described by the values listed. You could use the COUPDAYS function to determine the number of days in the settlement date coupon period. The function returns 91, since there are 91 days in the coupon period beginning April 1, 2010, and ending on June 30, 2010. settle maturity frequency days-basis =COUPDAYS(B2, C2, D2, E2, F2, G2) 4/2/2010 12/31/2015 4 1 Related Topics For related functions and additional information, see: “COUPDAYBS” on page 105 “COUPDAYSNC” on page 108 “Common Arguments Used in Financial Functions” on page 341 “Listing of Financial Functions” on page 96 “Value Types” on page 36 “The Elements of Formulas” on page 15 “Using the Keyboard and Mouse to Create and Edit Formulas” on page 26 “Pasting from Examples in Help” on page 41 COUPDAYSNC The COUPDAYSNC function returns the number of days between the settlement date and the end of the coupon period in which settlement occurs. COUPDAYSNC(settle, maturity, frequency, days-basis)  settle:  The trade settlement date. settle is a date/time value. The trade settlement date is usually one or more days after the trade date.  maturity:  The date when the security matures. maturity is a date/time value. It must be after settle.  frequency:  The number of coupon payments each year. annual (1): One payment per year. semiannual (2): Two payments per year. quarterly (4): Four payments per year.  days-basis:  An optional argument specifying the number of days per month and days per year used in the calculations. 30/360 (0 or omitted):  30 days in a month, 360 days in a year, using the NASD method for dates falling on the 31st of a month. actual/actual (1):  Actual days in each month, actual days in each year. actual/360 (2):  Actual days in each month, 360 days in a year. actual/365 (3):  Actual days in each month, 365 days in a year. 30E/360 (4):  30 days in a month, 360 days in a year, using the European method for dates falling on the 31st of a month (European 30/360). 108 Chapter 6 Financial Functions Chapter 6 Financial Functions 109 Example Assume you are considering the purchase of the hypothetical security described by the values listed. You could use the COUPDAYSNC function to determine the number of days until the next coupon payment date. This would be the number of days until the first coupon payment you would receive. The function returns 89, since there are 89 days between settlement date of April 2, 2010, and the next coupon payment date of June 30, 2010. settle maturity frequency days-basis =COUPDAYSNC(B2, C2, D2, E2, F2, G2) 4/2/2010 12/31/2015 4 1 Related Topics For related functions and additional information, see: “COUPDAYS” on page 107 “COUPDAYBS” on page 105 “Common Arguments Used in Financial Functions” on page 341 “Listing of Financial Functions” on page 96 “Value Types” on page 36 “The Elements of Formulas” on page 15 “Using the Keyboard and Mouse to Create and Edit Formulas” on page 26 “Pasting from Examples in Help” on page 41 COUPNUM The COUPNUM function returns the number of coupons remaining to be paid between the settlement date and the maturity date. COUPNUM(settle, maturity, frequency, days-basis)  settle:  The trade settlement date. settle is a date/time value. The trade settlement date is usually one or more days after the trade date.  maturity:  The date when the security matures. maturity is a date/time value. It must be after settle.  frequency:  The number of coupon payments each year. annual (1): One payment per year. semiannual (2): Two payments per year. quarterly (4): Four payments per year.  days-basis:  An optional argument specifying the number of days per month and days per year used in the calculations. 30/360 (0 or omitted):  30 days in a month, 360 days in a year, using the NASD method for dates falling on the 31st of a month. actual/actual (1):  Actual days in each month, actual days in each year. actual/360 (2):  Actual days in each month, 360 days in a year. actual/365 (3):  Actual days in each month, 365 days in a year. 30E/360 (4):  30 days in a month, 360 days in a year, using the European method for dates falling on the 31st of a month (European 30/360). Example Assume you are considering the purchase of the hypothetical security described by the values listed. You could use the COUPNUM function to determine the number of coupons you could expect between the settlement date and the security’s maturity date. The function returns 23, since there are 23 quarterly coupon payment dates between April 2, 2010, and December 31, 2015, with the first being on June 30, 2010. settle maturity frequency days-basis =COUPNUM(B2, C2, D2, E2, F2, G2) 4/2/2010 12/31/2015 4 1 Related Topics For related functions and additional information, see: “Common Arguments Used in Financial Functions” on page 341 “Listing of Financial Functions” on page 96 “Value Types” on page 36 “The Elements of Formulas” on page 15 “Using the Keyboard and Mouse to Create and Edit Formulas” on page 26 “Pasting from Examples in Help” on page 41 CUMIPMT The CUMIPMT function returns the total interest included in loan or annuity payments over a chosen time interval based on fixed periodic payments and a fixed interest rate. CUMIPMT(periodic-rate, num-periods, present-value, starting-per, ending-per, when-due)  periodic-rate:  The interest rate per period. periodic-rate is a number value and is either entered as a decimal (for example, 0.08) or with a percent sign (for example, 8%). 110 Chapter 6 Financial Functions Chapter 6 Financial Functions 111  num-periods:  The number of periods. num-periods is a number value and must be greater than or equal to 0.  present-value:  The value of the initial investment, or the amount of the loan or annuity. present-value is a number value. At time 0, an amount received is a positive amount and an amount invested is a negative amount. For example, it could be an amount borrowed (positive) or the initial payment made on an annuity contract (negative).  starting-per:  First period to include in the calculation. starting-per is a number value.  ending-per:  Last period to include in the calculation. ending-per is a number value and must be greater than 0 and also greater than starting-per.  when-due:  Specifies whether payments are due at the beginning or end of each period. end (0):  Payments are due at the end of each period. beginning (1):  Payments are due at the beginning of each period. Usage Notes  If settle is before first, the function returns the interest accrued since issue. If settle is after first, the function returns the interest accrued since the coupon payment date that most immediately precedes settle.  Use ACCRINTM for a security that pays interest only at maturity. Examples It is generally understood that the amount of interest paid on a loan is higher in the early years, as compared to the later years. This example demonstrates just how much higher the early years can be. Assume a mortgage loan with an initial loan amount of $550,000, an interest rate of 6%, and a 30-year term. The CUMIPMT function can be used to determine the interest for any period. In the following table, CUMIPMT has been used to determine the interest for the first year (payments 1 through 12) and for the last year (payments 349 through 360) of the loan term. The function evaluates to $32,816.27 and $1,256.58, respectively. The amount of interest paid in the first year is more than 26 times the amount of interest paid in the last year. periodic-rate num-periods present-value starting-per ending-per when-due =CUMIPMT (B2, C2, D2, E2, F2, G2) =0.06/12 360 =550000 1 12 0 =CUMIPMT (B2, C2, D2, E3, F3, G2) 349 360 Related Topics For related functions and additional information, see: “CUMPRINC” on page 112 “IPMT” on page 123 “PMT” on page 134 “PPMT” on page 135 “Example of a Loan Amortization Table” on page 353 “Common Arguments Used in Financial Functions” on page 341 “Listing of Financial Functions” on page 96 “Value Types” on page 36 “The Elements of Formulas” on page 15 “Using the Keyboard and Mouse to Create and Edit Formulas” on page 26 “Pasting from Examples in Help” on page 41 CUMPRINC The CUMPRINC function returns the total principal included in loan or annuity payments over a chosen time interval based on fixed periodic payments and a fixed interest rate. CUMPRINC(periodic-rate, num-periods, present-value, starting-per, ending-per, cum-when-due)  periodic-rate:  The interest rate per period. periodic-rate is a number value and is either entered as a decimal (for example, 0.08) or with a percent sign (for example, 8%).  num-periods:  The number of periods. num-periods is a number value and must be greater than or equal to 0.  present-value:  The value of the initial investment, or the amount of the loan or annuity. present-value is a number value. At time 0, an amount received is a positive amount and an amount invested is a negative amount. For example, it could be an amount borrowed (positive) or the initial payment made on an annuity contract (negative).  starting-per:  First period to include in the calculation. starting-per is a number value.  ending-per:  Last period to include in the calculation. ending-per is a number value and must be greater than 0 and greater than starting-per.  when-due:  Specifies whether payments are due at the beginning or end of each period. 112 Chapter 6 Financial Functions Chapter 6 Financial Functions 113 end (0):  Payments are due at the end of each period. beginning (1):  Payments are due at the beginning of each period. Examples It is generally understood that the amount of the principal reduction on a loan is higher in the later years, as compared to the early years. This example demonstrates just how much higher the later years can be. Assume a mortgage loan with an initial loan amount of $550,000, an interest rate of 6%, and a 30-year term. The CUMPRINC function can be used to determine the interest for any period. In the following table, CUMPRINC has been used to determine the principal repaid in the first year (payments 1 through 12) and in the last year (payments 349 through 360) of the loan term. The function evaluates to $6,754.06 and $38,313.75, respectively. The amount of principal paid in the first year is only about 18% of the amount of principal paid in the last year. periodic-rate num-periods present-value starting-per ending-per when-due =CUMPRINC (B2, C2, D2, E2, F2, G2) =0.06/12 360 =550000 1 12 0 =CUMPRINC (B2, C2, D2, E3, F3, G2) 349 360 Related Topics For related functions and additional information, see: “CUMIPMT” on page 110 “IPMT” on page 123 “PMT” on page 134 “PPMT” on page 135 “Example of a Loan Amortization Table” on page 353 “Common Arguments Used in Financial Functions” on page 341 “Listing of Financial Functions” on page 96 “Value Types” on page 36 “The Elements of Formulas” on page 15 “Using the Keyboard and Mouse to Create and Edit Formulas” on page 26 “Pasting from Examples in Help” on page 41 DB The DB function returns the amount of depreciation of an asset for a specified period using the fixed-declining balance method. DB(cost, salvage, life, depr-period, first-year-months)  cost:  The initial cost of the asset. cost is a number value and must be greater than or equal to 0.  salvage:  The salvage value of the asset. salvage is a number value and must be greater than or equal to 0.  life:  The number of periods over which the asset is depreciating. life is a number value and must be greater than 0. A decimal (fractional) part of life is allowed (for example, 5.5 for a five and one-half year depreciable life).  depr-period:  The period for which you want to calculate depreciation. depr-period is a number value and must be greater than 0. Any decimal (fractional) part of deprperiod is ignored.  first-year-months: An optional argument specifying the number of months of depreciation in the first year. first-year-months is a number value and must be in the range 1 to 12. Any decimal (fractional) part of first-year-months is ignored. Example 1 Constructing a Depreciation Schedule Assume you have just purchased an asset with a cost of $1,000, a salvage value of $100, and an expected useful life of 4 years. Assume the asset will be depreciated 12 months in the first year. Using the DB function, you can construct a depreciation table showing the depreciation for each year. cost salvage life depr-period first-year-months 1000 100 4 12 First year (returns $438) =DB(B2, C2, D2, E3, F2) 1 Second year (returns $246.16) =DB(B2, C2, D2, E4, F2) 2 Third year (returns $138.74) =DB(B2, C2, D2, E5, F2) 3 Fourth year (returns $77.75) =DB(B2, C2, D2, E6, F2) 4 114 Chapter 6 Financial Functions Chapter 6 Financial Functions 115 Example 2 Depreciation for Partial First Year Assume the same facts as Example 1, except that the asset will be depreciated for less than 12 months in the first year. cost salvage life depr-period first-year-months 1000 100 4 1 Depreciate 9 months (returns $328.50) =DB(B2, C2, D2, E2, F3) 9 Depreciate 6 months (returns $219) =DB(B2, C2, D2, E2, F4) 3 Depreciate 3 months (returns $109.50) =DB(B2, C2, D2, E2, F5) 6 Depreciate 1 month (returns $36.50) =DB(B2, C2, D2, E2, F6) 1 Related Topics For related functions and additional information, see: “DDB” on page 116 “SLN” on page 147 “SYD” on page 148 “VDB” on page 149 “Common Arguments Used in Financial Functions” on page 341 “Listing of Financial Functions” on page 96 “Value Types” on page 36 “The Elements of Formulas” on page 15 “Using the Keyboard and Mouse to Create and Edit Formulas” on page 26 “Pasting from Examples in Help” on page 41 DDB The DDB function returns the amount of depreciation of an asset based on a specified depreciation rate. DDB(cost, salvage, life, depr-period, depr-factor)  cost:  The initial cost of the asset. cost is a number value and must be greater than or equal to 0.  salvage:  The salvage value of the asset. salvage is a number value and must be greater than or equal to 0.  life:  The number of periods over which the asset is depreciating. life is a number value and must be greater than 0. A decimal (fractional) part of life is allowed (for example, 5.5 for a five and one-half year depreciable life).  depr-period:  The period for which you want to calculate depreciation. depr-period is a number value and must be greater than 0. Any decimal (fractional) part of deprperiod is ignored.  depr-factor:  An optional number that determines the depreciation rate. depr-factor is a number value. If omitted, 2 (200% for double-declining) is assumed. The higher the number, the more rapid the depreciation. For example, if a depreciation rate of one and one-half times the straight line depreciation is desired, use 1.5 or 150%. Examples Assume you have just purchased an asset with a cost of $1,000, a salvage value of $100, and an expected useful life of 4 years. Using the DDB function, you can determine the depreciation for different periods and different depreciation rates. cost salvage life depr-period depr-factor 1000 100 4 First year, doubledeclining balance (returns $500) =DDB(B2, C2, D2, E3, F3) 1 2 Second year, double-declining balance (returns $250) =DDB(B2, C2, D2, E4, F4) 2 2 Third year, doubledeclining balance (returns $125) =DDB(B2, C2, D2, E5, F5) 3 2 Fourth year, double-declining balance (returns $25) =DDB(B2, C2, D2, E6, F6) 4 2 116 Chapter 6 Financial Functions Chapter 6 Financial Functions 117 cost salvage life depr-period depr-factor First year, straightline (returns $250) =DDB(B2, C2, D2, E7, F7) 1 1 First year, tripledeclining balance (returns $750) =DDB(B2, C2, D2, E8, F8) 3 1 Related Topics For related functions and additional information, see: “DB” on page 114 “SLN” on page 147 “SYD” on page 148 “VDB” on page 149 “Common Arguments Used in Financial Functions” on page 341 “Listing of Financial Functions” on page 96 “Value Types” on page 36 “The Elements of Formulas” on page 15 “Using the Keyboard and Mouse to Create and Edit Formulas” on page 26 “Pasting from Examples in Help” on page 41 DISC The DISC function returns the annual discount rate of a security that pays no interest and is sold at a discount to its redemption value. DISC(settle, maturity, price, redemption, days-basis)  settle:  The trade settlement date. settle is a date/time value. The trade settlement date is usually one or more days after the trade date.  maturity:  The date when the security matures. maturity is a date/time value. It must be after settle.  price:  The cost of the security per $100 of par value. price is a number value.  redemption:  The redemption value per $100 of par value. redemption is a number value that must be greater than 0. redemption is the amount that will be received per $100 of face value. Often, it is 100, meaning that the security’s redemption value is equal to its face value.  days-basis:  An optional argument specifying the number of days per month and days per year used in the calculations. 30/360 (0 or omitted):  30 days in a month, 360 days in a year, using the NASD method for dates falling on the 31st of a month. actual/actual (1):  Actual days in each month, actual days in each year. actual/360 (2):  Actual days in each month, 360 days in a year. actual/365 (3):  Actual days in each month, 365 days in a year. 30E/360 (4):  30 days in a month, 360 days in a year, using the European method for dates falling on the 31st of a month (European 30/360). Example In this example, the DISC function is used to determine the annual discount rate of the hypothetical security described by the values listed. The function evaluates to 5.25%, the annual discount rate. settle maturity price redemption days-basis =DISC(B2, C2, D2, E2, F2) 05/01/2009 06/30/2015 67.64 100 0 Related Topics For related functions and additional information, see: “PRICEDISC” on page 138 “YIELDDISC” on page 152 “Common Arguments Used in Financial Functions” on page 341 “Listing of Financial Functions” on page 96 “Value Types” on page 36 “The Elements of Formulas” on page 15 “Using the Keyboard and Mouse to Create and Edit Formulas” on page 26 “Pasting from Examples in Help” on page 41 118 Chapter 6 Financial Functions Chapter 6 Financial Functions 119 EFFECT The EFFECT function returns the effective annual interest rate from the nominal annual interest rate based on the number of compounding periods per year. EFFECT(nominal-rate, num-periods-year)  nominal-rate:  The nominal rate of interest of a security. nominal-rate is a number value and is either entered as a decimal (for example, 0.08) or with a percent sign (for example, 8%).  num-periods-year:  The number of compounding periods per year. num-periodsyear is a number value and must be greater than 0. Examples =EFFECT(0.05, 365) returns approximately 5.13%, the effective annual interest rate if 5% is compounded daily. =EFFECT(0.05, 12) returns approximately 5.12%, the effective annual interest rate if 5% is compounded monthly. =EFFECT(0.05, 4) returns approximately 5.09%, the effective annual interest rate if 5% is compounded quarterly. =EFFECT(0.05, 2) returns approximately 5.06%, the effective annual interest rate if 5% is compounded semiannually. =EFFECT(0.05, 1) returns approximately 5.00%, the effective annual interest rate if 5% is compounded annually. Related Topics For related functions and additional information, see: “NOMINAL” on page 129 “Common Arguments Used in Financial Functions” on page 341 “Listing of Financial Functions” on page 96 “Value Types” on page 36 “The Elements of Formulas” on page 15 “Using the Keyboard and Mouse to Create and Edit Formulas” on page 26 “Pasting from Examples in Help” on page 41 FV The FV function returns the future value of an investment based on a series of regular periodic cash flows (payments of a constant amount and all cash flows at constant intervals) and a fixed interest rate. FV(periodic-rate, num-periods, payment, present-value, when-due)  periodic-rate:  The interest rate per period. periodic-rate is a number value and is either entered as a decimal (for example, 0.08) or with a percent sign (for example, 8%).  num-periods:  The number of periods. num-periods is a number value and must be greater than or equal to 0.  payment:  The payment made or amount received each period. payment is a number value. At each period, an amount received is a positive amount and an amount invested is a negative amount. For example, it could be a monthly loan payment (negative) or the periodic payment received on an annuity (positive).  present-value:  An optional argument that specifies the value of the initial investment, or the amount of the loan or annuity. present-value is a number value. At time 0, an amount received is a positive amount and an amount invested is a negative amount. For example, it could be an amount borrowed (positive) or the initial payment made on an annuity contract (negative).  when-due:  An optional argument that specifies whether payments are due at the beginning or end of each period. Most mortgage and other loans require the first payment at the end of the first period (0), which is the default. Most lease and rent payments, and some other types of payments, are due at the beginning of each period (1). end (0 or omitted):  Payments are due at the end of each period. beginning (1):  Payments are due at the beginning of each period. Usage Notes  If payment is specified and there is no initial investment, present-value may be omitted. Example 1 Assume you are planning for your daughter’s college education. She has just turned 3 and you expect she will begin college in 15 years. You have $50,000 to set aside in a savings account today and can add $200 to the account at the end of each month. Over the next 15 years, the savings account is expected to earn an annual interest rate of 4.5%, and pays interest monthly. Using the FV function, you can determine the expected value of this savings account at the time your daughter begins college. Based on the assumptions given, it would be $149,553.00. periodic-rate num-periods payment present-value when-due =FV(B2, C2, D2, E2, F2) =0.045/12 =15*12 -200 -50000 1 120 Chapter 6 Financial Functions Chapter 6 Financial Functions 121 Example 2 Assume you are presented with an investment opportunity. The opportunity requires that you invest $50,000 in a discount security today and then nothing further. The discount security matures in 14 years and has a redemption value of $100,000. Your alternative is to leave your money in your money market savings account where it is expected to earn an annual yield of 5.25%. One way to evaluate this opportunity would be to consider how much the $50,000 would be worth at the end of the investment period and compare that to the redemption value of the security. Using the FV function, you can determine the expected future value of the money market account. Based on the assumptions given, it would be $102,348.03. Therefore, if all assumptions happen as expected, it would be better to keep the money in the money market account since its value after 14 years ($102,348.03) exceeds the redemption value of the security ($100,000). periodic-rate num-periods payment present-value when-due =FV(B2, C2, D2, E2, F2) 0.0525 14 0 -50000 1 Related Topics For related functions and additional information, see: “NPER” on page 130 “NPV” on page 132 “PMT” on page 134 “PV” on page 141 “RATE” on page 144 “Choosing Which Time Value of Money Function to Use” on page 348 “Common Arguments Used in Financial Functions” on page 341 “Listing of Financial Functions” on page 96 “Value Types” on page 36 “The Elements of Formulas” on page 15 “Using the Keyboard and Mouse to Create and Edit Formulas” on page 26 “Pasting from Examples in Help” on page 41 INTRATE The INTRATE function returns the effective annual interest rate for a security that pays interest only at maturity. INTRATE(settle, maturity, invest-amount, redemption, days-basis)  settle:  The trade settlement date. settle is a date/time value. The trade settlement date is usually one or more days after the trade date.  maturity:  The date when the security matures. maturity is a date/time value. It must be after settle.  invest-amount:  The amount invested in the security. invest-amount is a number value and must be greater than or equal to 0.  redemption:  The redemption value per $100 of par value. redemption is a number value that must be greater than 0. redemption is the amount that will be received per $100 of face value. Often, it is 100, meaning that the security’s redemption value is equal to its face value.  days-basis:  An optional argument specifying the number of days per month and days per year used in the calculations. 30/360 (0 or omitted):  30 days in a month, 360 days in a year, using the NASD method for dates falling on the 31st of a month. actual/actual (1):  Actual days in each month, actual days in each year. actual/360 (2):  Actual days in each month, 360 days in a year. actual/365 (3):  Actual days in each month, 365 days in a year. 30E/360 (4):  30 days in a month, 360 days in a year, using the European method for dates falling on the 31st of a month (European 30/360). Example In this example, the INTRATE function is used to determine the effective annual interest rate of the hypothetical security described by the values listed. The security pays interest only at maturity. The function evaluates to approximately 10.85%. settle maturity invest-amount par days-basis =INTRATE(B2, C2, D2, E2, F2) 05/01/2009 06/30/2015 990.02 1651.83 0 122 Chapter 6 Financial Functions Chapter 6 Financial Functions 123 Related Topics For related functions and additional information, see: “RECEIVED” on page 146 “Common Arguments Used in Financial Functions” on page 341 “Listing of Financial Functions” on page 96 “Value Types” on page 36 “The Elements of Formulas” on page 15 “Using the Keyboard and Mouse to Create and Edit Formulas” on page 26 “Pasting from Examples in Help” on page 41 IPMT The IPMT function returns the interest portion of a specified loan or annuity payment based on fixed, periodic payments and a fixed interest rate. IPMT(periodic-rate, period, num-periods, present-value, future-value, when-due)  periodic-rate:  The interest rate per period. periodic-rate is a number value and is either entered as a decimal (for example, 0.08) or with a percent sign (for example, 8%).  period:  The payment period for which you want to calculate the amount of principal or interest. period is a number and must be greater than 0.  num-periods:  The number of periods. num-periods is a number value and must be greater than or equal to 0.  present-value:  The value of the initial investment, or the amount of the loan or annuity. present-value is a number value. At time 0, an amount received is a positive amount and an amount invested is a negative amount. For example, it could be an amount borrowed (positive) or the initial payment made on an annuity contract (negative).  future-value:  An optional argument that represents the value of the investment or remaining cash value of the annuity (positive amount), or the remaining loan balance (negative amount), after the final payment. future-value is a number value. At the end of the investment period, an amount received is a positive amount and an amount invested is a negative amount. For example, It could be the balloon payment due on a loan (negative) or the remaining value of an annuity contract (positive). If omitted, it is assumed to be 0.  when-due:  An optional argument that specifies whether payments are due at the beginning or end of each period. Most mortgage and other loans require the first payment at the end of the first period (0), which is the default. Most lease and rent payments, and some other types of payments, are due at the beginning of each period (1). end (0 or omitted):  Payments are due at the end of each period. beginning (1):  Payments are due at the beginning of each period. Example In this example, IPMT is used to determine the interest portion of the first payment of the third year of the loan term (payment 25) given the loan facts presented. The function evaluates to approximately –$922.41 representing the interest portion of loan payment 25. periodic-rate period num-periods present-value future-value when-due =IPMT(B2, C2, D2, E2, F2, G2) =0.06/12 25 =10*12 200000 -100000 0 Related Topics For related functions and additional information, see: “CUMIPMT” on page 110 “CUMPRINC” on page 112 “PMT” on page 134 “PPMT” on page 135 “Example of a Loan Amortization Table” on page 353 “Choosing Which Time Value of Money Function to Use” on page 348 “Common Arguments Used in Financial Functions” on page 341 “Listing of Financial Functions” on page 96 “Value Types” on page 36 “The Elements of Formulas” on page 15 “Using the Keyboard and Mouse to Create and Edit Formulas” on page 26 “Pasting from Examples in Help” on page 41 124 Chapter 6 Financial Functions Chapter 6 Financial Functions 125 IRR The IRR function returns the internal rate of return for an investment that is based on a series of potentially irregular cash flows (payments that do not need to be a constant amount) that occur at regular time intervals. IRR(flows-range, estimate)  flows-range: A collection that contains the cash flow values. flows-range is a collection containing number values. Income (a cash inflow) is specified as a positive number, and an expenditure (a cash outflow) is specified as a negative number. There must be at least one positive and one negative value included within the collection. Cash flows must be specified in chronological order and equally spaced in time (for example, each month). If a period does not have a cash flow, use 0 for that period.  estimate:  An optional argument specifying the initial estimate for the rate of return. estimate is a number value and is either entered as a decimal (for example, 0.08) or with a percent sign (for example, 8%). If omitted, 10% is assumed. If the default value does not result in a solution, initially try a larger positive value. If this does not result in an outcome, try a small negative value. The minimum value allowed is –1. Usage Notes  If the periodic cash flows are the same, consider using the NPV function. Example 1 Assume you are planning for your daughter’s college education. She has just turned 13 and you expect she will begin college in 5 years. You have $75,000 to set aside in a savings account today and will add the bonus you receive from your employer at the end of each year. Since you expect your bonus to increase each year, you expect to be able to set aside $5,000, $7,000, $8,000, $9,000, and $10,000, respectively, at the end of each of the next 5 years. You think you will need to have $150,000 set aside for her education by the time your daughter reaches college. Using the IRR function, you can determine the rate you would need to receive on invested amounts in order to have $150,000. Based on the assumptions given, the rate would be 5.70%. Initial Deposit Year 1 Year 2 Year 3 Year 4 Year 5 Amount Required =IRR(B2:H2) -75000 -5000 -7000 -8000 -9000 -10000 150000 Example 2 Assume you are presented with the opportunity to invest in a partnership. The initial investment required is $50,000. Because the partnership is still developing its product, an additional $25,000 and $10,000 must be invested at the end of the first and second years, respectively. In the third year the partnership expects to be self-funding but not return any cash to investors. In the fourth and fifth years, investors are projected to receive $10,000 and $30,000, respectively. At the end of the sixth year, the company expects to sell and investors are projected to receive $100,000. Using the IRR function, you can determine the expected rate of return on this investment. Based on the assumptions given, the rate would be 10.24%. Initial Deposit Year 1 Year 2 Year 3 Year 4 Year 5 Sales proceeds =IRR(B2:H2) -50000 -25000 -10000 0 10000 30000 100000 Related Topics For related functions and additional information, see: “MIRR” on page 128 “NPV” on page 132 “Choosing Which Time Value of Money Function to Use” on page 348 “Common Arguments Used in Financial Functions” on page 341 “Listing of Financial Functions” on page 96 “Value Types” on page 36 “The Elements of Formulas” on page 15 “Using the Keyboard and Mouse to Create and Edit Formulas” on page 26 “Pasting from Examples in Help” on page 41 ISPMT The ISPMT function returns the interest portion of a specified loan or annuity payment based on fixed, periodic payments and a fixed interest rate. This function is provided for compatibility with tables imported from other spreadsheet applications. 126 Chapter 6 Financial Functions Chapter 6 Financial Functions 127 ISPMT(annual-rate, period, num-periods, present-value)  annual-rate:  The annual coupon rate or stated annual interest rate of the security. annual-rate is a number value and is either entered as a decimal (for example, 0.08) or with a percent sign (for example, 8%).  period:  The payment period for which you want to calculate the amount of principal or interest. period is a number and must be greater than 0.  num-periods:  The number of periods. num-periods is a number value and must be greater than or equal to 0.  present-value:  The value of the initial investment, or the amount of the loan or annuity. present-value is a number value. At time 0, an amount received is a positive amount and an amount invested is a negative amount. For example, it could be an amount borrowed (positive) or the initial payment made on an annuity contract (negative). Usage Notes  The IPMT function has additional functionality and should be used instead of ISPMT. Example In this example, ISPMT is used to determine the interest portion of the first payment of the third year of the loan term (payment 25) given the loan facts presented. The function evaluates to approximately –$791.67, which represents the interest portion of loan payment 25. periodic-rate period num-periods present-value =ISPMT(B2, C2, D2, E2) =0.06/12 25 =10*12 200000 Related Topics For related functions and additional information, see: “IPMT” on page 123 “Common Arguments Used in Financial Functions” on page 341 “Listing of Financial Functions” on page 96 “Value Types” on page 36 “The Elements of Formulas” on page 15 “Using the Keyboard and Mouse to Create and Edit Formulas” on page 26 “Pasting from Examples in Help” on page 41 MIRR The MIRR function returns the modified internal rate of return for an investment that is based on a series of potentially irregular cash flows (payments that do not need to be a constant amount) that occur at regular time intervals. The rate earned on positive cash flows and the rate paid to finance negative cash flows can differ. MIRR(flows-range, finance-rate, reinvest-rate)  flows-range: A collection that contains the cash flow values. flows-range is a collection containing number values. Income (a cash inflow) is specified as a positive number, and an expenditure (a cash outflow) is specified as a negative number. There must be at least one positive and one negative value included within the collection. Cash flows must be specified in chronological order and equally spaced in time (for example, each month). If a period does not have a cash flow, use 0 for that period.  finance-rate: Interest rate paid on negative cash flows (outflows). finance-rate is a number value and is either entered as a decimal (for example, 0.08) or with a percent sign (for example, 8%) and represents the rate at which the amounts invested (negative cash flows) can be financed. For example, a company’s cost of capital might be used.  reinvest-rate:  Rate at which positive cash flows (inflows) can be reinvested. reinvestrate is a number value and is either entered as a decimal (for example, 0.08) or with a percent sign (for example, 8%) and represents the rate at which the amounts received (positive cash flows) can be reinvested. For example, a company’s shortterm investment rate might be used. Usage Notes  Cash flows must be equally spaced in time. If there is no cash flow in a particular time period, use 0. Example 1 Assume you are presented with the opportunity to invest in a partnership. The initial investment required is $50,000. Because the partnership is still developing its product, an additional $25,000 and $10,000 must be invested at the end of the first and second years, respectively. In the third year the partnership expects to be self-funding but not return any cash to investors. In the fourth and fifth years, investors are projected to receive $10,000 and $30,000, respectively. At the end of the sixth year, the company expects to sell and investors are projected to receive $100,000. Assume that you can currently borrow money at 9.00% (finance-rate) and can earn 4.25% on short-term savings (reinvest-rate). Using the IRR function, you can determine the expected rate of return on this investment. Based on the assumptions given, the rate would be approximately 9.75%. 128 Chapter 6 Financial Functions Chapter 6 Financial Functions 129 Initial Deposit Year 1 Year 2 Year 3 Year 4 Year 5 Sales proceeds =MIRR (B2:H2, 0.09, 0.0425) -50000 -25000 -10000 0 10000 30000 100000 Example 2 Assume the same information as in Example 1, but rather than placing the cash flows in individual cells, you specify the cash flows as an array constant. The MIRR function would then be as follows: =MIRR({-50000, -25000, -10000, 0, 10000, 30000, 100000}, 0.09, 0.0425) returns approximately 9.75%. Related Topics For related functions and additional information, see: “IRR” on page 125 “NPV” on page 132 “PV” on page 141 “Choosing Which Time Value of Money Function to Use” on page 348 “Common Arguments Used in Financial Functions” on page 341 “Listing of Financial Functions” on page 96 “Value Types” on page 36 “The Elements of Formulas” on page 15 “Using the Keyboard and Mouse to Create and Edit Formulas” on page 26 “Pasting from Examples in Help” on page 41 NOMINAL The NOMINAL function returns the nominal annual interest rate from the effective annual interest rate based on the number of compounding periods per year. NOMINAL(effective-int-rate, num-periods-year)  effective-int-rate: The effective interest rate of a security. effective-int-rate is a number value and is either entered as a decimal (for example, 0.08) or with a percent sign (for example, 8%).  num-periods-year:  The number of compounding periods per year. num-periodsyear is a number value and must be greater than 0. Examples =NOMINAL(0.0513, 365) returns approximately 5.00%, the nominal annual interest rate if the effective rate of 5.13% was based on daily compounding. =NOMINAL(0.0512, 12) returns approximately 5.00%, the nominal annual interest rate if the effective rate of 5.12% was based on monthly compounding. =NOMINAL(0.0509, 4) returns approximately 5.00%, the nominal annual interest rate if the effective rate of 5.09% was based on quarterly compounding. =NOMINAL(0.0506, 2) returns approximately 5.00%, the nominal annual interest rate if the effective rate of 5.06% was based on semiannual compounding. =NOMINAL(0.0500, 1) returns approximately 5.00%, the nominal annual interest rate if the effective rate of 5.00% was based on annual compounding. Related Topics For related functions and additional information, see: “EFFECT” on page 119 “Common Arguments Used in Financial Functions” on page 341 “Listing of Financial Functions” on page 96 “Value Types” on page 36 “The Elements of Formulas” on page 15 “Using the Keyboard and Mouse to Create and Edit Formulas” on page 26 “Pasting from Examples in Help” on page 41 NPER The NPER function returns the number of payment periods for a loan or annuity based on a series of regular periodic cash flows (payments of a constant amount and all cash flows at constant intervals) and a fixed interest rate. NPER(periodic-rate, payment, present-value, future-value, when-due)  periodic-rate:  The interest rate per period. periodic-rate is a number value and is either entered as a decimal (for example, 0.08) or with a percent sign (for example, 8%).  payment:  The payment made or amount received each period. payment is a number value. At each period, an amount received is a positive amount and an amount invested is a negative amount. For example, it could be a monthly loan payment (negative) or the periodic payment received on an annuity (positive). 130 Chapter 6 Financial Functions Chapter 6 Financial Functions 131  present value:  The value of the initial investment, or the amount of the loan or annuity, specified as a negative number. present-value is a number value. At time 0, an amount received is a positive amount and an amount invested is a negative amount. For example, It could be an amount borrowed (positive) or the initial payment made on an annuity contract (negative).  future-value:  An optional argument specifying the value of the investment or remaining cash value of the annuity (positive amount), or the remaining loan balance (negative amount), after the final payment. future-value is a number value. At the end of the investment period, an amount received is a positive amount and an amount invested is a negative amount. For example, It could be the balloon payment due on a loan (negative) or the remaining value of an annuity contract (positive).  when-due:  An optional argument that specifies whether payments are due at the beginning or end of each period. Most mortgage and other loans require the first payment at the end of the first period (0), which is the default. Most lease and rent payments, and some other types of payments, are due at the beginning of each period (1). end (0 or omitted):  Payments are due at the end of each period. beginning (1):  Payments are due at the beginning of each period. Example 1 Assume you are planning for your daughter’s college education. You have $50,000 to set aside in a savings account today and can add $200 to the account at the end of each month. The savings account is expected to earn an annual interest rate of 4.5%, and pays interest monthly. You believe you will need to have set aside $150,000 by the time your daughter reaches college. Using the NPER function, you can determine the number of periods you would need to make the $200 payment. Based on the assumptions given, it would be approximately 181 periods or 15 years, 1 month. periodic-rate payment present-value future-value when-due =NPER(B2, C2, D2, E2, F2) =0.045/12 -200 -50000 150000 1 Example 2 Assume you are planning to purchase your uncle’s mountain cabin. You have $30,000 to use as a down payment today and can afford to make a monthly payment of $1,500. Your uncle says he is willing to lend you the difference between the cabin’s sale price of $200,000 and your down payment (so you would borrow $170,000) at an annual rate of 7%. Using the NPER function, you can determine the number of months it would take you to repay your uncle’s loan. Based on the assumptions given, it would be approximately 184 months or 15 years, 4 months. periodic-rate payment present-value future-value when-due =NPER(B2, C2, D2, E2, F2) =0.07/12 -1500 170000 0 1 Related Topics For related functions and additional information, see: “FV” on page 120 “PMT” on page 134 “PV” on page 141 “RATE” on page 144 “Choosing Which Time Value of Money Function to Use” on page 348 “Common Arguments Used in Financial Functions” on page 341 “Listing of Financial Functions” on page 96 “Value Types” on page 36 “The Elements of Formulas” on page 15 “Using the Keyboard and Mouse to Create and Edit Formulas” on page 26 “Pasting from Examples in Help” on page 41 NPV The NPV function returns the net present value of an investment based on a series of potentially irregular cash flows that occur at regular time intervals. NPV(periodic-discount-rate, cash-flow, cash-flow…)  periodic-discount-rate:  The discount rate per period. periodic-discount-rate is a number value and is either entered as a decimal (for example, 0.08) or with a percent sign (for example, 8%). periodic-discount-rate must be greater than or equal to 0.  cash-flow: A cash flow. cash-flow is a number value. A positive value represents income (cash inflow). A negative value represents an expenditure (cash outflow). Cash flows must be equally spaced in time.  cash-flow…: Optionally include one or more additional cash flows. 132 Chapter 6 Financial Functions Chapter 6 Financial Functions 133 Usage Notes  periodic-discount-rate is specified using the same time frame as the time frame used for the cash flows. For example, if the cash flows are monthly and the desired annual discount rate is 8%, periodic-discount-rate must be specified as 0.00667 or 0.667% (0.08 divided by 12).  If cash flows are irregular, use the IRR function. Example Assume you are presented with the opportunity to invest in a partnership. Because the partnership is still developing its product, an additional $25,000 and $10,000 must be invested at the end of the first and second years, respectively. In the third year the partnership expects to be self-funding but not return any cash to investors. In the fourth and fifth years, investors are projected to receive $10,000 and $30,000, respectively. At the end of the sixth year, the company expects to sell and investors are projected to receive $100,000. In order to invest, you want to achieve an annual return of at least 10%. Using the NPV function, you can determine the maximum amount you are willing to initially invest. Based on the assumptions given, the NPV would be $50,913.43. Therefore if the required initial investment is this amount or less, this opportunity meets your 10% goal. periodic-rate Year 1 Year 2 Year 3 Year 4 Year 5 Sales proceeds =NPV(B2, C2:H2) 0.10 -25000 -10000 0 10000 30000 100000 Related Topics For related functions and additional information, see: “IRR” on page 125 “PV” on page 141 “Choosing Which Time Value of Money Function to Use” on page 348 “Common Arguments Used in Financial Functions” on page 341 “Listing of Financial Functions” on page 96 “Value Types” on page 36 “The Elements of Formulas” on page 15 “Using the Keyboard and Mouse to Create and Edit Formulas” on page 26 “Pasting from Examples in Help” on page 41 PMT The PMT function returns the fixed periodic payment for a loan or annuity based on a series of regular periodic cash flows (payments of a constant amount and all cash flows at constant intervals) and a fixed interest rate. PMT(periodic-rate, num-periods, present-value, future-value, when-due)  periodic-rate:  The interest rate per period. periodic-rate is a number value and is either entered as a decimal (for example, 0.08) or with a percent sign (for example, 8%).  num-periods:  The number of periods. num-periods is a number value and must be greater than or equal to 0.  present-value:  The value of the initial investment, or the amount of the loan or annuity. present-value is a number value. At time 0, an amount received is a positive amount and an amount invested is a negative amount. For example, it could be an amount borrowed (positive) or the initial payment made on an annuity contract (negative).  future-value:  An optional argument that represents the value of the investment or remaining cash value of the annuity (positive amount), or the remaining loan balance (negative amount), after the final payment. future-value is a number value. At the end of the investment period, an amount received is a positive amount and an amount invested is a negative amount. For example, It could be the balloon payment due on a loan (negative) or the remaining value of an annuity contract (positive). If omitted, it is assumed to be 0.  when-due:  An optional argument that specifies whether payments are due at the beginning or end of each period. Most mortgage and other loans require the first payment at the end of the first period (0), which is the default. Most lease and rent payments, and some other types of payments, are due at the beginning of each period (1). end (0 or omitted):  Payments are due at the end of each period. beginning (1):  Payments are due at the beginning of each period. Example In this example, PMT is used to determine the fixed payment given the loan facts presented. The function evaluates to –$1,610.21, which represents the fixed payment you would make (negative because it is a cash outflow) for this loan. periodic-rate num-periods present-value future-value when-due =PMT(B2, C2, D2, E2, F2) =0.06/12 =10*12 200000 -100000 0 134 Chapter 6 Financial Functions Chapter 6 Financial Functions 135 Related Topics For related functions and additional information, see: “FV” on page 120 “IPMT” on page 123 “NPER” on page 130 “PPMT” on page 135 “PV” on page 141 “RATE” on page 144 “Example of a Loan Amortization Table” on page 353 “Choosing Which Time Value of Money Function to Use” on page 348 “Common Arguments Used in Financial Functions” on page 341 “Listing of Financial Functions” on page 96 “Value Types” on page 36 “The Elements of Formulas” on page 15 “Using the Keyboard and Mouse to Create and Edit Formulas” on page 26 “Pasting from Examples in Help” on page 41 PPMT The PPMT function returns the principal portion of a specified loan or annuity payment based on fixed periodic payments and a fixed interest rate. PPMT(periodic-rate, period, num-periods, present-value, future-value, when-due)  periodic-rate:  The interest rate per period. periodic-rate is a number value and is either entered as a decimal (for example, 0.08) or with a percent sign (for example, 8%).  period:  The payment period for which you want to calculate the amount of principal or interest. period is a number and must be greater than 0.  num-periods:  The number of periods. num-periods is a number value and must be greater than or equal to 0.  present-value:  The value of the initial investment, or the amount of the loan or annuity. present-value is a number value. At time 0, an amount received is a positive amount and an amount invested is a negative amount. For example, it could be an amount borrowed (positive) or the initial payment made on an annuity contract (negative).  future-value:  An optional argument that represents the value of the investment or remaining cash value of the annuity (positive amount), or the remaining loan balance (negative amount), after the final payment. future-value is a number value. At the end of the investment period, an amount received is a positive amount and an amount invested is a negative amount. For example, It could be the balloon payment due on a loan (negative) or the remaining value of an annuity contract (positive). If omitted, it is assumed to be 0.  when-due:  An optional argument that specifies whether payments are due at the beginning or end of each period. Most mortgage and other loans require the first payment at the end of the first period (0), which is the default. Most lease and rent payments, and some other types of payments, are due at the beginning of each period (1). end (0 or omitted):  Payments are due at the end of each period. beginning (1):  Payments are due at the beginning of each period. Example In this example, PPMT is used to determine the principal portion of the first payment of the third year of the loan term (payment 25) given the loan facts presented. The function evaluates to approximately –$687.80, which represents the principal portion of payment 25. periodic-rate period num-periods present-value future-value when-due =PPMT(B2, C2, D2, E2, F2, G2) =0.06/12 25 =10*12 200000 -100000 0 Related Topics For related functions and additional information, see: “CUMIPMT” on page 110 “CUMPRINC” on page 112 “IPMT” on page 123 “PMT” on page 134 “Example of a Loan Amortization Table” on page 353 “Choosing Which Time Value of Money Function to Use” on page 348 “Common Arguments Used in Financial Functions” on page 341 136 Chapter 6 Financial Functions Chapter 6 Financial Functions 137 “Listing of Financial Functions” on page 96 “Value Types” on page 36 “The Elements of Formulas” on page 15 “Using the Keyboard and Mouse to Create and Edit Formulas” on page 26 “Pasting from Examples in Help” on page 41 PRICE The PRICE function returns the price of a security that pays periodic interest per $100 of redemption (par) value. PRICE(settle, maturity, annual-rate, annual-yield, redemption, frequency, days-basis)  settle:  The trade settlement date. settle is a date/time value. The trade settlement date is usually one or more days after the trade date.  maturity:  The date when the security matures. maturity is a date/time value. It must be after settle.  annual-rate:  The annual coupon rate or stated annual interest rate of the security. annual-rate is a number value and is either entered as a decimal (for example, 0.08) or with a percent sign (for example, 8%).  annual-yield:  The annual yield of the security. annual-yield is a number value and is either entered as a decimal (for example, 0.08) or with a percent sign (for example, 8%).  redemption:  The redemption value per $100 of par value. redemption is a number value that must be greater than 0. redemption is the amount that will be received per $100 of face value. Often, it is 100, meaning that the security’s redemption value is equal to its face value.  frequency:  The number of coupon payments each year. annual (1): One payment per year. semiannual (2): Two payments per year. quarterly (4): Four payments per year.  days-basis:  An optional argument specifying the number of days per month and days per year used in the calculations. 30/360 (0 or omitted):  30 days in a month, 360 days in a year, using the NASD method for dates falling on the 31st of a month. actual/actual (1):  Actual days in each month, actual days in each year. actual/360 (2):  Actual days in each month, 360 days in a year. actual/365 (3):  Actual days in each month, 365 days in a year. 30E/360 (4):  30 days in a month, 360 days in a year, using the European method for dates falling on the 31st of a month (European 30/360). Example In this example, the PRICE function is used to determine the purchase price when trading the hypothetical security described by the values listed. The security pays periodic interest. The function evaluates to $106.50, which represents the price per $100 of face value. settle maturity annual-rate annual-yield redemption frequency days-basis =PRICE (B2, C2, D2, E2, F2, G2, H2) 05/01/2009 06/30/2015 0.065 0.0525 100 2 0 Related Topics For related functions and additional information, see: “PRICEDISC” on page 138 “PRICEMAT” on page 140 “YIELD” on page 150 “Common Arguments Used in Financial Functions” on page 341 “Listing of Financial Functions” on page 96 “Value Types” on page 36 “The Elements of Formulas” on page 15 “Using the Keyboard and Mouse to Create and Edit Formulas” on page 26 “Pasting from Examples in Help” on page 41 PRICEDISC The PRICEDISC function returns the price of a security that is sold at a discount to redemption value and does not pay interest per $100 of redemption (par) value. PRICEDISC(settle, maturity, annual-yield, redemption, days-basis)  settle:  The trade settlement date. settle is a date/time value. The trade settlement date is usually one or more days after the trade date.  maturity:  The date when the security matures. maturity is a date/time value. It must be after settle.  annual-yield:  The annual yield of the security. annual-yield is a number value and is either entered as a decimal (for example, 0.08) or with a percent sign (for example, 8%). 138 Chapter 6 Financial Functions Chapter 6 Financial Functions 139  redemption:  The redemption value per $100 of par value. redemption is a number value that must be greater than 0. redemption is the amount that will be received per $100 of face value. Often, it is 100, meaning that the security’s redemption value is equal to its face value.  days-basis:  An optional argument specifying the number of days per month and days per year used in the calculations. 30/360 (0 or omitted):  30 days in a month, 360 days in a year, using the NASD method for dates falling on the 31st of a month. actual/actual (1):  Actual days in each month, actual days in each year. actual/360 (2):  Actual days in each month, 360 days in a year. actual/365 (3):  Actual days in each month, 365 days in a year. 30E/360 (4):  30 days in a month, 360 days in a year, using the European method for dates falling on the 31st of a month (European 30/360). Example In this example, the PRICEDISC function is used to determine the purchase price when trading the hypothetical security described by the values listed. The security does not pay interest and is sold at a discount. The function evaluates to approximately $65.98, which represents the price per $100 of face value. settle maturity discount redemption days-basis =PRICEDISC (B2, C2, D2, E2, F2) 05/01/2009 06/30/2015 0.0552 100 0 Related Topics For related functions and additional information, see: “PRICE” on page 137 “PRICEMAT” on page 140 “YIELDDISC” on page 152 “Common Arguments Used in Financial Functions” on page 341 “Listing of Financial Functions” on page 96 “Value Types” on page 36 “The Elements of Formulas” on page 15 “Using the Keyboard and Mouse to Create and Edit Formulas” on page 26 “Pasting from Examples in Help” on page 41 PRICEMAT The PRICEMAT function returns the price of a security that pays interest only at maturity per $100 of redemption (par) value. PRICEMAT(settle, maturity, issue, annual-rate, annual-yield, days-basis)  settle:  The trade settlement date. settle is a date/time value. The trade settlement date is usually one or more days after the trade date.  maturity:  The date when the security matures. maturity is a date/time value. It must be after settle.  issue:  The date the security was originally issued. issue is a date/time value and must be the earliest date given.  annual-rate:  The annual coupon rate or stated annual interest rate of the security. annual-rate is a number value and is either entered as a decimal (for example, 0.08) or with a percent sign (for example, 8%).  annual-yield:  The annual yield of the security. annual-yield is a number value and is either entered as a decimal (for example, 0.08) or with a percent sign (for example, 8%).  days-basis:  An optional argument specifying the number of days per month and days per year used in the calculations. 30/360 (0 or omitted):  30 days in a month, 360 days in a year, using the NASD method for dates falling on the 31st of a month. actual/actual (1):  Actual days in each month, actual days in each year. actual/360 (2):  Actual days in each month, 360 days in a year. actual/365 (3):  Actual days in each month, 365 days in a year. 30E/360 (4):  30 days in a month, 360 days in a year, using the European method for dates falling on the 31st of a month (European 30/360). Example In this example, the PRICEMAT function is used to determine the purchase price when trading the hypothetical security described by the values listed. The security pays interest only at maturity. The function evaluates to $99.002, which represents the price per $100 of face value. settle maturity issue annual-rate annual-yield days-basis =PRICEMAT (B2, C2, D2, E2, F2, G2) 05/01/2009 06/30/2015 12/14/2008 0.065 0.06565 0 140 Chapter 6 Financial Functions Chapter 6 Financial Functions 141 Related Topics For related functions and additional information, see: “PRICE” on page 137 “PRICEDISC” on page 138 “YIELDMAT” on page 153 “Common Arguments Used in Financial Functions” on page 341 “Listing of Financial Functions” on page 96 “Value Types” on page 36 “The Elements of Formulas” on page 15 “Using the Keyboard and Mouse to Create and Edit Formulas” on page 26 “Pasting from Examples in Help” on page 41 PV The PV function returns the present value of an investment or annuity based on a series of regular periodic cash flows (payments of a constant amount and all cash flows at constant intervals) and a fixed interest rate. PV(periodic-rate, num-periods, payment, future-value, when-due)  periodic-rate:  The interest rate per period. periodic-rate is a number value and is either entered as a decimal (for example, 0.08) or with a percent sign (for example, 8%).  num-periods:  The number of periods. num-periods is a number value and must be greater than or equal to 0.  payment:  The payment made or amount received each period. payment is a number value. At each period, an amount received is a positive amount and an amount invested is a negative amount. For example, it could be a monthly loan payment (negative) or the periodic payment received on an annuity (positive).  future-value:  An optional argument specifying the value of the investment or remaining cash value of the annuity (positive amount), or the remaining loan balance (negative amount), after the final payment. future-value is a number value. At the end of the investment period, an amount received is a positive amount and an amount invested is a negative amount. For example, It could be the balloon payment due on a loan (negative) or the remaining value of an annuity contract (positive).  when-due:  An optional argument that specifies whether payments are due at the beginning or end of each period. Most mortgage and other loans require the first payment at the end of the first period (0), which is the default. Most lease and rent payments, and some other types of payments, are due at the beginning of each period (1). end (0 or omitted):  Payments are due at the end of each period. beginning (1):  Payments are due at the beginning of each period. Usage Notes  periodic-rate is specified using the time frame of num-periods. For example, if numperiods represents months and the annual interest rate is 8%, periodic-rate must be specified as 0.00667 or 0.667% (0.08 divided by 12).  If payment is specified and there is no investment value, cash value, or loan balance remaining, future-value may be omitted.  If payment is omitted, you must include future-value. Example 1 Assume you are planning for your daughter’s college education. She has just turned 3 and you expect she will begin college in 15 years. You think you will need to have $150,000 set aside in a savings account by the time she reaches college. You can add $200 to the account at the end of each month. Over the next 15 years, the savings account is expected to earn an annual interest rate of 4.5%, and earns interest monthly. Using the PV function, you can determine the amount that must be deposited to this savings account today so that the value of the savings account will reach $150,000 by the time your daughter begins college. Based on the assumptions given, the function returns –$50,227.88 as the amount that would need to be deposited today (function returns a negative because the deposit to the savings account today is a cash outflow). periodic-rate num-periods payment future-value when-due =PV(B2, C2, D2, E2, F2) =0.045/12 =15*12 -200 150000 1 142 Chapter 6 Financial Functions Chapter 6 Financial Functions 143 Example 2 In this example, you are presented with an investment opportunity. The opportunity is to invest in a discount security today and then pay or receive nothing further until the security matures. The discount security matures in 14 years and has a redemption value of $100,000. Your alternative is to leave your money in your money market savings account where it is expected to earn an annual yield of 5.25%. Using the PV function, you can determine the maximum amount you should be willing to pay for this discount security today, assuming you want at least as good an interest rate as you expect to get on your money market account. Based on the assumptions given, it would be –$48,852.92 (the function returns a negative amount since this is a cash outflow). periodic-rate num-periods payment future-value when-due =PV(B2, C2, D2, E2, F2) 0.0525 14 0 100000 1 Related Topics For related functions and additional information, see: “FV” on page 120 “IRR” on page 125 “NPER” on page 130 “PMT” on page 134 “RATE” on page 144 “Choosing Which Time Value of Money Function to Use” on page 348 “Common Arguments Used in Financial Functions” on page 341 “Listing of Financial Functions” on page 96 “Value Types” on page 36 “The Elements of Formulas” on page 15 “Using the Keyboard and Mouse to Create and Edit Formulas” on page 26 “Pasting from Examples in Help” on page 41 RATE The RATE function returns the interest rate of an investment, loan, or annuity based on a series of regular periodic cash flows (payments of a constant amount and all cash flows at constant intervals) and a fixed interest rate. RATE(num-periods, payment, present-value, future-value, when-due, estimate)  num-periods:  The number of periods. num-periods is a number value and must be greater than or equal to 0.  payment:  The payment made or amount received each period. payment is a number value. At each period, an amount received is a positive amount and an amount invested is a negative amount. For example, it could be a monthly loan payment (negative) or the periodic payment received on an annuity (positive).  present-value:  The value of the initial investment, or the amount of the loan or annuity. present-value is a number value. At time 0, an amount received is a positive amount and an amount invested is a negative amount. For example, it could be an amount borrowed (positive) or the initial payment made on an annuity contract (negative).  future-value:  An optional argument that represents the value of the investment or remaining cash value of the annuity (positive amount), or the remaining loan balance (negative amount), after the final payment. future-value is a number value. At the end of the investment period, an amount received is a positive amount and an amount invested is a negative amount. For example, It could be the balloon payment due on a loan (negative) or the remaining value of an annuity contract (positive).  when-due:  An optional argument that specifies whether payments are due at the beginning or end of each period. Most mortgage and other loans require the first payment at the end of the first period (0), which is the default. Most lease and rent payments, and some other types of payments, are due at the beginning of each period (1). end (0 or omitted):  Payments are due at the end of each period. beginning (1):  Payments are due at the beginning of each period.  estimate:  An optional argument specifying the initial estimate for the rate of return. estimate is a number value and is either entered as a decimal (for example, 0.08) or with a percent sign (for example, 8%). If omitted, 10% is assumed. If the default value does not result in a solution, initially try a larger positive value. If this does not result in an outcome, try a small negative value. The minimum value allowed is –1. 144 Chapter 6 Financial Functions Chapter 6 Financial Functions 145 Example Assume you are planning for your daughter’s college education. She has just turned 3 and you expect she will begin college in 15 years. You think you will need to have $150,000 set aside in a savings account by the time she reaches college. You can set aside $50,000 today and add $200 to the account at the end of each month. Over the next 15 years, the savings account is expected to earn an annual interest rate of 4.5%, and earns interest monthly. Using the RATE function, you can determine the rate that must be earned on the savings account so that it will reach $150,000 by the time your daughter begins college. Based on the assumptions given, the rate returned by the function is approximately 0.377%, which is per month since num-periods was monthly, or 4.52% annually. num-periods payment present-value future-value when-due estimate =RATE(B2, C2, D2, E2, F2, G2) =15*12 -200 -50000 150000 1 =0.1/12 Related Topics For related functions and additional information, see: “FV” on page 120 “IRR” on page 125 “NPER” on page 130 “PMT” on page 134 “PV” on page 141 “Choosing Which Time Value of Money Function to Use” on page 348 “Common Arguments Used in Financial Functions” on page 341 “Listing of Financial Functions” on page 96 “Value Types” on page 36 “The Elements of Formulas” on page 15 “Using the Keyboard and Mouse to Create and Edit Formulas” on page 26 “Pasting from Examples in Help” on page 41 RECEIVED The RECEIVED function returns the maturity value for a security that pays interest only at maturity. RECEIVED(settle, maturity, invest-amount, annual-rate, days-basis)  settle:  The trade settlement date. settle is a date/time value. The trade settlement date is usually one or more days after the trade date.  maturity:  The date when the security matures. maturity is a date/time value. It must be after settle.  invest-amount:  The amount invested in the security. invest-amount is a number value and must be greater than or equal to 0.  annual-rate:  The annual coupon rate or stated annual interest rate of the security. annual-rate is a number value and is either entered as a decimal (for example, 0.08) or with a percent sign (for example, 8%).  days-basis:  An optional argument specifying the number of days per month and days per year used in the calculations. 30/360 (0 or omitted):  30 days in a month, 360 days in a year, using the NASD method for dates falling on the 31st of a month. actual/actual (1):  Actual days in each month, actual days in each year. actual/360 (2):  Actual days in each month, 360 days in a year. actual/365 (3):  Actual days in each month, 365 days in a year. 30E/360 (4):  30 days in a month, 360 days in a year, using the European method for dates falling on the 31st of a month (European 30/360). Example In this example, the RECEIVED function is used to determine the amount received at the maturity of the hypothetical security described by the values listed. The security pays interest only at maturity. The function evaluates to $1,651.83, the amount to be received at maturity including both principal and interest. settle maturity invest-amount annual-rate days-basis =RECEIVED (B2, C2, D2, E2, F2) 05/01/2009 06/30/2015 990.02 0.065 0 Related Topics For related functions and additional information, see: “INTRATE” on page 122 “Common Arguments Used in Financial Functions” on page 341 “Listing of Financial Functions” on page 96 146 Chapter 6 Financial Functions Chapter 6 Financial Functions 147 “Value Types” on page 36 “The Elements of Formulas” on page 15 “Using the Keyboard and Mouse to Create and Edit Formulas” on page 26 “Pasting from Examples in Help” on page 41 SLN The SLN function returns the depreciation of an asset for a single period using the straight-line method. SLN(cost, salvage, life)  cost:  The initial cost of the asset. cost is a number value and must be greater than or equal to 0.  salvage:  The salvage value of the asset. salvage is a number value and must be greater than or equal to 0.  life:  The number of periods over which the asset is depreciating. life is a number value and must be greater than 0. A decimal (fractional) part of life is allowed (for example, 5.5 for a five and one-half year depreciable life). Example =SLN(10000, 1000, 6) returns $1500, the depreciation per year, in dollars, of an asset that originally costs $10,000 and has an estimated salvage value of $1,000 after 6 years. Related Topics For related functions and additional information, see: “DB” on page 114 “DDB” on page 116 “SYD” on page 148 “VDB” on page 149 “Common Arguments Used in Financial Functions” on page 341 “Listing of Financial Functions” on page 96 “Value Types” on page 36 “The Elements of Formulas” on page 15 “Using the Keyboard and Mouse to Create and Edit Formulas” on page 26 “Pasting from Examples in Help” on page 41 SYD The SYD function returns the amount of depreciation of an asset for a specified period using the sum-of-the-years-digits method. SYD(cost, salvage, life, depr-period)  cost:  The initial cost of the asset. cost is a number value and must be greater than or equal to 0.  salvage:  The salvage value of the asset. salvage is a number value and must be greater than or equal to 0.  life:  The number of periods over which the asset is depreciating. life is a number value and must be greater than 0. A decimal (fractional) part of life is allowed (for example, 5.5 for a five and one-half year depreciable life).  depr-period:  The period for which you want to calculate depreciation. depr-period is a number value and must be greater than 0. Any decimal (fractional) part of deprperiod is ignored. Examples =SYD(10000, 1000, 9, 1) returns $1,800, the depreciation amount for the first year for an asset with an initial cost of $10,000 and a salvage value of $1,000 after a 9-year life. =SYD(10000, 1000, 9, 2) returns $1,600, the depreciation amount for the second year. =SYD(10000, 1000, 9, 8) returns $400, the depreciation amount for the eighth year. Related Topics For related functions and additional information, see: “DB” on page 114 “DDB” on page 116 “SLN” on page 147 “VDB” on page 149 “Common Arguments Used in Financial Functions” on page 341 “Listing of Financial Functions” on page 96 “Value Types” on page 36 “The Elements of Formulas” on page 15 “Using the Keyboard and Mouse to Create and Edit Formulas” on page 26 “Pasting from Examples in Help” on page 41 148 Chapter 6 Financial Functions Chapter 6 Financial Functions 149 VDB The VDB (variable declining balance) function returns the amount of depreciation of an asset over a chosen time interval, based on a specified depreciation rate. VDB(cost, salvage, life, starting-per, ending-per, depr-factor, no-switch)  cost:  The initial cost of the asset. cost is a number value and must be greater than or equal to 0.  salvage:  The salvage value of the asset. salvage is a number value and must be greater than or equal to 0.  life:  The number of periods over which the asset is depreciating. life is a number value and must be greater than 0. A decimal (fractional) part of life is allowed (for example, 5.5 for a five and one-half year depreciable life).  starting-per:  First period to include in the calculation. starting-per is a number value.  ending-per:  Last period to include in the calculation. ending-per is a number value and must be greater than 0 and greater than starting-per.  depr-factor:  An optional number that determines the depreciation rate. depr-factor is a number value. If omitted, 2 (200% for double-declining) is assumed. The higher the number, the more rapid the depreciation. For example, if a depreciation rate of one and one-half times the straight line depreciation is desired, use 1.5 or 150%.  no-switch:  An optional value indicating whether depreciation switches over to the straight-line method. switch (0, FALSE, or omitted):  Switch to the straight line method in the year that straight-line depreciation exceeds declining balance depreciation. no switch (1, TRUE):  Do not switch to the straight-line method. Usage Notes  starting-per should be specified as the period prior to the first period you wish to include in the calculation. If you wish to include the first period, use 0 for starting-per.  If you wish to determine depreciation that includes only the first period, ending-per should be 1. Examples Assume you have purchased an asset at a cost of $11,000.00, that it has a salvage value of $1,000.00, and that it has an estimated useful life of 5 years. You intend to depreciate the asset using the 1.5 (150%) declining balance method. =VDB(11000, 1000, 5, 0, 1, 1.5, 0) returns $3,300, the depreciation for the first year. =VDB(11000, 1000, 5, 4, 5, 1.5, 0) returns $1,386.50, the depreciation for the fifth (last) year, assuming straight-line depreciation is used when greater than the declining-balance depreciation. =VDB(11000, 1000, 5, 4, 5, 1.5, 1) returns $792.33, the depreciation for the fifth (last) year, assuming that declining-balance depreciation is used at all times (no-switch is TRUE). Related Topics For related functions and additional information, see: “DB” on page 114 “DDB” on page 116 “SLN” on page 147 “SYD” on page 148 “Common Arguments Used in Financial Functions” on page 341 “Listing of Financial Functions” on page 96 “Value Types” on page 36 “The Elements of Formulas” on page 15 “Using the Keyboard and Mouse to Create and Edit Formulas” on page 26 “Pasting from Examples in Help” on page 41 YIELD The YIELD function returns the effective annual interest rate for a security that pays regular periodic interest. YIELD(settle, maturity, annual-rate, price, redemption, frequency, days-basis)  settle:  The trade settlement date. settle is a date/time value. The trade settlement date is usually one or more days after the trade date.  maturity:  The date when the security matures. maturity is a date/time value. It must be after settle.  annual-rate:  The annual coupon rate or stated annual interest rate of the security. annual-rate is a number value and is either entered as a decimal (for example, 0.08) or with a percent sign (for example, 8%).  price:  The cost of the security per $100 of par value. price is a number value.  redemption:  The redemption value per $100 of par value. redemption is a number value that must be greater than 0. redemption is the amount that will be received per $100 of face value. Often, it is 100, meaning that the security’s redemption value is equal to its face value.  frequency:  The number of coupon payments each year. annual (1): One payment per year. semiannual (2): Two payments per year. quarterly (4): Four payments per year. 150 Chapter 6 Financial Functions Chapter 6 Financial Functions 151  days-basis:  An optional argument specifying the number of days per month and days per year used in the calculations. 30/360 (0 or omitted):  30 days in a month, 360 days in a year, using the NASD method for dates falling on the 31st of a month. actual/actual (1):  Actual days in each month, actual days in each year. actual/360 (2):  Actual days in each month, 360 days in a year. actual/365 (3):  Actual days in each month, 365 days in a year. 30E/360 (4):  30 days in a month, 360 days in a year, using the European method for dates falling on the 31st of a month (European 30/360). Example In this example, the YIELD function is used to determine the annual yield of the hypothetical security described by the values listed. The security pays periodic interest. The function evaluates to approximately 5.25%. settle maturity annual-rate price redemption frequency days-basis =YIELD (B2, C2, D2, E2, F2, G2, H2) 05/01/2009 06/30/2015 0.065 106.50 100 2 0 Related Topics For related functions and additional information, see: “PRICE” on page 137 “YIELDDISC” on page 152 “YIELDMAT” on page 153 “Common Arguments Used in Financial Functions” on page 341 “Listing of Financial Functions” on page 96 “Value Types” on page 36 “The Elements of Formulas” on page 15 “Using the Keyboard and Mouse to Create and Edit Formulas” on page 26 “Pasting from Examples in Help” on page 41 YIELDDISC The YIELDDISC function returns the effective annual interest rate for a security that is sold at a discount to redemption value and pays no interest. YIELDDISC(settle, maturity, price, redemption, days-basis)  settle:  The trade settlement date. settle is a date/time value. The trade settlement date is usually one or more days after the trade date.  maturity:  The date when the security matures. maturity is a date/time value. It must be after settle.  price:  The cost of the security per $100 of par value. price is a number value.  redemption:  The redemption value per $100 of par value. redemption is a number value that must be greater than 0. redemption is the amount that will be received per $100 of face value. Often, it is 100, meaning that the security’s redemption value is equal to its face value.  days-basis:  An optional argument specifying the number of days per month and days per year used in the calculations. 30/360 (0 or omitted):  30 days in a month, 360 days in a year, using the NASD method for dates falling on the 31st of a month. actual/actual (1):  Actual days in each month, actual days in each year. actual/360 (2):  Actual days in each month, 360 days in a year. actual/365 (3):  Actual days in each month, 365 days in a year. 30E/360 (4):  30 days in a month, 360 days in a year, using the European method for dates falling on the 31st of a month (European 30/360). Example In this example, the YIELDDISC function is used to determine the effective annual yield of the hypothetical security described by the values listed. The security does not pay interest and is sold at a discount. The function evaluates to approximately 8.37%, which represents the annual yield at a price of approximately $65.98 per $100 of face value. settle maturity price redemption days-basis =YIELDDISC (B2, C2, D2, E2, F2) 05/01/2009 06/30/2015 65.98 100 0 152 Chapter 6 Financial Functions Chapter 6 Financial Functions 153 Related Topics For related functions and additional information, see: “PRICEDISC” on page 138 “YIELD” on page 150 “YIELDMAT” on page 153 “Common Arguments Used in Financial Functions” on page 341 “Listing of Financial Functions” on page 96 “Value Types” on page 36 “The Elements of Formulas” on page 15 “Using the Keyboard and Mouse to Create and Edit Formulas” on page 26 “Pasting from Examples in Help” on page 41 YIELDMAT The YIELDMAT function returns the effective annual interest rate for a security that only pays interest at maturity. YIELDMAT(settle, maturity, issue, annual-rate, price, days-basis)  settle:  The trade settlement date. settle is a date/time value. The trade settlement date is usually one or more days after the trade date.  maturity:  The date when the security matures. maturity is a date/time value. It must be after settle.  issue:  The date the security was originally issued. issue is a date/time value and must be the earliest date given.  annual-rate:  The annual coupon rate or stated annual interest rate of the security. annual-rate is a number value and is either entered as a decimal (for example, 0.08) or with a percent sign (for example, 8%).  price:  The cost of the security per $100 of par value. price is a number value.  days-basis:  An optional argument specifying the number of days per month and days per year used in the calculations. 30/360 (0 or omitted):  30 days in a month, 360 days in a year, using the NASD method for dates falling on the 31st of a month. actual/actual (1):  Actual days in each month, actual days in each year. actual/360 (2):  Actual days in each month, 360 days in a year. actual/365 (3):  Actual days in each month, 365 days in a year. 30E/360 (4):  30 days in a month, 360 days in a year, using the European method for dates falling on the 31st of a month (European 30/360). Example In this example, the YIELDMAT function is used to determine the effective annual yield of the hypothetical security described by the values listed. The security pays interest only at maturity. The function evaluates to 6.565%. settle maturity issue annual-rate price days-basis =YIELDMAT (B2, C2, D2, E2, F2, G2) 05/01/2009 06/30/2015 12/14/2008 0.065 99.002 0 Related Topics For related functions and additional information, see: “PRICEMAT” on page 140 “YIELD” on page 150 “YIELDDISC” on page 152 “Common Arguments Used in Financial Functions” on page 341 “Listing of Financial Functions” on page 96 “Value Types” on page 36 “The Elements of Formulas” on page 15 “Using the Keyboard and Mouse to Create and Edit Formulas” on page 26 “Pasting from Examples in Help” on page 41 154 Chapter 6 Financial Functions 155 The logical and information functions help you to evaluate the contents of cells and help in determining how to evaluate or otherwise work with cell contents or formula results. Listing of Logical and Information Functions iWork provides these logical and information functions for use with tables. Function Description “AND” (page 156) The AND function returns TRUE if all arguments are true, and FALSE otherwise. “FALSE” (page 157) The FALSE function returns the Boolean value FALSE. This function is included for compatibility with tables imported from other spreadsheet applications. “IF” (page 158) The IF function returns one of two values depending on whether a specified expression evaluates to a Boolean value of TRUE or FALSE. “IFERROR” (page 159) The IFERROR function returns a value that you specify if a given value evaluates to an error; otherwise it returns the given value. “ISBLANK” (page 160) The ISBLANK function returns TRUE if the specified cell is empty and FALSE otherwise. “ISERROR” (page 161) The ISERROR function returns TRUE if a given expression evaluates to an error and FALSE otherwise. Logical and Information Functions 7 Function Description “ISEVEN” (page 162) The ISEVEN function returns TRUE if the value is even (leaves no remainder when divided by 2); otherwise it returns FALSE. “ISODD” (page 163) The ISODD function returns TRUE if the value is odd (leaves a remainder when divided by 2); otherwise it returns FALSE. “NOT” (page 164) The NOT function returns the opposite of the Boolean value of a specified expression. “OR” (page 165) The OR function returns TRUE if any argument is true; otherwise it returns FALSE. “TRUE” (page 166) The TRUE function returns the Boolean value TRUE. This function is included for compatibility with tables imported from other spreadsheet applications. AND The AND function returns TRUE if all arguments are true, and FALSE otherwise. AND(test-expression, test-expression…)  test-expression:  An expression. test-expression can contain anything as long as the expression can be evaluated as a Boolean. If the expression evaluates to a number, 0 is considered to be FALSE, and any other number is considered to be TRUE.  test-expression…: Optionally include one or more additional expressions. Usage Notes  The AND function is equivalent to the logical conjunction operator used in mathematics or logic. It first evaluates each test-expression. If all the given expressions evaluate to TRUE, the AND function returns TRUE; otherwise FALSE. Examples =AND(TRUE, TRUE) returns TRUE because both arguments are true. =AND(1, 0, 1, 1) returns FALSE because one of the arguments is a numeric 0, which is interpreted as FALSE. =AND(A5>60, A5<=100) returns TRUE if cell A5 contains a number in the range 61 to 100, otherwise FALSE. The following two IF functions will return the same value: =IF(B2>60, IF(B2<=100, TRUE, FALSE), FALSE) =IF(AND(B2>60, B2<=100), TRUE, FALSE) 156 Chapter 7 Logical and Information Functions Chapter 7 Logical and Information Functions 157 Related Topics For related functions and additional information, see: “IF” on page 158 “NOT” on page 164 “OR” on page 165 “Specifying Conditions and Using Wildcards” on page 360 “Adding Comments Based on Cell Contents” on page 358 “Using Logical and Information Functions Together” on page 358 “Listing of Logical and Information Functions” on page 155 “Value Types” on page 36 “The Elements of Formulas” on page 15 “Using the Keyboard and Mouse to Create and Edit Formulas” on page 26 “Pasting from Examples in Help” on page 41 FALSE The FALSE function returns the Boolean value FALSE. This function is included for compatibility with tables imported from other spreadsheet applications. FALSE() Usage Notes The F  ALSE function does not have any arguments. However, you must include the parentheses: =FALSE().  Instead of using the FALSE function, you can specify a Boolean value of FALSE by simply typing FALSE (or false) into a cell or as a function argument. Examples =FALSE() returns the Boolean value FALSE. =AND(1, FALSE()) returns the Boolean value FALSE. Related Topics For related functions and additional information, see: “TRUE” on page 166 “Listing of Logical and Information Functions” on page 155 “Value Types” on page 36 “The Elements of Formulas” on page 15 “Using the Keyboard and Mouse to Create and Edit Formulas” on page 26 “Pasting from Examples in Help” on page 41 IF The IF function returns one of two values depending on whether a specified expression evaluates to a Boolean value of TRUE or FALSE. IF(if-expression, if-true, if-false)  if-expression:  A logical expression. if-expression can contain anything as long as the expression can be evaluated as a Boolean. If the expression evaluates to a number, 0 is considered to be FALSE, and any other number is considered to be TRUE.  if-true:  The value returned if the expression is TRUE. if-true can contain any value type. If omitted (comma but no value), IF will return 0.  if-false:  An optional argument specifying the value returned if the expression is FALSE. if-false can contain any value type. If omitted (comma but no value), IF will return 0. If entirely omitted (no comma after if-false) and if-expression evaluates to FALSE, IF will return FALSE. Usage Notes  If the Boolean value of if-expression is TRUE, the function returns the if-true expression; otherwise it returns the if-false expression.  Both if-true and if-false can contain additional IF functions (nested IF functions). Examples =IF(A5>=0, “Nonnegative”, “Negative”) returns the text “Nonnegative” if cell A5 contains a number greater than or equal to zero or a nonnumeric value. If cell A5 contains a value less than 0, the function returns “Negative”. =IF(IFERROR(OR(ISEVEN(B4+B5),ISODD(B4+B5), FALSE),), “All numbers”, “Not all numbers”) returns the text “All numbers” if both cells B4 and B5 contain numbers; otherwise the text “Not all numbers.” This is accomplished by testing to see if the sum of the two cells is either even or odd. If the cell is not a number, the EVEN and ODD functions will return an error and the IFERROR function will return FALSE; otherwise it will return TRUE since either EVEN or ODD is TRUE. So if either B4 or B5 is not a number or Boolean, the IF statement will return the if-false expression, “Not all numbers”; otherwise it will return the if-true expression “All numbers.” 158 Chapter 7 Logical and Information Functions Chapter 7 Logical and Information Functions 159 Related Topics For related functions and additional information, see: “AND” on page 156 “NOT” on page 164 “OR” on page 165 “Specifying Conditions and Using Wildcards” on page 360 “Trapping Division by Zero” on page 360 “Adding Comments Based on Cell Contents” on page 358 “Using Logical and Information Functions Together” on page 358 “Listing of Logical and Information Functions” on page 155 “Value Types” on page 36 “The Elements of Formulas” on page 15 “Using the Keyboard and Mouse to Create and Edit Formulas” on page 26 “Pasting from Examples in Help” on page 41 IFERROR The IFERROR function returns a value that you specify if a given value evaluates to an error; otherwise it returns the given value. IFERROR(any-expression, if-error)  any-expression:  An expression to be tested. any-expression can contain any value type.  if-error:  The value returned if any-expression evaluates to an error. if-error can contain any value type. Usage Notes  Use IFERROR to handle errors in a formula. For example, if you are working with data where a valid value for cell D1 is 0, the formula =B1/D1 would result in an error (division by zero). This error can be prevented by using a formula such as =IFERROR(B1/D1, 0) which returns the actual division if D1 is not zero; otherwise it returns 0. Examples If B1 is a number value and D1 evaluates to 0, then: =IFERROR(B1/D1,0) returns 0 since division by zero results in an error. =IF(ISERROR(B1/D1),0,B1/D1) is equivalent to the previous IFERROR example, but requires the use of both IF and ISERROR. =IF(IFERROR(OR(ISEVEN(B4+B5),ISODD(B4+B5), FALSE),), “All numbers”, “Not all numbers”) returns the text “All numbers” if both cells B4 and B5 contain numbers; otherwise the text “Not all numbers.” This is accomplished by testing to see if the sum of the two cells is either even or odd. If the cell is not a number, the EVEN and ODD functions will return an error and the IFERROR function will return FALSE; otherwise it will return TRUE since either EVEN or ODD is TRUE. So if either B4 or B5 is not a number or a Boolean, the IF statement will return the if-false expression, “Not all numbers”; otherwise it will return the if-true expression “All numbers.” Related Topics For related functions and additional information, see: “ISBLANK” on page 160 “ISERROR” on page 161 “Listing of Logical and Information Functions” on page 155 “Value Types” on page 36 “The Elements of Formulas” on page 15 “Using the Keyboard and Mouse to Create and Edit Formulas” on page 26 “Pasting from Examples in Help” on page 41 ISBLANK The ISBLANK function returns TRUE if the specified cell is empty and FALSE otherwise. ISBLANK(cell)  cell:  A reference to a single table cell. cell is a reference value to a single cell that can contain any value or be empty. Usage Notes  If the cell is completely blank (empty), the function returns TRUE; otherwise it returns FALSE. If the cell contains a space or a nonprinting character, the function will return FALSE, even though the cell appears to be blank. 160 Chapter 7 Logical and Information Functions Chapter 7 Logical and Information Functions 161 Examples If the table cell A1 is empty and cell B2 is equal to 100: =ISBLANK(A1) returns TRUE. =ISBLANK(B2) returns FALSE. Related Topics For related functions and additional information, see: “IFERROR” on page 159 “ISERROR” on page 161 “Adding Comments Based on Cell Contents” on page 358 “Using Logical and Information Functions Together” on page 358 “Listing of Logical and Information Functions” on page 155 “Value Types” on page 36 “The Elements of Formulas” on page 15 “Using the Keyboard and Mouse to Create and Edit Formulas” on page 26 “Pasting from Examples in Help” on page 41 ISERROR The ISERROR function returns TRUE if a given expression evaluates to an error and FALSE otherwise. ISERROR(any-expression)  any-expression:  An expression to be tested. any-expression can contain any value type. Usage Notes  It is often better to use the IFERROR function. The IFERROR function provides all the functionality of ISERROR, but allows for trapping, not just identifying, the error. Examples If B1 is a number value and D1 evaluates to 0, then =IF(ISERROR(B1/D1),0,B1/D1) returns 0 since division by zero results in an error. =IFERROR(B1/D1,0) is equivalent to the previous example, but requires only one function. Related Topics For related functions and additional information, see: “IFERROR” on page 159 “ISBLANK” on page 160 “Listing of Logical and Information Functions” on page 155 “Value Types” on page 36 “The Elements of Formulas” on page 15 “Using the Keyboard and Mouse to Create and Edit Formulas” on page 26 “Pasting from Examples in Help” on page 41 ISEVEN The ISEVEN function returns TRUE if the given number is even (leaves no remainder when divided by 2); otherwise it returns FALSE. ISEVEN(num)  num:  A number. num is a number value. Usage Notes  If num is text, the function returns an error. If num is the Boolean TRUE (value of 1), the function returns FALSE. If num is the Boolean FALSE (value of 0), the function returns TRUE. Examples =ISEVEN(2) returns TRUE. =ISEVEN(2.75) returns TRUE. =ISEVEN(3) returns FALSE. Related Topics For related functions and additional information, see: “ISODD” on page 163 “Listing of Logical and Information Functions” on page 155 “Value Types” on page 36 “The Elements of Formulas” on page 15 “Using the Keyboard and Mouse to Create and Edit Formulas” on page 26 “Pasting from Examples in Help” on page 41 162 Chapter 7 Logical and Information Functions Chapter 7 Logical and Information Functions 163 ISODD The ISODD function returns TRUE if the given number is odd (leaves a remainder when divided by 2); otherwise it returns FALSE. ISODD(num)  num:  A number. num is a number value. Usage Notes  If num is text, the function returns an error. If num is the Boolean TRUE (value of 1), the function returns TRUE. If num is the Boolean FALSE (value of 0), the function returns FALSE. Examples =ISODD(3) returns TRUE. =ISODD(3.75) returns TRUE. =ISODD(2) returns FALSE. Related Topics For related functions and additional information, see: “ISEVEN” on page 162 “Listing of Logical and Information Functions” on page 155 “Value Types” on page 36 “The Elements of Formulas” on page 15 “Using the Keyboard and Mouse to Create and Edit Formulas” on page 26 “Pasting from Examples in Help” on page 41 NOT The NOT function returns the opposite of the Boolean value of a specified expression. NOT(any-expression)  any-expression:  An expression to be tested. any-expression can contain anything as long as the expression can be evaluated as a Boolean. If the expression evaluates to a number, 0 is considered to be FALSE, and any other number is considered to be TRUE. Examples =NOT(0) returns TRUE because 0 is interpreted as FALSE. =OR(A9, NOT(A9)) always returns TRUE because either A9 or its opposite will always be true. =NOT(OR(FALSE, FALSE)) returns TRUE because neither argument of the logical OR is true. Related Topics For related functions and additional information, see: “AND” on page 156 “IF” on page 158 “OR” on page 165 “Listing of Logical and Information Functions” on page 155 “Value Types” on page 36 “The Elements of Formulas” on page 15 “Using the Keyboard and Mouse to Create and Edit Formulas” on page 26 “Pasting from Examples in Help” on page 41 164 Chapter 7 Logical and Information Functions Chapter 7 Logical and Information Functions 165 OR The OR function returns TRUE if any argument is true; otherwise it returns FALSE. OR(any-expression, any-expression…)  any-expression:  An expression to be tested. any-expression can contain anything as long as the expression can be evaluated as a Boolean. If the expression evaluates to a number, 0 is considered to be FALSE, and any other number is considered to be TRUE.  any-expression…: Optionally include one or more additional expressions to be tested. Usage Notes  The OR function is equivalent to the logical disjunction or inclusive disjunction used in mathematics or logic. It first evaluates each expression. If any of the given expressions evaluate to TRUE, the OR function returns TRUE; otherwise FALSE.  If an expression is numeric, a value of 0 is interpreted as FALSE and any nonzero value is interpreted as TRUE.  OR is often used with the IF function when more than one condition must be considered. Examples =OR(A1+A2<100, B1+B2<100) returns FALSE if the sums of the indicated cells are both greater than or equal to 100, and TRUE if at least one of the sums is less than 100. =OR(5, 0, 6) returns TRUE because at least one argument is not zero. Related Topics For related functions and additional information, see: “AND” on page 156 “IF” on page 158 “NOT” on page 164 “Specifying Conditions and Using Wildcards” on page 360 “Adding Comments Based on Cell Contents” on page 358 “Using Logical and Information Functions Together” on page 358 “Listing of Logical and Information Functions” on page 155 “Value Types” on page 36 “The Elements of Formulas” on page 15 “Using the Keyboard and Mouse to Create and Edit Formulas” on page 26 “Pasting from Examples in Help” on page 41 TRUE The TRUE function returns the Boolean value TRUE. This function is included for compatibility with tables imported from other spreadsheet applications. TRUE() Usage Notes The TRUE func  tion does not have any arguments. However, you must include the parentheses: =TRUE().  Instead of using the TRUE function, you can specify a Boolean value of TRUE by simply typing TRUE (or true) into a cell or function argument. Examples =TRUE() returns the Boolean value TRUE. =AND(1, TRUE()) returns the Boolean value TRUE. =AND(1, TRUE) works exactly the same as the preceding example. Related Topics For related functions and additional information, see: “FALSE” on page 157 “Listing of Logical and Information Functions” on page 155 “Value Types” on page 36 “The Elements of Formulas” on page 15 “Using the Keyboard and Mouse to Create and Edit Formulas” on page 26 “Pasting from Examples in Help” on page 41 166 Chapter 7 Logical and Information Functions 167 The numeric functions help you to calculate commonly used mathematical values. Listing of Numeric Functions iWork provides these numeric functions for use with tables. Function Description “ABS” (page 170) The ABS function returns the absolute value of a number or duration. “CEILING” (page 170) The CEILING function rounds a number away from zero to the nearest multiple of the specified factor. “COMBIN” (page 172) The COMBIN function returns the number of different ways you can combine a number of items into groups of a specific size, ignoring the order within the groups. “EVEN” (page 173) The EVEN function rounds a number away from zero to the next even number. “EXP” (page 174) The EXP function returns e (the base of natural logarithms) raised to the specified power. “FACT” (page 174) The FACT function returns the factorial of a number. “FACTDOUBLE” (page 175) The FACTDOUBLE function returns the double factorial of a number. “FLOOR” (page 176) The FLOOR function rounds a number toward zero to the nearest multiple of the specified factor. “GCD” (page 177) The GCD function returns the greatest common divisor of the specified numbers. Numeric Functions 8 Function Description “INT” (page 178) The INT function returns the nearest integer that is less than or equal to the number. “LCM” (page 179) The LCM function returns the least common multiple of the specified numbers. “LN” (page 179) The LN function returns the natural logarithm of a number, the power to which e must be raised to result in the number. “LOG” (page 180) The LOG function returns the logarithm of a number using a specified base. “LOG10” (page 181) The LOG10 function returns the base-10 logarithm of a number. “MOD” (page 182) The MOD function returns the remainder from a division. “MROUND” (page 183) The MROUND function rounds a number to the nearest multiple of a specified factor. “MULTINOMIAL” (page 184) The MULTINOMIAL function returns the closed form of the multinomial coefficient of the given numbers. “ODD” (page 185) The ODD function rounds a number away from zero to the next odd number. “PI” (page 186) The PI function returns the approximate value of π (pi), the ratio of a circle’s circumference to its diameter. “POWER” (page 186) The POWER function returns a number raised to a power. “PRODUCT” (page 187) The PRODUCT function returns the product of one or more numbers. “QUOTIENT” (page 188) The QUOTIENT function returns the integer quotient of two numbers. “RAND” (page 189) The RAND function returns a random number that is greater than or equal to 0 and less than 1. “RANDBETWEEN” (page 189) The RANDBETWEEN function returns a random integer within the specified range. “ROMAN” (page 190) The ROMAN function converts a number to Roman numerals. 168 Chapter 8 Numeric Functions Chapter 8 Numeric Functions 169 Function Description “ROUND” (page 191) The ROUND function returns a number rounded to the specified number of places. “ROUNDDOWN” (page 192) The ROUNDDOWN function returns a number rounded toward zero (rounded down) to the specified number of places. “ROUNDUP” (page 193) The ROUNDUP function returns a number rounded away from zero (rounded up) to the specified number of places. “SIGN” (page 195) The SIGN function returns 1 when a given number is positive, –1 when it is negative, and 0 when it is zero. “SQRT” (page 195) The SQRT function returns the square root of a number. “SQRTPI” (page 196) The SQRTPI function returns the square root of a number multiplied by π (pi). “SUM” (page 196) The SUM function returns the sum of a collection of numbers. “SUMIF” (page 197) The SUMIF function returns the sum of a collection of numbers, including only numbers that satisfy a specified condition. “SUMIFS” (page 198) The SUMIFS function returns the sum of the cells in a collection where the test values meet the given conditions. “SUMPRODUCT” (page 200) The SUMPRODUCT function returns the sum of the products of corresponding numbers in one or more ranges. “SUMSQ” (page 201) The SUMSQ function returns the sum of the squares of a collection of numbers. “SUMX2MY2” (page 202) The SUMX2MY2 function returns the sum of the difference of the squares of corresponding values in two collections. “SUMX2PY2” (page 203) The SUMX2PY2 function returns the sum of the squares of corresponding values in two collections. “SUMXMY2” (page 204) The SUMXMY2 function returns the sum of the squares of the differences between corresponding values in two collections. “TRUNC” (page 204) The TRUNC function truncates a number to the specified number of digits. ABS The ABS function returns the absolute value of a number or duration. ABS(num-dur)  num-dur:  A number or duration value. num-dur is a number or duration value. Usage Notes  The result returned by ABS is either a positive number or 0. Examples =ABS(A1) returns 5, if cell A1 contains 5. =ABS(8-5) returns 3. =ABS(5-8) returns 3. =ABS(0) returns 0. =ABS(A1) returns 0, if cell A1 is empty. Related Topics For related functions and additional information, see: “Listing of Numeric Functions” on page 167 “Value Types” on page 36 “The Elements of Formulas” on page 15 “Using the Keyboard and Mouse to Create and Edit Formulas” on page 26 “Pasting from Examples in Help” on page 41 CEILING The CEILING function rounds a number away from zero to the nearest multiple of the specified factor. CEILING(num-to-round, multiple-factor)  num-to-round:  The number to be rounded. num-to-round is a number value.  multiple-factor:  The number to use to determine the closet multiple. multiple-factor is a number value and must have the same sign as num-to-round. 170 Chapter 8 Numeric Functions Chapter 8 Numeric Functions 171 Examples =CEILING(0.25, 1) returns 1. =CEILING(1.25, 1) returns 2. =CEILING(-1.25, -1) returns -2. =CEILING(5, 2) returns 6. =CEILING(73, 10) returns 80. =CEILING(7, 2.5) returns 7.5. Related Topics For related functions and additional information, see: “EVEN” on page 173 “FLOOR” on page 176 “INT” on page 178 “MROUND” on page 183 “ODD” on page 185 “ROUND” on page 191 “ROUNDDOWN” on page 192 “ROUNDUP” on page 193 “TRUNC” on page 204 “More on Rounding” on page 355 “Listing of Numeric Functions” on page 167 “Value Types” on page 36 “The Elements of Formulas” on page 15 “Using the Keyboard and Mouse to Create and Edit Formulas” on page 26 “Pasting from Examples in Help” on page 41 COMBIN The COMBIN function returns the number of different ways you can combine a number of items into groups of a specific size, ignoring the order within the groups. COMBIN(total-items, group-size)  total-items:  The total number of items. total-items is a number value and must be greater than or equal to 0. If total-items has a decimal (fractional) part, it is ignored.  group-size:  The number of items combined in each group. group-size is a number value and must be greater than or equal to 0. If group-size has a decimal (fractional) part, it is ignored. Usage Notes  Combinations are not the same as permutations. The order of the items in a group is ignored for combinations but not for permutations. For example, (1, 2, 3) and (3, 2, 1) are the same combination but two unique permutations. If you want the number of permutations rather than the number of combinations, use the PERMUT function. Examples =COMBIN(3, 2) returns 3, the number of unique groups you can create if you start with 3 items and group them 2 at a time. =COMBIN(3.2, 2.3) returns 3. Fractional parts are dropped. =COMBIN(5, 2) and =COMBIN(5, 3) both return 10. Related Topics For related functions and additional information, see: “PERMUT” on page 281 “Listing of Numeric Functions” on page 167 “Value Types” on page 36 “The Elements of Formulas” on page 15 “Using the Keyboard and Mouse to Create and Edit Formulas” on page 26 “Pasting from Examples in Help” on page 41 172 Chapter 8 Numeric Functions Chapter 8 Numeric Functions 173 EVEN The EVEN function rounds a number away from zero to the next even number. EVEN(num-to-round)  num-to-round:  The number to be rounded. num-to-round is a number value. Usage Notes  To round to an odd number, use the ODD function. Examples =EVEN(1) returns 2. =EVEN(2) returns 2. =EVEN(2.5) returns 4. =EVEN(-2.5) returns -4. =EVEN(0) returns 0. Related Topics For related functions and additional information, see: “CEILING” on page 170 “FLOOR” on page 176 “INT” on page 178 “MROUND” on page 183 “ODD” on page 185 “ROUND” on page 191 “ROUNDDOWN” on page 192 “ROUNDUP” on page 193 “TRUNC” on page 204 “More on Rounding” on page 355 “Listing of Numeric Functions” on page 167 “Value Types” on page 36 “The Elements of Formulas” on page 15 “Using the Keyboard and Mouse to Create and Edit Formulas” on page 26 “Pasting from Examples in Help” on page 41 EXP The EXP function returns e (the base of natural logarithms) raised to the specified power. EXP(exponent)  exponent:  The power to which you want to raise e. exponent is a number value. Usage Notes  EXP and LN are mathematically inverses over the domain where LN is defined, but because of floating-point rounding, EXP(LN(x)) may not give exactly x. Example =EXP(1) returns 2.71828182845905, an approximation of e. Related Topics For related functions and additional information, see: “LN” on page 179 “Listing of Numeric Functions” on page 167 “Value Types” on page 36 “The Elements of Formulas” on page 15 “Using the Keyboard and Mouse to Create and Edit Formulas” on page 26 “Pasting from Examples in Help” on page 41 FACT The FACT function returns the factorial of a number. FACT(fact-num)  fact-num:  A number. fact-num is a number value and must be greater than or equal to 0. Any decimal (fractional) part of fact-num is ignored. Examples =FACT(5) returns 120, or 1 * 2 * 3 * 4 * 5. =FACT(0) returns 1. =FACT(4.5) returns 24. The fraction is dropped and 4 factorial is computed. =FACT(-1) returns an error; the number must be nonnegative. 174 Chapter 8 Numeric Functions Chapter 8 Numeric Functions 175 Related Topics For related functions and additional information, see: “FACTDOUBLE” on page 175 “MULTINOMIAL” on page 184 “Listing of Numeric Functions” on page 167 “Value Types” on page 36 “The Elements of Formulas” on page 15 “Using the Keyboard and Mouse to Create and Edit Formulas” on page 26 “Pasting from Examples in Help” on page 41 FACTDOUBLE The FACTDOUBLE function returns the double factorial of a number. FACTDOUBLE(fact-num)  fact-num:  A number. fact-num is a number value and must be greater than or equal to –1. Values in the range –1 to 1 return 1. Any decimal (fractional) part of fact-num is ignored. Usage Notes  For an even integer, the double factorial is the product of all even integers less than or equal to the given integer and greater than or equal to 2. For an odd integer, the double factorial is the product of all odd integers less than or equal to the given integer and greater than or equal to 1. Examples =FACTDOUBLE(4) returns 8, the product of 2 and 4. =FACTDOUBLE(4.7) returns 8, the product of 2 and 4. The decimal portion is ignored. =FACTDOUBLE (10) returns 3840, the product of 2, 4, 6, 8, and 10. =FACTDOUBLE(1) returns 1, as all numbers between –1 and 1 return 1. =FACTDOUBLE(-1) returns 1, as all numbers between –1 and 1 return 1. =FACTDOUBLE (7) returns 105, the product of 1, 3, 5, and 7. Related Topics For related functions and additional information, see: “FACT” on page 174 “MULTINOMIAL” on page 184 “Listing of Numeric Functions” on page 167 “Value Types” on page 36 “The Elements of Formulas” on page 15 “Using the Keyboard and Mouse to Create and Edit Formulas” on page 26 “Pasting from Examples in Help” on page 41 FLOOR The FLOOR function rounds a number toward zero to the nearest multiple of the specified factor. FLOOR(num-to-round, factor)  num-to-round:  The number to be rounded. num-to-round is a number value.  factor:  The number to use to determine the closet multiple. factor is a number value. It must have the same sign as num-to-round. Examples =FLOOR(0.25, 1) returns 0. =FLOOR(1.25, 1) returns 1. =FLOOR(5, 2) returns 4. =FLOOR(73, 10) returns 70. =FLOOR(-0.25, -1) returns 0. =FLOOR(9, 2.5) returns 7.5. Related Topics For related functions and additional information, see: “CEILING” on page 170 “EVEN” on page 173 “INT” on page 178 “MROUND” on page 183 “ODD” on page 185 “ROUND” on page 191 “ROUNDDOWN” on page 192 “ROUNDUP” on page 193 176 Chapter 8 Numeric Functions Chapter 8 Numeric Functions 177 “TRUNC” on page 204 “More on Rounding” on page 355 “Listing of Numeric Functions” on page 167 “Value Types” on page 36 “The Elements of Formulas” on page 15 “Using the Keyboard and Mouse to Create and Edit Formulas” on page 26 “Pasting from Examples in Help” on page 41 GCD The GCD function returns the greatest common divisor of the specified numbers. GCD(num-value, num-value…)  num-value:  A number. num-value is a number value. If there is a decimal portion it is ignored.  num-value…: Optionally include one or more additional numbers. Usage Notes  Sometimes called the greatest common factor, the greatest common divisor is the largest integer that divides into each of the numbers with no remainder. Examples =GCD(8, 10) returns 2. =GCD(99, 102, 105) returns 3. =GCD(34, 51) returns 17. Related Topics For related functions and additional information, see: “LCM” on page 179 “Listing of Numeric Functions” on page 167 “Value Types” on page 36 “The Elements of Formulas” on page 15 “Using the Keyboard and Mouse to Create and Edit Formulas” on page 26 “Pasting from Examples in Help” on page 41 INT The INT function returns the nearest integer that is less than or equal to the number. INT(num-to-round)  num-to-round:  The number to be rounded. num-to-round is a number value. Examples =INT(1.49) returns 1. =INT(1.50) returns 1. =INT(1.23456) returns 1. =INT(1111.222) returns 1111. =INT(-2.2) returns -3. =INT(-2.8) returns -3. Related Topics For related functions and additional information, see: “CEILING” on page 170 “EVEN” on page 173 “FLOOR” on page 176 “MROUND” on page 183 “ODD” on page 185 “ROUND” on page 191 “ROUNDDOWN” on page 192 “ROUNDUP” on page 193 “TRUNC” on page 204 “More on Rounding” on page 355 “Listing of Numeric Functions” on page 167 “Value Types” on page 36 “The Elements of Formulas” on page 15 “Using the Keyboard and Mouse to Create and Edit Formulas” on page 26 “Pasting from Examples in Help” on page 41 178 Chapter 8 Numeric Functions Chapter 8 Numeric Functions 179 LCM The LCM function returns the least common multiple of the specified numbers. LCM(num-value, num-value…)  num-value:  A number. num-value is a number value.  num-value…: Optionally include one or more additional numbers. Usage Notes  Sometimes called the lowest or smallest common multiple, the least common multiple is the smallest integer that is a multiple of the specified numbers. Examples =LCM(2, 3) returns 6. =LCM(34, 68) returns 68. =LCM(30, 40, 60) returns 120. =LCM(30.25, 40.333, 60.5) returns 120 (the fractional parts are ignored). =LCM(2, -3) displays an error (negative numbers are not allowed). Related Topics For related functions and additional information, see: “GCD” on page 177 “Listing of Numeric Functions” on page 167 “Value Types” on page 36 “The Elements of Formulas” on page 15 “Using the Keyboard and Mouse to Create and Edit Formulas” on page 26 “Pasting from Examples in Help” on page 41 LN The LN function returns the natural logarithm of a number, the power to which e must be raised to result in the number. LN(pos-num)  pos-num:  A positive number. pos-num is a number value and must be greater than 0. Usage Notes  EXP and LN are mathematically inverses over the domain where LN is defined, but because of floating-point rounding, =LN(EXP(x)) may not give exactly x. Example =LN(2.71828) returns approximately 1, the power to which e must be raised to produce 2.71828. Related Topics For related functions and additional information, see: “EXP” on page 174 “LOG” on page 180 “LOGINV” on page 268 “LOGNORMDIST” on page 269 “Listing of Numeric Functions” on page 167 “Value Types” on page 36 “The Elements of Formulas” on page 15 “Using the Keyboard and Mouse to Create and Edit Formulas” on page 26 “Pasting from Examples in Help” on page 41 LOG The LOG function returns the logarithm of a number using a specified base. LOG(pos-num, base)  pos-num:  A positive number. pos-num is a number value and must be greater than 0.  base:  An optional value specifying the base of the logarithm. base is a number value and must be greater than 0. If base is 1, a division by zero will result and the function will return an error. If base is omitted, it is assumed to be 10. Examples =LOG(8, 2) returns 3. =LOG(100, 10) and LOG(100) both return 2. =LOG(5.0625, 1.5) returns 4. Related Topics For related functions and additional information, see: “LOG10” on page 181 “Listing of Numeric Functions” on page 167 180 Chapter 8 Numeric Functions Chapter 8 Numeric Functions 181 “Value Types” on page 36 “The Elements of Formulas” on page 15 “Using the Keyboard and Mouse to Create and Edit Formulas” on page 26 “Pasting from Examples in Help” on page 41 LOG10 The LOG10 function returns the base-10 logarithm of a number. LOG10(pos-num)  pos-num:  A positive number. pos-num is a number value and must be greater than 0. Usage Notes  To find the logarithm for a base other than 10, use the LOG function. Examples =LOG10(1) returns 0. =LOG10(10) returns 1. =LOG10(100) returns 2. =LOG10(1000) returns 3. Related Topics For related functions and additional information, see: “LN” on page 179 “LOG” on page 180 “Listing of Numeric Functions” on page 167 “Value Types” on page 36 “The Elements of Formulas” on page 15 “Using the Keyboard and Mouse to Create and Edit Formulas” on page 26 “Pasting from Examples in Help” on page 41 MOD The MOD function returns the remainder from a division. MOD(dividend, divisor)  dividend:  A number to be divided by another number. dividend is a number value.  divisor:  A number to divide into another number. divisor is a number value. If 0, a division by zero will result and the function will return an error. Usage Notes  The sign of the result matches that of the divisor.  When computing MOD(a, b), MOD gives a number r such that a = bk + r, where r is between 0 and b, and k is an integer.  MOD(a, b) is equivalent to a–b*INT(a/b). Examples =MOD(6, 3) returns 0. =MOD(7, 3) returns 1. =MOD(8, 3) returns 2. =MOD(-8, 3) returns 1. =MOD(4.5, 2) returns 0.5. =MOD(7, 0.75) returns 0.25. Related Topics For related functions and additional information, see: “QUOTIENT” on page 188 “Listing of Numeric Functions” on page 167 “Value Types” on page 36 “The Elements of Formulas” on page 15 “Using the Keyboard and Mouse to Create and Edit Formulas” on page 26 “Pasting from Examples in Help” on page 41 182 Chapter 8 Numeric Functions Chapter 8 Numeric Functions 183 MROUND The MROUND function rounds a number to the nearest multiple of a specified factor. MROUND(num-to-round, factor)  num-to-round:  The number to be rounded. num-to-round is a number value.  factor:  The number to use to determine the closet multiple. factor is a number value. It must have the same sign as num-to-round. Examples =MROUND(2, 3) returns 3. =MROUND(4, 3) returns 3. =MROUND(4.4999, 3) returns 3. =MROUND(4.5, 3) returns 6. =MROUND(-4.5, 3) returns an error. Related Topics For related functions and additional information, see: “CEILING” on page 170 “EVEN” on page 173 “FLOOR” on page 176 “INT” on page 178 “ODD” on page 185 “ROUND” on page 191 “ROUNDDOWN” on page 192 “ROUNDUP” on page 193 “TRUNC” on page 204 “More on Rounding” on page 355 “Listing of Numeric Functions” on page 167 “Value Types” on page 36 “The Elements of Formulas” on page 15 “Using the Keyboard and Mouse to Create and Edit Formulas” on page 26 “Pasting from Examples in Help” on page 41 MULTINOMIAL The MULTINOMIAL function returns the multinomial coefficient of the given numbers. It accomplishes this by determining the ratio of the factorial of the sum of the given numbers to the product of the factorials of the given numbers. MULTINOMIAL(non-neg-num, non-neg-num…)  non-neg-num:  A number. non-neg-num is a number value and must be greater than or equal to 0.  non-neg-num…: Optionally include one or more additional numbers. Examples =MULTINOMIAL(2) returns 1. The factorial of the 2 is 2. The product of 1 and 2 is 2. The ratio of 2:2 is 1. =MULTINOMIAL(1, 2, 3) returns 60. The factorial of the sum of 1, 2, and 3 is 720. The product of the factorials of 1, 2, and 3 is 12. The ratio of 720:12 is 60. =MULTINOMIAL(4, 5, 6) returns 630630. The factorial of the sum of 4, 5, and 6 is 1.30767E+12. The product of the factorials of 4, 5, and 6 is 2073600. The ratio of 1.30767E+12:2073600 is 630630. Related Topics For related functions and additional information, see: “FACT” on page 174 “FACTDOUBLE” on page 175 “Listing of Numeric Functions” on page 167 “Value Types” on page 36 “The Elements of Formulas” on page 15 “Using the Keyboard and Mouse to Create and Edit Formulas” on page 26 “Pasting from Examples in Help” on page 41 184 Chapter 8 Numeric Functions Chapter 8 Numeric Functions 185 ODD The ODD function rounds a number away from zero to the next odd number. ODD(num-to-round)  num-to-round:  The number to be rounded. num-to-round is a number value. Usage Notes  To round to an even number, use the EVEN function. Examples =ODD(1) returns 1. =ODD(2) returns 3. =ODD(2.5) returns 3. =ODD(-2.5) returns -3. =ODD(0) returns 1. Related Topics For related functions and additional information, see: “CEILING” on page 170 “EVEN” on page 173 “FLOOR” on page 176 “INT” on page 178 “MROUND” on page 183 “ROUND” on page 191 “ROUNDDOWN” on page 192 “ROUNDUP” on page 193 “TRUNC” on page 204 “More on Rounding” on page 355 “Listing of Numeric Functions” on page 167 “Value Types” on page 36 “The Elements of Formulas” on page 15 “Using the Keyboard and Mouse to Create and Edit Formulas” on page 26 “Pasting from Examples in Help” on page 41 PI The PI function returns the approximate value of π (pi), the ratio of a circle’s circumference to its diameter. PI() Usage Notes  The PI function does not have any arguments. However, you must include the parentheses: =PI().  PI is accurate to 15 decimal places. Examples =PI() returns 3.14159265358979. =SIN(PI()/2) returns 1, the sine of π/2 radians or 90 degrees. Related Topics For related functions and additional information, see: “COS” on page 333 “SIN” on page 336 “TAN” on page 338 “Listing of Numeric Functions” on page 167 “Value Types” on page 36 “The Elements of Formulas” on page 15 “Using the Keyboard and Mouse to Create and Edit Formulas” on page 26 “Pasting from Examples in Help” on page 41 POWER The POWER function returns a number raised to a power. POWER(number, exponent)  number:  A number. number is a number value.  exponent:  The power to which to raise the given number. exponent is a number value. Usage Notes  The POWER function produces the same result as the ^ operator: =POWER(x, y) returns the same result as =x^y. 186 Chapter 8 Numeric Functions Chapter 8 Numeric Functions 187 Examples =POWER(2, 3) returns 8. =POWER(2, 10) returns 1024. =POWER(0.5, 3) returns 0.125. =POWER(100, 0.5) returns 10. Related Topics For related functions and additional information, see: “Listing of Numeric Functions” on page 167 “Value Types” on page 36 “The Elements of Formulas” on page 15 “Using the Keyboard and Mouse to Create and Edit Formulas” on page 26 “Pasting from Examples in Help” on page 41 PRODUCT The PRODUCT function returns the product of one or more numbers. PRODUCT(num-value, num-value…)  num-value:  A number. num-value is a number value.  num-value…: Optionally include one or more additional numbers. Usage Notes  Empty cells included within the values are ignored and do not affect the result. Examples =PRODUCT(2, 4) returns 8. =PRODUCT(0.5, 5, 4, 5) returns 50. Related Topics For related functions and additional information, see: “SUM” on page 196 “Listing of Numeric Functions” on page 167 “Value Types” on page 36 “The Elements of Formulas” on page 15 “Using the Keyboard and Mouse to Create and Edit Formulas” on page 26 “Pasting from Examples in Help” on page 41 QUOTIENT The QUOTIENT function returns the integer quotient of two numbers. QUOTIENT(dividend, divisor)  dividend:  A number to be divided by another number. dividend is a number value.  divisor:  A number to divide into another number. divisor is a number value. If 0, a division by zero will result and the function will return an error. Usage Notes  If either, but not both, the dividend or divisor is negative, the result will be negative. If the sign of both the dividend and the divisor is the same, the result will be positive.  Only the whole part of the quotient is returned. The fractional part (or remainder) is ignored. Examples =QUOTIENT(5, 2) returns 2. =QUOTIENT(5.99, 2) returns 2. =QUOTIENT(-5, 2) returns -2. =QUOTIENT(6, 2) returns 3. =QUOTIENT(5, 6) returns 0. Related Topics For related functions and additional information, see: “MOD” on page 182 “Listing of Numeric Functions” on page 167 “Value Types” on page 36 “The Elements of Formulas” on page 15 “Using the Keyboard and Mouse to Create and Edit Formulas” on page 26 “Pasting from Examples in Help” on page 41 188 Chapter 8 Numeric Functions Chapter 8 Numeric Functions 189 RAND The RAND function returns a random number that is greater than or equal to 0 and less than 1. RAND() Usage Notes The R  AND function does not have any arguments. However, you must include the parentheses: =RAND().  Any time you change a value in the table, a new random number greater than or equal to 0 and less than 1 is generated. Example =RAND() returns, for example, 0.217538648284972, 0.6137690856, 0.0296026556752622, and 0.4684193600 for four recalculations. Related Topics For related functions and additional information, see: “RANDBETWEEN” on page 189 “Listing of Numeric Functions” on page 167 “Value Types” on page 36 “The Elements of Formulas” on page 15 “Using the Keyboard and Mouse to Create and Edit Formulas” on page 26 “Pasting from Examples in Help” on page 41 RANDBETWEEN The RANDBETWEEN function returns a random integer within the specified range. RANDBETWEEN(lower, upper)  lower:  The lower limit or bound. lower is a number value.  upper:  The upper limit or bound. upper is a number value. Usage Notes  Any time you change a value in the table, a new random number between the lower and upper limits is generated. Example =RANDBETWEEN(1, 10) returns, for example, 8, 6, 2, 3, and 5 for five recalculations. Related Topics For related functions and additional information, see: “RAND” on page 189 “Listing of Numeric Functions” on page 167 “Value Types” on page 36 “The Elements of Formulas” on page 15 “Using the Keyboard and Mouse to Create and Edit Formulas” on page 26 “Pasting from Examples in Help” on page 41 ROMAN The ROMAN function converts a number to Roman numerals. ROMAN(arabic-num, roman-style)  arabic-num:  The Arabic numeral that you want to convert. arabic-num is a number value in the range 0 to 3999.  roman-style:  An optional value that determines how strictly the classical rules for forming Roman numerals are applied. strict (0 or TRUE, or omitted):  Use the most strict classical rules. When a smaller numeral precedes a larger to indicate subtraction, the smaller must be a power of 10 and can precede a number no more than 10 times its size. For example, 999 is represented as CMXCIX, but not LMVLIV. relax by one degree (1):  Relax the strict classical rule by one degree. When a smaller number precedes a larger, the smaller need not be a power of 10 and the relative size rule is extended by one numeral. For example, 999 can be represented as LMVLIV, but not XMIX. relax by two degrees (2):  Relax the classical rule by two degrees. When a smaller number precedes a larger, the relative size rule is extended by two numerals. For example, 999 can be represented as XMIX, but not VMIV. relax by three degrees (3):  Relax the classical rule by three degrees. When a smaller number precedes a larger, the relative size rule is extended by three numerals. For example, 999 can be represented as VMIV, but not IM. relax by four degrees (4 or FALSE):  Relax the classical rule by four degrees. When a smaller number precedes a larger, the relative size rule is extended by four numerals. For example, 999 can be represented as IM. 190 Chapter 8 Numeric Functions Chapter 8 Numeric Functions 191 Examples =ROMAN(12) returns XII. =ROMAN(999) returns CMXCIX. =ROMAN(999, 1) returns LMVLIV. =ROMAN(999, 2) returns XMIX. =ROMAN(999, 3) returns VMIV. Related Topics For related functions and additional information, see: “Listing of Numeric Functions” on page 167 “Value Types” on page 36 “The Elements of Formulas” on page 15 “Using the Keyboard and Mouse to Create and Edit Formulas” on page 26 “Pasting from Examples in Help” on page 41 ROUND The ROUND function returns a number rounded to the specified number of places. ROUND(num-to-round, digits)  num-to-round:  The number to be rounded. num-to-round is a number value.  digits:  The number of digits you want to retain, relative to the decimal point. digits is a number value. A positive number represents digits (decimal places) to the right of the decimal point to include. A negative number specifies digits to the left of the decimal point to replace with zeros (the number of zeros at the end of the number). Examples =ROUND(1.49, 0) returns 1. =ROUND(1.50, 0) returns 2. =ROUND(1.23456, 3) returns 1.235. =ROUND(1111.222, -2) returns 1100. =ROUND(-2.2, 0) returns -2. =ROUND(-2.8, 0) returns -3. Related Topics For related functions and additional information, see: “CEILING” on page 170 “EVEN” on page 173 “FLOOR” on page 176 “INT” on page 178 “MROUND” on page 183 “ODD” on page 185 “ROUNDDOWN” on page 192 “ROUNDUP” on page 193 “TRUNC” on page 204 “More on Rounding” on page 355 “Listing of Numeric Functions” on page 167 “Value Types” on page 36 “The Elements of Formulas” on page 15 “Using the Keyboard and Mouse to Create and Edit Formulas” on page 26 “Pasting from Examples in Help” on page 41 ROUNDDOWN The ROUNDDOWN function returns a number rounded toward zero (rounded down) to the specified number of places. ROUNDDOWN(num-to-round, digits)  num-to-round:  The number to be rounded. num-to-round is a number value.  digits:  The number of digits you want to retain, relative to the decimal point. digits is a number value. A positive number represents digits (decimal places) to the right of the decimal point to include. A negative number specifies digits to the left of the decimal point to replace with zeros (the number of zeros at the end of the number). Examples =ROUNDDOWN(1.49, 0) returns 1. =ROUNDDOWN(1.50, 0) returns 1. =ROUNDDOWN(1.23456, 3) returns 1.234. =ROUNDDOWN(1111.222, -2) returns 1100. =ROUNDDOWN(-2.2, 0) returns -2. =ROUNDDOWN(-2.8, 0) returns -2. 192 Chapter 8 Numeric Functions Chapter 8 Numeric Functions 193 Related Topics For related functions and additional information, see: “CEILING” on page 170 “EVEN” on page 173 “FLOOR” on page 176 “INT” on page 178 “MROUND” on page 183 “ODD” on page 185 “ROUND” on page 191 “ROUNDUP” on page 193 “TRUNC” on page 204 “More on Rounding” on page 355 “Listing of Numeric Functions” on page 167 “Value Types” on page 36 “The Elements of Formulas” on page 15 “Using the Keyboard and Mouse to Create and Edit Formulas” on page 26 “Pasting from Examples in Help” on page 41 ROUNDUP The ROUNDUP function returns a number rounded away from zero (rounded up) to the specified number of places. ROUNDUP(num-to-round, digits)  num-to-round:  The number to be rounded. num-to-round is a number value.  digits:  The number of digits you want to retain, relative to the decimal point. digits is a number value. A positive number represents digits (decimal places) to the right of the decimal point to include. A negative number specifies digits to the left of the decimal point to replace with zeros (the number of zeros at the end of the number). Examples =ROUNDUP(1.49, 0) returns 2. =ROUNDUP(1.50, 0) returns 2. =ROUNDUP(1.23456, 3) returns 1.235. =ROUNDUP(1111.222, -2) returns 1200. =ROUNDUP(-2.2, 0) returns -3. =ROUNDUP(-2.8, 0) returns -3. Related Topics For related functions and additional information, see: “CEILING” on page 170 “EVEN” on page 173 “FLOOR” on page 176 “INT” on page 178 “MROUND” on page 183 “ODD” on page 185 “ROUND” on page 191 “ROUNDDOWN” on page 192 “TRUNC” on page 204 “More on Rounding” on page 355 “Listing of Numeric Functions” on page 167 “Value Types” on page 36 “The Elements of Formulas” on page 15 “Using the Keyboard and Mouse to Create and Edit Formulas” on page 26 “Pasting from Examples in Help” on page 41 194 Chapter 8 Numeric Functions Chapter 8 Numeric Functions 195 SIGN The SIGN function returns 1 when the argument number is positive, –1 when it is negative, and 0 when it is zero. SIGN(num)  num:  A number. number is a number value. Examples =SIGN(2) returns 1. =SIGN(0) returns 0. =SIGN(-2) returns -1. =SIGN(A4) returns -1, if cell A4 contains -2. Related Topics For related functions and additional information, see: “Listing of Numeric Functions” on page 167 “Value Types” on page 36 “The Elements of Formulas” on page 15 “Using the Keyboard and Mouse to Create and Edit Formulas” on page 26 “Pasting from Examples in Help” on page 41 SQRT The SQRT function returns the square root of a number. SQRT(num)  num:  A number. number is a number value. Examples =SQRT(16) returns 4. =SQRT(12.25) returns 3.5, the square root of 12.25. Related Topics For related functions and additional information, see: “Listing of Numeric Functions” on page 167 “Value Types” on page 36 “The Elements of Formulas” on page 15 “Using the Keyboard and Mouse to Create and Edit Formulas” on page 26 “Pasting from Examples in Help” on page 41 SQRTPI The SQRTPI function returns the square root of a number after it has been multiplied by π (pi). SQRTPI(non-neg-number)  non-neg-number:  A nonnegative number. non-neg-num is a number value and must be greater than or equal to 0. Examples =SQRTPI(5) returns 3.96332729760601. =SQRTPI(8) returns 5.013256549262. Related Topics For related functions and additional information, see: “Listing of Numeric Functions” on page 167 “Value Types” on page 36 “The Elements of Formulas” on page 15 “Using the Keyboard and Mouse to Create and Edit Formulas” on page 26 “Pasting from Examples in Help” on page 41 SUM The SUM function returns the sum of a collection of numbers. SUM(num-date-dur, num-date-dur…)  num-date-dur:  A value. num-date-dur is a number value, a date/time value, or a duration value.  num-date-dur…: Optionally include one or more additional values. If more than one num-date-dur value is specified, they must all be of the same type. Usage Notes  There is one case where all values do not have to be of the same type. If exactly one date/time value is included, any number values are considered to be numbers of days and all numbers and duration values are added to the date/time value. 196 Chapter 8 Numeric Functions Chapter 8 Numeric Functions 197  Date/time values can’t be added together, so only one date/time value (as discussed above) is permitted.  The values can be in individual cells, ranges of cells, or included directly as arguments to the function. Examples =SUM(A1:A4) adds the numbers in four cells. =SUM(A1:D4) adds the numbers in a square array of sixteen cells. =SUM(A1:A4, 100) adds the numbers in four cells plus 100. Related Topics For related functions and additional information, see: “PRODUCT” on page 187 “Listing of Numeric Functions” on page 167 “Value Types” on page 36 “The Elements of Formulas” on page 15 “Using the Keyboard and Mouse to Create and Edit Formulas” on page 26 “Pasting from Examples in Help” on page 41 SUMIF The SUMIF function returns the sum of a collection of numbers, including only numbers that satisfy a specified condition. SUMIF(test-values, condition, sum-values)  test-values:  The collection containing the values to be tested. test-values is a collection containing any value type.  condition:  An expression that results in a logical TRUE or FALSE. condition is an expression that can contain anything as long as the result from comparing condition to a value in test-values can be expressed as a Boolean value of TRUE or FALSE.  sum-values:  An optional collection containing the numbers to be summed. sumvalues is a collection containing number, date/time, or duration values. It should have the same dimensions as test-values. Usage Notes  If sum-values is omitted, the default value is test-values.  Although test-values can contain any type of value, it should usually contain values all of the same type.  If sum-values is omitted, test-values would normally contain only number or duration values. Examples Given the following table: =SUMIF(A1:A8, “<5”) returns 10. =SUMIF(A1:A8, “<5”, B1:B8) returns 100. =SUMIF(D1:F3, “=c”, D5:F7) returns 27. =SUMIF(B1:D1, 1) or SUMIF(B1:D1, SUM(1)) both total all the occurrences of 1 in the range. Related Topics For related functions and additional information, see: “AVERAGEIF” on page 233 “AVERAGEIFS” on page 234 “COUNTIF” on page 247 “COUNTIFS” on page 248 “SUMIFS” on page 198 “Specifying Conditions and Using Wildcards” on page 360 “Listing of Numeric Functions” on page 167 “Value Types” on page 36 “The Elements of Formulas” on page 15 “Using the Keyboard and Mouse to Create and Edit Formulas” on page 26 “Pasting from Examples in Help” on page 41 SUMIFS The SUMIFS function returns the sum of the cells in a collection where the test values meet the given conditions. 198 Chapter 8 Numeric Functions Chapter 8 Numeric Functions 199 SUMIFS(sum-values, test-values, condition, test-values…, condition…)  sum-values:  A collection containing the values to be summed. sum-values is a collection containing number, date/time, or duration values.  test-values:  A collection containing values to be tested. test-values is a collection containing any type of value.  condition:  An expression that results in a logical TRUE or FALSE. condition is an expression that can contain anything as long as the result from comparing condition to a value in test-values can be expressed as a Boolean value of TRUE or FALSE.  test-values…: Optionally include one or more additional collections containing values to be tested. Each test-values collection must be followed immediately with a condition expression. This pattern of test-values, condition can be repeated as many times as needed.  condition…: If an optional collection of test-values is included, an expression that results in a logical TRUE or FALSE. There must be one condition following each testvalues collection; therefore, this function will always have an odd number of arguments. Usage Notes  For each of the test and condition value pairs, the corresponding (same position within range or array) cell or value is compared to the condition. If all of the conditions are met, the corresponding cell or value in sum-values is included in the sum.  All arrays must be of the same size. Examples The following table shows part of a ledger of deliveries of a certain commodity. Each load is weighed, rated either 1 or 2, and the date of the delivery is noted. =SUMIFS(A2:A13,B2:B13,”=1”,C2:C13,”>=12/13/2010”,C2:C13,”<=12/17/2010”) returns 23, the number of tons of the commodity delivered during the week of December 17 that were rated “1.” =SUMIFS(A2:A13,B2:B13,”=2”,C2:C13,”>=12/13/2010”,C2:C13,”<=12/17/2010”) returns 34, the number of tons of the commodity delivered during the same week that were rated “2.” Related Topics For related functions and additional information, see: “AVERAGEIF” on page 233 “AVERAGEIFS” on page 234 “COUNTIF” on page 247 “COUNTIFS” on page 248 “SUMIF” on page 197 “Specifying Conditions and Using Wildcards” on page 360 “Listing of Numeric Functions” on page 167 “Value Types” on page 36 “The Elements of Formulas” on page 15 “Using the Keyboard and Mouse to Create and Edit Formulas” on page 26 “Pasting from Examples in Help” on page 41 SUMPRODUCT The SUMPRODUCT function returns the sum of the products of corresponding numbers in one or more ranges. SUMPRODUCT(range, range…)  range:  A range of cells. range is a reference to a single range of cells containing values of any type. If string or Boolean values are included in range, they are ignored.  range…: Optionally include one or more additional ranges of cells. The ranges must all have the same dimensions. Usage Notes  The SUMPRODUCT function multiplies the corresponding numbers in each range and then sums each of the products. If only one range is specified, SUMPRODUCT returns the sum of the range. Examples =SUMPRODUCT(3, 4) returns 12. =SUMPRODUCT({1, 2}, {3, 4}) = 3 + 8 = 11. 200 Chapter 8 Numeric Functions Chapter 8 Numeric Functions 201 Related Topics For related functions and additional information, see: “Listing of Numeric Functions” on page 167 “Value Types” on page 36 “The Elements of Formulas” on page 15 “Using the Keyboard and Mouse to Create and Edit Formulas” on page 26 “Pasting from Examples in Help” on page 41 SUMSQ The SUMSQ function returns the sum of the squares of a collection of numbers. SUMSQ(num-value, num-value…)  num-value:  A number. num-value is a number value.  num-value…: Optionally include one or more additional numbers. Usage Notes  The numbers can be in individual cells, or ranges of cells, or be included directly as arguments to the function. Examples =SUMSQ(3, 4) returns 25. =SUMSQ(A1:A4) adds the squares of the list of four numbers. =SUMSQ(A1:D4) adds the squares of the 16 numbers in a square array of cells. =SUMSQ(A1:A4, 100) adds the squares of the numbers in four cells plus 100. =SQRT(SUMSQ(3, 4)) returns 5, using the Pythagorean theorem to find the length of the hypotenuse of a triangle with sides 3 and 4. Related Topics For related functions and additional information, see: “Listing of Numeric Functions” on page 167 “Value Types” on page 36 “The Elements of Formulas” on page 15 “Using the Keyboard and Mouse to Create and Edit Formulas” on page 26 “Pasting from Examples in Help” on page 41 SUMX2MY2 The SUMX2MY2 function returns the sum of the difference of the squares of corresponding values in two collections. SUMX2MY2(set-1-values, set-2-values)  set-1-values:  The first collection of values. set-1-values is a collection containing number values.  set-2-values:  The second collection of values. set-2-values is a collection containing number values. Example Given the following table: =SUMX2MY2(A1:A6,B1:B6) returns –158, the sum of the differences of the squares of the values in column A and the squares of the values in column B. The formula for the first such difference is A12 – B12. Related Topics For related functions and additional information, see: “Listing of Numeric Functions” on page 167 “Value Types” on page 36 “The Elements of Formulas” on page 15 “Using the Keyboard and Mouse to Create and Edit Formulas” on page 26 “Pasting from Examples in Help” on page 41 202 Chapter 8 Numeric Functions Chapter 8 Numeric Functions 203 SUMX2PY2 The SUMX2PY2 function returns the sum of the squares of corresponding values in two collections. SUMX2PY2(set-1-values, set-2-values)  set-1-values:  The first collection of values. set-1-values is a collection containing number values.  set-2-values:  The second collection of values. set-2-values is a collection containing number values. Example Given the following table: =SUMX2PY2(A1:A6,B1:B6) returns 640, the sum of the squares of the values in column A and the squares of the values in column B. The formula for the first such sum is A12+ B12. Related Topics For related functions and additional information, see: “Listing of Numeric Functions” on page 167 “Value Types” on page 36 “The Elements of Formulas” on page 15 “Using the Keyboard and Mouse to Create and Edit Formulas” on page 26 “Pasting from Examples in Help” on page 41 SUMXMY2 The SUMXMY2 function returns the sum of the squares of the differences between corresponding values in two collections. SUMXMY2(set-1-values, set-2-values)  set-1-values:  The first collection of values. set-1-values is a collection containing number values.  set-2-values:  The second collection of values. set-2-values is a collection containing number values. Example Given the following table: =SUMXMY2(A1:A6,B1:B6) returns 196, the sum of the squares of the values in column A and the squares of the values in column B. The formula for the first such sum is (A1 – B1)2. Related Topics For related functions and additional information, see: “Listing of Numeric Functions” on page 167 “Value Types” on page 36 “The Elements of Formulas” on page 15 “Using the Keyboard and Mouse to Create and Edit Formulas” on page 26 “Pasting from Examples in Help” on page 41 TRUNC The TRUNC function truncates a number to the specified number of digits. TRUNC(number, digits)  number:  A number. number is a number value.  digits:  An optional value specifying the number of digits you want to retain, relative to the decimal point. digits is a number value. A positive number represents digits (decimal places) to the right of the decimal point to include. A negative number specifies digits to the left of the decimal point to replace with zeros (the number of zeros at the end of the number). 204 Chapter 8 Numeric Functions Chapter 8 Numeric Functions 205 Usage Notes  If digits is omitted, it is assumed to be 0. Examples =TRUNC(1.49, 0) returns 1. =TRUNC(1.50, 0) returns 1. =TRUNC(1.23456, 3) returns 1.234. =TRUNC(1111.222, -2) returns 1100. =TRUNC(-2.2, 0) returns -2. =TRUNC(-2.8, 0) returns -2. Related Topics For related functions and additional information, see: “CEILING” on page 170 “EVEN” on page 173 “FLOOR” on page 176 “INT” on page 178 “MROUND” on page 183 “ODD” on page 185 “ROUND” on page 191 “ROUNDDOWN” on page 192 “ROUNDUP” on page 193 “More on Rounding” on page 355 “Listing of Numeric Functions” on page 167 “Value Types” on page 36 “The Elements of Formulas” on page 15 “Using the Keyboard and Mouse to Create and Edit Formulas” on page 26 “Pasting from Examples in Help” on page 41 206 The reference functions help you find data within tables and retrieve data from cells. Listing of Reference Functions iWork provides these reference functions for use with tables. Function Description “ADDRESS” (page 207) The ADDRESS function constructs a cell address string from separate row, column, and table identifiers. “AREAS” (page 209) The AREAS function returns the number of ranges the function references. “CHOOSE” (page 209) The CHOOSE function returns a value from a collection of values based on a specified index value. “COLUMN” (page 210) The COLUMN function returns the column number of the column containing a specified cell. “COLUMNS” (page 211) The COLUMNS function returns the number of columns included in a specified range of cells. “HLOOKUP” (page 211) The HLOOKUP function returns a value from a range of rows by using the top row of values to pick a column and a row number to pick a row within that column. “HYPERLINK” (page 213) The HYPERLINK function creates a clickable link that opens a webpage or new email message. “INDEX” (page 214) The INDEX function returns the value in the cell located at the intersection of the specified row and column within a range of cells. “INDIRECT” (page 216) The INDIRECT function returns the contents of a cell or range referenced by an address specified as a string. Reference Functions 9 Chapter 9 Reference Functions 207 Function Description “LOOKUP” (page 217) The LOOKUP function finds a match for a given search value in one range, and then returns the value in the cell with the same relative position in a second range. “MATCH” (page 218) The MATCH function returns the position of a value within a range. “OFFSET” (page 219) The OFFSET function returns a range of cells that is the specified number of rows and columns away from the specified base cell. “ROW” (page 221) The ROW function returns the row number of the row containing a specified cell. “ROWS” (page 221) The ROWS function returns the number of rows included in a specified range of cells. “TRANSPOSE” (page 222) The transpose function returns a vertical range of cells as a horizontal range of cells, or vice versa. “VLOOKUP” (page 223) The VLOOKUP function returns a value from a range of columns by using the left column of values to pick a row and a column number to pick a column in that row. ADDRESS The ADDRESS function constructs a cell address string from separate row, column, and table identifiers. ADDRESS(row, column, addr-type, addr-style, table)  row:  The row number of the address. row is a number value that must be in the range 1 to 65,535.  column:  The column number of the address. column is a number value that must be in the range 1 to 256.  addr-type:  An optional value specifying whether the row and column numbers are relative or absolute. all absolute (1 or omitted):  Row and column references are absolute. row absolute, column relative (2):  Row references are absolute and column references are relative. row relative, column absolute (3):  Row references are relative and column references are absolute. all relative (4):  Row and column references are relative.  addr-style:  An optional value specifying the address style. A1 (TRUE, 1, or omitted):  The address format should use letters for columns and numbers for rows. R1C1 (FALSE):  The address format isn’t supported, returning an error.  table:  An optional value specifying the name of the table. table is a string value. If the table is on another sheet, you must also include the name of the sheet. If omitted, table is assumed to be the current table on the current sheet (that is, the table where the ADDRESS function resides). Usage Notes  An address style of R1C1 is not supported and this modal argument is provided only for compatibility with other spreadsheet programs. Examples =ADDRESS(3, 5) creates the address $E$3. =ADDRESS(3, 5, 2) creates the address E$3. =ADDRESS(3, 5, 3) creates the address $E3. =ADDRESS(3, 5, 4) creates the address E3. =ADDRESS(3, 3, ,, “Sheet 2 :: Table 1”) creates the address Sheet 2 :: Table 1 :: $C$3. Related Topics For related functions and additional information, see: “Listing of Reference Functions” on page 206 “Value Types” on page 36 “The Elements of Formulas” on page 15 “Using the Keyboard and Mouse to Create and Edit Formulas” on page 26 “Pasting from Examples in Help” on page 41 208 Chapter 9 Reference Functions Chapter 9 Reference Functions 209 AREAS The AREAS function returns the number of ranges the function references. AREAS(areas)  areas:  The areas the function should count. areas is a list value. It is either a single range or more than one range separated by commas and enclosed in an additional set of parentheses; for example, AREAS((B1:B5, C10:C12)). Examples =AREAS(A1:F8) returns 1. =AREAS(C2:C8 B6:E6) returns 1. =AREAS((A1:F8, A10:F18)) returns 2. =AREAS((A1:C1, A3:C3, A5:C5)) returns 3. Related Topics For related functions and additional information, see: “Listing of Reference Functions” on page 206 “Value Types” on page 36 “The Elements of Formulas” on page 15 “Using the Keyboard and Mouse to Create and Edit Formulas” on page 26 “Pasting from Examples in Help” on page 41 CHOOSE The CHOOSE function returns a value from a collection of values based on a specified index value. CHOOSE(index, value, value…)  index:  The index of the value to be returned. index is a number value and must be greater than 0.  value:  A value. value can contain any value type.  value…: Optionally include one or more additional values. Examples =CHOOSE(4, “Monday”, “Tuesday”, “Wednesday”, “Thursday”, “Friday”, “Saturday”, “Sunday”) returns Thursday, the fourth value in the list. =CHOOSE(3, “1st”, “second”, 7, “last”) returns 7, the third value in the list. Related Topics For related functions and additional information, see: “Listing of Reference Functions” on page 206 “Value Types” on page 36 “The Elements of Formulas” on page 15 “Using the Keyboard and Mouse to Create and Edit Formulas” on page 26 “Pasting from Examples in Help” on page 41 COLUMN The COLUMN function returns the column number of the column containing a specified cell. COLUMN(cell)  cell:  An optional reference to a single table cell. cell is a reference value to a single cell that can contain any value, or be empty. If cell is omitted, as in =COLUMN(), the function returns the column number of the cell that contains the formula. Examples =COLUMN(B7) returns 2, the absolute column number of column B. =COLUMN() returns the column number of the cell that contains the function. Related Topics For related functions and additional information, see: “INDEX” on page 214 “ROW” on page 221 “Listing of Reference Functions” on page 206 “Value Types” on page 36 “The Elements of Formulas” on page 15 “Using the Keyboard and Mouse to Create and Edit Formulas” on page 26 “Pasting from Examples in Help” on page 41 210 Chapter 9 Reference Functions Chapter 9 Reference Functions 211 COLUMNS The COLUMNS function returns the number of columns included in a specified range of cells. COLUMNS(range)  range:  A range of cells. range is a reference to a single range of cells, which may contain values of any type. Usage Notes  If you select an entire table row for range, COLUMNS returns the total number of columns in the row, which changes when you resize the table. Examples =COLUMNS(B3:D10) returns 3, the number of columns in the range (columns B, C, and D). =COLUMNS(5:5) returns the total number of columns in row 5. Related Topics For related functions and additional information, see: “ROWS” on page 221 “Listing of Reference Functions” on page 206 “Value Types” on page 36 “The Elements of Formulas” on page 15 “Using the Keyboard and Mouse to Create and Edit Formulas” on page 26 “Pasting from Examples in Help” on page 41 HLOOKUP The HLOOKUP function returns a value from a range of rows by using the top row of values to pick a column and a row number to pick a row within that column. HLOOKUP(search-for, rows-range, return-row, close-match)  search-for:  The value to find. search-for can contain any value type.  rows-range:  A range of cells. range is a reference to a single range of cells which may contain values of any type.  return-row:  The row number from which to return the value. return-row is a number value and must be greater than or equal to 1 and less than or equal to the number of rows in the specified range.  close-match:  An optional value that specifies whether an exact match is required. close match (TRUE, 1, or omitted):  If there’s no exact match, select the column with the largest top-row value that is less than the search value. Wildcards can’t be used in search-for. exact match (FALSE or 0):  If there’s no exact match, return an error. Wildcards can be used in search-for. Usage Notes  HLOOKUP compares a search value to the values in the top row of a specified range. Unless an exact match is required, the column containing the largest top-row value that is less than the search value is selected. Then, the value from the specified row in that column is returned by the function. If an exact match is required and none of the top-row values match the search value, the function returns an error. Examples Given the following table: =HLOOKUP(20, A1:E4, 2) returns “E.” =HLOOKUP(39, A1:E4, 2) returns “E.” =HLOOKUP(”M”, A2:E4, 2) returns “dolor.” =HLOOKUP(”C”, A2:E3, 2) returns “lorem.” =HLOOKUP(”blandit”, A3:E4, 2) returns “5.” =HLOOKUP(”C”, A2:E4, 3, TRUE) returns “1.” =HLOOKUP(”C”, A2:E4, 3, FALSE) returns an error because the value can’t be found (there is no exact match). Related Topics For related functions and additional information, see: “LOOKUP” on page 217 “MATCH” on page 218 “VLOOKUP” on page 223 “Specifying Conditions and Using Wildcards” on page 360 “Listing of Reference Functions” on page 206 “Value Types” on page 36 212 Chapter 9 Reference Functions Chapter 9 Reference Functions 213 “The Elements of Formulas” on page 15 “Using the Keyboard and Mouse to Create and Edit Formulas” on page 26 “Pasting from Examples in Help” on page 41 HYPERLINK The HYPERLINK function creates a clickable link that opens a webpage or new email message. HYPERLINK(url, link-text)  url:  A standard universal resource locator. url is a string value that should contain a properly formatted universal resource locator string.  link-text:  An optional value that specifies the text that appears as a clickable link in the cell. link-text is a string value. If omitted, url is used as the link-text. Examples =HYPERLINK(”http://www.apple.com”, “Apple”) creates a link with the text Apple that opens the default web browser to the Apple homepage. =HYPERLINK(”mailto:janedoe@example.com?subject=Quote Request”, “Get Quote”) creates a link with the text Get Quote that opens the default email application and addresses a new message to janedoe@example.com with the subject line Quote Request. Related Topics For related functions and additional information, see: “Listing of Reference Functions” on page 206 “Value Types” on page 36 “The Elements of Formulas” on page 15 “Using the Keyboard and Mouse to Create and Edit Formulas” on page 26 “Pasting from Examples in Help” on page 41 INDEX The INDEX function returns the value in the cell located at the intersection of the specified row and column within a range of cells or an array. INDEX(range, row-index, column-index, area-index)  range:  A range of cells. range may contain values of any type. range is either a single range or more than one range separated by commas and enclosed in an additional set of parentheses. For example, ((B1:B5, C10:C12)).  row-index:  The row number of the value to be returned. row-index is a number value and must be greater than or equal to 0 and less than or equal to the number of rows in range.  column-index:  An optional value specifying the column number of the value to be returned. column-index is a number value and must be greater than or equal to 0 and less than or equal to the number of columns in range.  area-index:  An optional value specifying the area number of the value to be returned. area-index is a number value and must be greater than or equal to 1 and less than or equal to the number of areas in range. If omitted, 1 is used. Usage Notes  INDEX can return the value at the specified intersection of a two-dimensional range of values. For example, assume that cells B2:E7 contain the values. =INDEX(B2:D7, 2, 3) returns the value found at the intersection of the second row and third column (the value in cell D3).  More than one area can be specified by enclosing the ranges in an additional pair of parentheses. For example, =INDEX((B2:D5,B7:D10), 2, 3, 2) returns the value at the intersection of the second column and the third row in the second area (the value in cell D8).  INDEX can return a one-row or one-column array for another function. In this form, either row-index or column-index is required, but the other argument may be omitted. For example =SUM(INDEX(B2:D5, , 3)) returns the sum of the values in the third column (cells D2 through D5). Similarly, =AVERAGE(INDEX(B2:D5, 2)) returns the average of the values in the second row (cells B3 through D3).  INDEX can return (or “read”) the value from an array returned by an array function (a function that returns an array of values, rather than a single value). The FREQUENCY function returns an array of values, based on specified intervals. =INDEX(FREQUENCY($A$1:$F$5, $B$8:$E$8), 1) would turn the first value in the array returned by the given FREQUENCY function. Similarly =INDEX(FREQUENCY($A$1:$F$5, $B$8:$E$8), 5) would return the fifth value in the array.  The location in the range or array is specified by indicating the number of rows down and the number of columns to the right in relation to the cell in the upperleft corner of the range or array. 214 Chapter 9 Reference Functions Chapter 9 Reference Functions 215  Except when INDEX is specified as shown in the third case above, row-index can’t be omitted, and if column-index is omitted, it is assumed to be 1. Examples Given the following table: =INDEX(B2:D5,2,3) returns 22, the value in the second row and third column (cell D3). =INDEX((B2:D5,B7:D10), 2, 3, 2) returns “f”, the value in the second row and third column of the second area (cell D8). =SUM(INDEX(B2:D5, , 3)) returns 90, the sum of the values in the third column (cells D2 through D5). =AVERAGE(INDEX(B2:D5,2)) returns 12, the average of the values in the second row (cells B3 through D3). Related Topics For related functions and additional information, see: “COLUMN” on page 210 “INDIRECT” on page 216 “OFFSET” on page 219 “ROW” on page 221 “Listing of Reference Functions” on page 206 “Value Types” on page 36 “The Elements of Formulas” on page 15 “Using the Keyboard and Mouse to Create and Edit Formulas” on page 26 “Pasting from Examples in Help” on page 41 INDIRECT The INDIRECT function returns the contents of a cell or range referenced by an address specified as a string. INDIRECT(addr-string, addr-style)  addr-string:  A string representing a cell address. addr-string is a string value.  addr-style:  An optional value specifying the address style. A1 (TRUE, 1, or omitted):  The address format should use letters for columns and numbers for rows. R1C1 (FALSE):  The address format isn’t supported, returning an error. Usage Notes  The given address can be a range reference, that is, “A1:C5”, not just a reference to a single cell. If used this way, INDIRECT returns an array that can be used as an argument to another function or directly read using the INDEX function. For example, =SUM(INDIRECT(A1:C5, 1)) returns the sum of the values in the cells referenced by the addresses in cells A1 through C5.  An address style of R1C1 is not supported and this modal argument is provided only for compatibility with other spreadsheet programs. Example If cell A1 contains 99 and A20 contains A1: =INDIRECT(A20) returns 99, the contents of cell A1. Related Topics For related functions and additional information, see: “INDEX” on page 214 “Listing of Reference Functions” on page 206 “Value Types” on page 36 “The Elements of Formulas” on page 15 “Using the Keyboard and Mouse to Create and Edit Formulas” on page 26 “Pasting from Examples in Help” on page 41 216 Chapter 9 Reference Functions Chapter 9 Reference Functions 217 LOOKUP The LOOKUP function finds a match for a given search value in one range, and then returns the value in the cell with the same relative position in a second range. LOOKUP(search-for, search-where, result-values)  search-for:  The value to find. search-value can contain any value type.  search-where:  The collection containing the values to be searched. search-where is a collection containing any value type.  result-values:  An optional collection containing the value to be returned based on the search. result-values is a collection containing any value type. Usage Notes  Both search-where and result-values are normally included and are specified as either multiple columns or multiple rows, but not both (one dimensional). However, for compatibility with other spreadsheet applications, search-where can be specified as both multiple columns and multiple rows (two dimensional) and result-values can be omitted.  If search-where is two dimensional and result-values is specified, the topmost row or leftmost column, whichever contains more cells, is searched and the corresponding value from result-values is returned.  If search-where is two dimensional and result-values is omitted, the corresponding value in the last row (if the number of columns included in the range is larger) or column (if the number of rows included in the range is larger) is returned. Examples Given the following table: =LOOKUP(”C”, A1:F1, A2:F2) returns 30. =LOOKUP(40, A2:F2, A1:F1) returns D. =LOOKUP(”B”, A1:C1, D2:F2) returns 50. =LOOKUP(”D”,A1:F2) returns 40, the value in the last row that corresponds to “D.” Related Topics For related functions and additional information, see: “HLOOKUP” on page 211 “MATCH” on page 218 “VLOOKUP” on page 223 “Listing of Reference Functions” on page 206 “Value Types” on page 36 “The Elements of Formulas” on page 15 “Using the Keyboard and Mouse to Create and Edit Formulas” on page 26 “Pasting from Examples in Help” on page 41 MATCH The MATCH function returns the position of a value within a range. MATCH(search-for, search-where, matching-method)  search-for:  The value to find. search-for can contain any value type.  search-where:  The collection containing the values to be searched. search-where is a collection containing any value type.  matching-method:  An optional value specifying how value matching is performed. find largest value (1 or omitted): Find the cell with the largest value less than or equal to search-for. Wildcards can’t be used in search-for. find value (0): Find the first cell with a value that exactly matches search-for. Wildcards can be used in search-for. find smallest value (–1): Find the cell with the smallest value greater than or equal to search-for. Wildcards can’t be used in search-for. Usage Notes  MATCH works only on a range that is part of a single row or column; you can’t use it to search a two-dimensional collection.  Cell numbering starts with 1 at the top or left cell for vertical and horizontal ranges, respectively. Searches are performed top-to-bottom or left-to-right.  When searching for text, case is ignored. 218 Chapter 9 Reference Functions Chapter 9 Reference Functions 219 Examples Given the following table: =MATCH(40, A1:A5) returns 4. =MATCH(40, E1:E5) returns 1. =MATCH(35, E1:E5, 1) returns 3 (30 is the largest value less than or equal to 35). =MATCH(35, E1:E5, -1) returns 1 (40 is the smallest value greater than or equal to 35). =MATCH(35, E1:E5, 0) displays an error (no exact match can be found). =MATCH(”lorem”, C1:C5) returns 1 (“lorem” appears in the first cell of the range). =MATCH(”*x”,C1:C5,0) returns 3 (“lorex”, which ends with an “x”, appears in the third cell of the range). Related Topics For related functions and additional information, see: “LOOKUP” on page 217 “Specifying Conditions and Using Wildcards” on page 360 “Listing of Reference Functions” on page 206 “Value Types” on page 36 “The Elements of Formulas” on page 15 “Using the Keyboard and Mouse to Create and Edit Formulas” on page 26 “Pasting from Examples in Help” on page 41 OFFSET The OFFSET function returns a range of cells that is the specified number of rows and columns away from the specified base cell. OFFSET(base, row-offset, column-offset, rows, columns)  base:  The address of the cell from which the offsets are measured. base is a reference value.  row-offset: The number of rows from the base cell to the target cell. row-offset is a number value. 0 means the target cell is in the same row as the base cell. A negative number means the target is in a row above the base.  column-offset: The number of columns from the base cell to the target cell. columnoffset is a number value. 0 means the target cell is in the same column as the base cell. A negative number means the target is in a column to the left of the base.  rows:  An optional value specifying the number of rows to return starting with the offset location.rows is a number value.  columns:  An optional value specifying the number of columns to return starting with the offset location.columns is a number value. Usage Notes  OFFSET can return an array for use with another function. For example, assume you have entered into A1, A2, and A3, the base cell, the number of rows, and the number of columns, respectively, that you wish to have summed. The sum could be found using =SUM(OFFSET(INDIRECT(A1),0,0,A2,A3)). Examples =OFFSET(A1, 5, 5) returns the value in cell F6, the cell five columns to the right and five rows below cell A1. =OFFSET(G33, 0, -1) returns the value in the cell to the left of G33, the value in F33. =SUM(OFFSET(A7, 2, 3, 5, 5)) returns the sum of the values in cells D9 through H13, the five rows and five columns that begin two rows to the right of and three columns below cell A7. Assume that you have entered 1 in cell D7, 2 in cell D8, 3 in cell D9, 4 in cell E7, 5 in cell E8, and 6 in cell E9. =OFFSET(D7,0,0,3,1) entered in cell B6 returns an error, since the 3 rows and 1 column returned (the range D7:D9) does not have one single intersection with B6 (it has none). =OFFSET(D7,0,0,3,1) entered in cell D4 returns an error, since the 3 rows and 1 column returned (the range D7:D9) does not have one single intersection with B6 (it has three). =OFFSET(D7,0,0,3,1) entered in cell B8 returns 2, since the 3 rows and 1 column returned (the range D7:D9) has one single intersection with B8 (cell D8, which contains 2). =OFFSET(D7:D9,0,1,3,1) entered in cell B7 returns 4, since the 3 rows and 1 column returned (the range E7:E9) has one single intersection with B7 (cell E7, which contains 4). Related Topics For related functions and additional information, see: “COLUMN” on page 210 “ROW” on page 221 “Listing of Reference Functions” on page 206 “Value Types” on page 36 “The Elements of Formulas” on page 15 “Using the Keyboard and Mouse to Create and Edit Formulas” on page 26 “Pasting from Examples in Help” on page 41 220 Chapter 9 Reference Functions Chapter 9 Reference Functions 221 ROW The ROW function returns the row number of the row containing a specified cell. ROW(cell)  cell:  An optional reference to a single table cell. cell is a reference value to a single cell that can contain any value, or be empty. If cell is omitted, as in =ROW(), the function returns the row number of the cell that contains the formula. Examples =ROW(B7) returns 7, the number of row 7. =ROW() returns the absolute row number of the cell containing the function. Related Topics For related functions and additional information, see: “COLUMN” on page 210 “INDEX” on page 214 “Listing of Reference Functions” on page 206 “Value Types” on page 36 “The Elements of Formulas” on page 15 “Using the Keyboard and Mouse to Create and Edit Formulas” on page 26 “Pasting from Examples in Help” on page 41 ROWS The ROWS function returns the number of rows included in a specified range of cells. ROWS(range)  range:  A range of cells. range is a reference to a single range of cells, which may contain values of any type. Usage Notes  If you select an entire table column for range, ROWS returns the total number of rows in the column, which changes when you resize the table. Examples =ROWS(A11:D20) returns 10, the number of rows from 11 through 20. =ROWS(D:D) returns the total number of rows in column D. Related Topics For related functions and additional information, see: “COLUMNS” on page 211 “Listing of Reference Functions” on page 206 “Value Types” on page 36 “The Elements of Formulas” on page 15 “Using the Keyboard and Mouse to Create and Edit Formulas” on page 26 “Pasting from Examples in Help” on page 41 TRANSPOSE The transpose function returns a vertical range of cells as a horizontal range of cells, or vice versa. TRANSPOSE(range-array)  range-array:  The collection containing the values to be transposed. range-array is a collection containing any type of value. Usage Notes  TRANSPOSE returns an array containing the transposed values. This array will contain a number of rows equal to the number of columns in the original range and a number of columns equal to the number of rows in the original range. The values in this array can be determined (“read”) using the INDEX function. Examples Given the following table: row/column A B C D E 1 5 15 10 9 7 2 11 96 29 11 23 3 37 56 23 1 12 222 Chapter 9 Reference Functions Chapter 9 Reference Functions 223 =INDEX(TRANSPOSE($A$1:$E$3),1,1) returns 5, the value in row 1. column 1 of the transposed range (was row 1, column A, of the original array). =INDEX(TRANSPOSE($A$1:$E$3),1,2) returns 11, the value in row 1, column 2 of the transposed range (was row 2, column A, of the original range). =INDEX(TRANSPOSE($A$1:$E$3),1,3) returns 37, the value in row 1, column 3 of the transposed range (was row 3, column A, of the original range). =INDEX(TRANSPOSE($A$1:$E$3),2,1 returns 15, the value in row 2, column 1 of the transposed range (was row 1, column 2, of the original range). =INDEX(TRANSPOSE($A$1:$E$3),3,2) returns 29, the value in row 3, column 2 of the transposed range (was row 2, column C, of the original range). =INDEX(TRANSPOSE($A$1:$E$3),4,3) returns 1, the value in row 4, column 3 of the transposed range (was row 3, column D, of the original range). Related Topics For related functions and additional information, see: “Listing of Reference Functions” on page 206 “Value Types” on page 36 “The Elements of Formulas” on page 15 “Using the Keyboard and Mouse to Create and Edit Formulas” on page 26 “Pasting from Examples in Help” on page 41 VLOOKUP The VLOOKUP function returns a value from a range of columns by using the left column of values to pick a row and a column number to pick a column in that row. VLOOKUP(search-for, columns-range, return-column, close-match)  search-for:  The value to find. search-value can contain any value type.  columns-range:  A range of cells. range is a reference to a single range of cells, which may contain values of any type.  return-column:  A number that specifies the relative column number of the cell from which to return the value. return-column is a number value. The leftmost column in the range is column 1.  close-match:  An optional value that determines whether an exact match is required. close match (TRUE, 1, or omitted):  If there’s no exact match, select the column with the largest top-row value that is less than the search value. Wildcards can’t be used in search-for. exact match (FALSE or 0):  If there’s no exact match, return an error. Wildcards can be used in search-for. Usage Notes  VLOOKUP compares a search value to the values in the leftmost column of a specified range. Unless an exact match is required, the row containing the largest left-column value that is less than the search value is selected. Then, the value from the specified column in that row is returned by the function. If an exact match is required and none of the leftmost-column values match the search value, the function returns an error. Examples Given the following table: =VLOOKUP(20, B2:E6, 2) returns E. =VLOOKUP(21, B2:E6, 2) returns E. =VLOOKUP(”M”, C2:E6, 2) returns dolor. =VLOOKUP(”blandit”, D2:E6, 2) returns 5. =VLOOKUP(21, B2:E6, 2, FALSE) returns an error because no value in the left column exactly matches 21. Related Topics For related functions and additional information, see: “HLOOKUP” on page 211 “LOOKUP” on page 217 “MATCH” on page 218 “Specifying Conditions and Using Wildcards” on page 360 “Listing of Reference Functions” on page 206 “Value Types” on page 36 “The Elements of Formulas” on page 15 “Using the Keyboard and Mouse to Create and Edit Formulas” on page 26 “Pasting from Examples in Help” on page 41 224 Chapter 9 Reference Functions 225 The statistical functions help you manipulate and analyze collections of data using a variety of measures and statistical techniques. Listing of Statistical Functions iWork provides these statistical functions for use with tables. Function Description “AVEDEV” (page 230) The AVEDEV function returns the average of the difference of a collection of numbers from their average (arithmetic mean). “AVERAGE” (page 231) The AVERAGE function returns the average (arithmetic mean) of a collection of numbers. “AVERAGEA” (page 232) The AVERAGEA function returns the average (arithmetic mean) of a collection of values, including text and Boolean values. “AVERAGEIF” (page 233) The AVERAGEIF function returns the average (arithmetic mean) of the cells in a range that meet a given condition. “AVERAGEIFS” (page 234) The AVERAGEIFS function returns the average (arithmetic mean) of the cells in a collection that meet all the given conditions. “BETADIST” (page 236) The BETADIST function returns the cumulative beta distribution probability value. Statistical Functions 10 Function Description “BETAINV” (page 237) The BETAINV function returns the inverse of the given cumulative beta distribution probability value. “BINOMDIST” (page 238) The BINOMDIST function returns the individual term binomial distribution probability of the specified form. “CHIDIST” (page 239) The CHIDIST function returns the one-tailed probability of the chi-square distribution. “CHIINV” (page 239) The CHIINV function returns the inverse of the one-tailed probability of the chi-square distribution. “CHITEST” (page 240) The CHITEST function returns the value from the chi-square distribution for the given data. “CONFIDENCE” (page 242) The CONFIDENCE function returns a value for creating a statistical confidence interval for a sample from a population with a known standard deviation. “CORREL” (page 242) The CORREL function returns the correlation between two collections using linear regression analysis. “COUNT” (page 244) The COUNT function returns the number of its arguments that contain numbers, numeric expressions, or dates. “COUNTA” (page 245) The COUNTA function returns the number of its arguments that are not empty. “COUNTBLANK” (page 246) The COUNTBLANK function returns the number of cells in a range that are empty. “COUNTIF” (page 247) The COUNTIF function returns the number of cells in a range that satisfy a given condition. “COUNTIFS” (page 248) The COUNTIFS function returns the number of cells in one or more ranges that satisfy given conditions (one condition per range). “COVAR” (page 250) The COVAR function returns the covariance of two collections. “CRITBINOM” (page 252) The CRITBINOM function returns the smallest value for which the cumulative binomial distribution is greater than or equal to a given value. “DEVSQ” (page 253) The DEVSQ function returns the sum of the squares of deviations of a collection of numbers from their average (arithmetic mean). 226 Chapter 10 Statistical Functions Chapter 10 Statistical Functions 227 Function Description “EXPONDIST” (page 253) The EXPONDIST function returns the exponential distribution of the specified form. “FDIST” (page 254) The FDIST function returns the F probability distribution. “FINV” (page 255) The FINV function returns the inverse of the F probability distribution. “FORECAST” (page 256) The FORECAST function returns the forecasted y value for a given x value based on sample values using linear regression analysis. “FREQUENCY” (page 257) The FREQUENCY function returns an array of how often data values occur within a range of interval values. “GAMMADIST” (page 259) The GAMMADIST function returns the gamma distribution in the specified form. “GAMMAINV” (page 260) The GAMMAINV function returns the inverse gamma cumulative distribution. “GAMMALN” (page 260) The GAMMALN function returns the natural logarithm of the gamma function, G(x). “GEOMEAN” (page 261) The GEOMEAN function returns the geometric mean. “HARMEAN” (page 262) The HARMEAN function returns the harmonic mean. “INTERCEPT” (page 262) The INTERCEPT function returns the y-intercept of the best-fit line for the collection using linear regression analysis. “LARGE” (page 264) The LARGE function returns the nth-largest value within a collection. The largest value is ranked number 1. “LINEST” (page 265) The LINEST function returns an array of the statistics for a straight line that best fits the given data using the least squares method. “LOGINV” (page 268) The LOGINV function returns the inverse of the log-normal cumulative distribution function of x. “LOGNORMDIST” (page 269) The LOGNORMDIST function returns the lognormal distribution. “MAX” (page 270) The MAX function returns the largest number in a collection. Function Description “MAXA” (page 270) The MAXA function returns the largest number in a collection of values that may include text and Boolean values. “MEDIAN” (page 271) The MEDIAN function returns the median value in a collection of numbers. The median is the value where half the numbers in the collection are less than the median and half are greater. “MIN” (page 272) The MIN function returns the smallest number in a collection. “MINA” (page 273) The MINA function returns the smallest number in a collection of values that may include text and Boolean values. “MODE” (page 274) The MODE function returns the most frequently occurring value in a collection of numbers. “NEGBINOMDIST” (page 275) The NEGBINOMDIST function returns the negative binomial distribution. “NORMDIST” (page 276) The NORMDIST function returns the normal distribution of the specified function form. “NORMINV” (page 277) The NORMINV function returns the inverse of the cumulative normal distribution. “NORMSDIST” (page 277) The NORMSDIST function returns the standard normal distribution. “NORMSINV” (page 278) The NORMSINV function returns the inverse of the cumulative standard normal distribution. “PERCENTILE” (page 279) The PERCENTILE function returns the value within a collection that corresponds to a particular percentile. “PERCENTRANK” (page 280) The PERCENTRANK function returns the rank of a value in a collection as a percentage of the collection. “PERMUT” (page 281) The PERMUT function returns the number of permutations for a given number of objects that can be selected from a total number of objects. “POISSON” (page 282) The POISSON function returns the probability that a specific number of events will occur using the Poisson distribution. “PROB” (page 282) The PROB function returns the probability of a range of values if you know the probabilities of the individual values. 228 Chapter 10 Statistical Functions Chapter 10 Statistical Functions 229 Function Description “QUARTILE” (page 284) The QUARTILE function returns the value for the specified quartile of a given collection. “RANK” (page 285) The RANK function returns the rank of a number within a range of numbers. “SLOPE” (page 287) The SLOPE function returns the slope of the bestfit line for the collection using linear regression analysis. “SMALL” (page 288) The SMALL function returns the nth-smallest value within a range. The smallest value is ranked number 1. “STANDARDIZE” (page 289) The STANDARDIZE function returns a normalized value from a distribution characterized by a given mean and standard deviation. “STDEV” (page 290) The STDEV function returns the standard deviation, a measure of dispersion, of a collection of values based on their sample (unbiased) variance. “STDEVA” (page 291) The STDEVA function returns the standard deviation, a measure of dispersion, of a collection of values that may include text and Boolean values, based on the sample (unbiased) variance. “STDEVP” (page 293) The STDEVP function returns the standard deviation, a measure of dispersion, of a collection of values based on their population (true) variance. “STDEVPA” (page 294) The STDEVPA function returns the standard deviation, a measure of dispersion, of a collection of values that may include text and Boolean values, based on the population (true) variance. “TDIST” (page 296) The TDIST function returns the probability from the Student’s t-distribution. “TINV” (page 297) The TINV functions returns the t value (a function of the probability and degrees of freedom) from the Student’s t-distribution. “TTEST” (page 297) The TTEST function returns the probability associated with a Student’s t-test, based on the t-distribution function. “VAR” (page 298) The VAR function returns the sample (unbiased) variance, a measure of dispersion, of a collection of values. Function Description “VARA” (page 300) The VARA function returns the sample (unbiased) variance, a measure of dispersion, of a collection of values, including text and Boolean values. “VARP” (page 302) The VARP function returns the population (true) variance, a measure of dispersion, of a collection of values. “VARPA” (page 303) The VARPA function returns the sample (unbiased) variance, a measure of dispersion, of a collection of values, including text and Boolean values. “ZTEST” (page 305) The ZTEST function returns the one-tailed probability value of the Z-test. AVEDEV The AVERAGE function returns the average (arithmetic mean) of a collection of numbers. AVEDEV(num-date-dur, num-date-dur…)  num-date-dur:  A value. num-date-dur is a number value, a date/time value, or a duration value.  num-date-dur…: Optionally include one or more additional values. If more than one num-date-dur value is specified, all must be of the same type. Usage Notes  AVEDEV divides the sum of the numbers by the number of numbers to get the average. The difference (absolute value) between the average and each number is summed and divided by the number of numbers.  If num-date-dur contains date/time values, a duration value is returned. Examples =AVEDEV(2, 2, 2, 4, 4, 4) returns 1. =AVEDEV(2, 2, 2, 2, 3, 3, 3, 3, 4, 4, 4, 4) returns 0.6666667. Related Topics For related functions and additional information, see: “Listing of Statistical Functions” on page 225 “Value Types” on page 36 “The Elements of Formulas” on page 15 “Using the Keyboard and Mouse to Create and Edit Formulas” on page 26 “Pasting from Examples in Help” on page 41 230 Chapter 10 Statistical Functions Chapter 10 Statistical Functions 231 AVERAGE The AVERAGE function returns the average (arithmetic mean) of a collection of numbers. AVERAGE(num-date-dur, num-date-dur…)  num-date-dur:  A value. num-date-dur is a number value, a date/time value, or a duration value.  num-date-dur…: Optionally include one or more additional values. If more than one num-date-dur value is specified, all must be of the same type. Usage Notes  AVERAGE divides the sum of the numbers by the number of numbers.  A string or Boolean value included in a referenced cell is ignored. If you wish to include string and Boolean values in the average, use the AVERAGEA function.  A reference included as an argument to the function can be either to a single cell or to a range of cells. Examples =AVERAGE(4, 4, 4, 6, 6, 6) returns 5. =AVERAGE(2, 2, 2, 2, 3, 3, 3, 3, 4, 4, 4, 4) returns 3. Related Topics For related functions and additional information, see: “AVERAGEA” on page 232 “AVERAGEIF” on page 233 “AVERAGEIFS” on page 234 “Listing of Statistical Functions” on page 225 “Value Types” on page 36 “The Elements of Formulas” on page 15 “Using the Keyboard and Mouse to Create and Edit Formulas” on page 26 “Pasting from Examples in Help” on page 41 AVERAGEA The AVERAGEA function returns the average (arithmetic mean) of a collection of values, including text and Boolean values. AVERAGEA(value, value…)  value:  A value. value can contain any value type.  value…: Optionally include one or more additional values. All numeric values must be of the same type. You cannot mix numbers, dates, and duration values. Usage Notes  A string value included in a referenced cell is given a value of 0. A Boolean FALSE is assigned a value of 0 and a Boolean TRUE is assigned a value of 1.  A reference included as an argument to the function can be either to a single cell or to a range of cells.  For a collection containing only numbers, AVERAGEA returns the same result as the AVERAGE function, which ignores cells that don’t contain numbers. Examples =AVERAGEA(A1:A4) returns 2.5 if cells A1 through A4 contain 4, a, 6, b. The text values are counted as zeros in the sum of 10 and included in the count of values (4). Compare with =AVERAGE(A1:A4), which ignores the text values completely for a sum of 10, a count of 2, and an average of 5. =AVERAGEA(A1:A4) returns 4 if cells A1 through A4 contain 5, a, TRUE, 10. The text value counts zero and TRUE counts 1 for a sum of 16 and a count of 4. =AVERAGEA(A1:A4) returns 0.25 if cells A1 through A4 contain FALSE, FALSE, FALSE, TRUE. Each FALSE counts zero and TRUE counts 1 for a sum of 1 and a count of 4. Related Topics For related functions and additional information, see: “AVERAGE” on page 231 “AVERAGEIF” on page 233 “AVERAGEIFS” on page 234 “Listing of Statistical Functions” on page 225 “Value Types” on page 36 “The Elements of Formulas” on page 15 “Using the Keyboard and Mouse to Create and Edit Formulas” on page 26 “Pasting from Examples in Help” on page 41 232 Chapter 10 Statistical Functions Chapter 10 Statistical Functions 233 AVERAGEIF The AVERAGEIF function returns the average (arithmetic mean) of the cells in a range that meet a given condition. AVERAGEIF(test-values, condition, avg-values)  test-values:  A collection containing values to be tested. test-values is a collection containing any type of value.  condition:  An expression that results in a logical TRUE or FALSE. condition is an expression that can contain anything as long as the result from comparing condition to a value in test-values can be expressed as a Boolean value of TRUE or FALSE.  avg-values:  An optional collection containing the values to be averaged. avg-values is a reference to a single range of cells or an array, which may contain only numbers, numeric expressions, or Boolean values. Usage Notes  Each value is compared to condition. If the value meets the conditional test, the corresponding value in avg-values is included in the average.  avg-values and test-values (if specified) must be the same size.  If avg-values is omitted, test-values is used for avg-values.  If avg-values is omitted or is the same as test-values, test-values can contain only numbers, numeric expressions, or Boolean values. Examples Given the following table: =AVERAGEIF(A2:A13, “<40”, D2:D13) returns approximately 57429, the average income of people under the age of forty. =AVERAGEIF(B2:B13, “=F”, D2:D13) returns 62200, the average income of females (indicated by an “F” in column B). =AVERAGEIF(C2:C13, “S”, D2:D13) returns 55800, the average income of people who are single (indicated by an “S” in column C). =AVERAGEIF(A2:A13, “>=40”, D2:D13) returns 75200, the average income of people who are forty or older. Related Topics For related functions and additional information, see: “AVERAGE” on page 231 “AVERAGEA” on page 232 “AVERAGEIFS” on page 234 “Specifying Conditions and Using Wildcards” on page 360 “Listing of Statistical Functions” on page 225 “Value Types” on page 36 “The Elements of Formulas” on page 15 “Using the Keyboard and Mouse to Create and Edit Formulas” on page 26 “Pasting from Examples in Help” on page 41 AVERAGEIFS The AVERAGEIFS function returns the average (arithmetic mean) of the cells in a given range where one or more ranges meet one or more related conditions. AVERAGEIFS(avg-values, test-values, condition, test-values…, condition…)  avg-values:  A collection containing the values to be averaged. avg-values is a reference to a single range of cells or an array, which may contain only numbers, numeric expressions, or Boolean values.  test-values:  A collection containing values to be tested. test-values is a collection containing any type of value.  condition:  An expression that results in a logical TRUE or FALSE. condition is an expression that can contain anything as long as the result from comparing condition to a value in test-values can be expressed as a Boolean value of TRUE or FALSE.  test-values…: Optionally include one or more additional collections containing values to be tested. Each test-values collection must be followed immediately with a condition expression. This pattern of test-values, condition can be repeated as many times as needed.  condition…: If an optional collection of test-values is included, an expression that results in a logical TRUE or FALSE. There must be one condition following each test-values collection; therefore, this function will always have an odd number of arguments. 234 Chapter 10 Statistical Functions Chapter 10 Statistical Functions 235 Usage Notes  For each of the test-values and condition pairs, the corresponding (same position within range or array) value is compared to the conditional test. If all of the conditional tests are met, the corresponding value in avg-values is included in the average.  avg-values and all test-values collections must be the same size. Examples Given the following table: =AVERAGEIFS(D2:D13,A2:A13,”<40”,B2:B13,”=M”) returns 56000, the average income of males (indicated by an “M” in column B) under the age of forty. =AVERAGEIFS(D2:D13,A2:A13,”<40”,B2:B13,”=M”,C2:C13,”=S”) returns 57000, the average income of males who are single (indicated by an “S” in column C) under the age of forty. =AVERAGEIFS(D2:D13,A2:A13,”<40”,B2:B13,”=M”,C2:C13,”=M”) returns 55000, the average income of males who are married (indicated by an “M” in column C) under the age of forty. =AVERAGEIFS(D2:D13,A2:A13,”<40”,B2:B13,”=F”) returns approximately 59333, the average income of females (indicated by an “F” in column B) who are under the age of forty. Related Topics For related functions and additional information, see: “AVERAGE” on page 231 “AVERAGEA” on page 232 “AVERAGEIF” on page 233 “Specifying Conditions and Using Wildcards” on page 360 “Listing of Statistical Functions” on page 225 “Value Types” on page 36 “The Elements of Formulas” on page 15 “Using the Keyboard and Mouse to Create and Edit Formulas” on page 26 “Pasting from Examples in Help” on page 41 BETADIST The BETADIST function returns the cumulative beta distribution probability value. BETADIST(x-value, alpha, beta, x-lower, x-upper)  x-value:  The x value at which you want to evaluate the function. x-value is a number value and must be in the range 0 to 1.  alpha:  One of the shape parameters of the distribution. alpha is a number value and must be greater than 0.  beta:  One of the shape parameters of the distribution. beta is a number value and must be greater than 0.  x-lower:  An optional lower limit or bound for the specified x value or probability. x-lower is a number value and must be less than or equal to the specified x value or probability. If omitted, 0 is used.  x-upper:  An optional upper limit or bound for the specified x value or probability. x-upper is a number value and must be greater than or equal to the specified x value or probability. If omitted, 1 is used. Examples =BETADIST(0.5, 1, 2, 0.3, 2) returns 0.221453287197232. =BETADIST(1, 1, 2, 0, 1) returns 1. =BETADIST(0.1, 2, 2, 0, 2) returns 0.00725. Related Topics For related functions and additional information, see: “BETAINV” on page 237 “Listing of Statistical Functions” on page 225 “Value Types” on page 36 “The Elements of Formulas” on page 15 “Using the Keyboard and Mouse to Create and Edit Formulas” on page 26 “Pasting from Examples in Help” on page 41 236 Chapter 10 Statistical Functions Chapter 10 Statistical Functions 237 BETAINV The BETAINV function returns the inverse of the given cumulative beta distribution probability value. BETAINV(probability, alpha, beta, x-lower, x-upper)  probability:  A probability associated with the distribution. probability is a number value and must be greater than 0 and less than 1.  alpha:  One of the shape parameters of the distribution. alpha is a number value and must be greater than 0.  beta:  One of the shape parameters of the distribution. beta is a number value and must be greater than 0.  x-lower:  An optional lower limit or bound for the specified x value or probability. x-lower is a number value and must be less than or equal to the specified x value or probability. If omitted, 0 is used.  x-upper:  An optional upper limit or bound for the specified x value or probability. x-upper is a number value and must be greater than or equal to the specified x value or probability. If omitted, 1 is used. Examples =BETAINV(0.5, 1, 2, 0.3, 2) returns 0.797918471982869. =BETAINV(0.99, 1, 2, 0, 1) returns 0.9. =BETAINV(0.1, 2, 2, 0, 2) returns 0.391600211318183. Related Topics For related functions and additional information, see: “BETADIST” on page 236 “Listing of Statistical Functions” on page 225 “Value Types” on page 36 “The Elements of Formulas” on page 15 “Using the Keyboard and Mouse to Create and Edit Formulas” on page 26 “Pasting from Examples in Help” on page 41 BINOMDIST The BINOMDIST function returns the individual term binomial distribution probability of the specified form. BINOMDIST(success-num, trials, prob-success, form-type)  success-num:  The number of successful trials or tests. success-num is a number value that must be greater than or equal to 1 and less than or equal to trials.  trials:  The total number of trials or tests. trials is a number value that must be greater than or equal to 0.  prob-success:  The probability of success for each trial or test. prob-success is a number value that must be greater than or equal to 0 and less than or equal to 1.  form-type:  A value that indicates which form of the exponential function to provide. cumulative form (TRUE or 1):  Return the value of the cumulative distribution function form (that the specified number or fewer successes or events will occur). probability mass form (FALSE or 0):  Return the value of the probability mass function form (that there are exactly the specified number of successes or events). Usage Notes  The BINOMDIST is appropriate for problems with a fixed number of independent trials that have a constant probability of success and where the outcomes of a trial are only success or failure. Examples =BINOMDIST(3, 98, 0.04, 1) returns 0.445507210083272 (cumulative distribution form). =BINOMDIST(3, 98, 0.04, 0) returns 0.201402522366024 (probability mass form). Related Topics For related functions and additional information, see: “CRITBINOM” on page 252 “NEGBINOMDIST” on page 275 “PERMUT” on page 281 “PROB” on page 282 “Listing of Statistical Functions” on page 225 “Value Types” on page 36 “The Elements of Formulas” on page 15 “Using the Keyboard and Mouse to Create and Edit Formulas” on page 26 “Pasting from Examples in Help” on page 41 238 Chapter 10 Statistical Functions Chapter 10 Statistical Functions 239 CHIDIST The CHIDIST function returns the one-tailed probability of the chi-square distribution. CHIDIST(non-neg-x-value, degrees-freedom)  non-neg-x-value:  The value at which you want to evaluate the function. non-neg-xvalue is a number value that must be greater than or equal to 0.  degrees-freedom:  Degrees of freedom. degrees-freedom is a number value and must be greater than or equal to 1. Examples =CHIDIST(5, 2) returns 0.0820849986238988. =CHIDIST(10, 10) returns 0.440493285065212. =CHIDIST(5, 1) returns 0.0253473186774683. Related Topics For related functions and additional information, see: “CHIINV” on page 239 “CHITEST” on page 240 “Listing of Statistical Functions” on page 225 “Value Types” on page 36 “The Elements of Formulas” on page 15 “Using the Keyboard and Mouse to Create and Edit Formulas” on page 26 “Pasting from Examples in Help” on page 41 CHIINV The CHIINV function returns the inverse of the one-tailed probability of the chi-square distribution. CHIINV(probability, degrees-freedom)  probability:  A probability associated with the distribution. probability is a number value and must be greater than 0 and less than 1.  degrees-freedom:  Degrees of freedom. degrees-freedom is a number value and must be greater than or equal to 1. Examples =CHIINV(0.5, 2) returns 1.38629436111989. =CHIINV(0.1, 10) returns 15.9871791721053. =CHIINV(0.5, 1) returns 0.454936423119572. Related Topics For related functions and additional information, see: “CHIDIST” on page 239 “CHITEST” on page 240 “Listing of Statistical Functions” on page 225 “Value Types” on page 36 “The Elements of Formulas” on page 15 “Using the Keyboard and Mouse to Create and Edit Formulas” on page 26 “Pasting from Examples in Help” on page 41 CHITEST The CHITEST function returns the value from the chi-square distribution for the given data. CHITEST(actual-values, expected-values)  actual-values:  The collection containing the actual values. actual-values is a collection containing number values.  expected-values:  The collection containing the expected values. expected-values is a collection containing number values. Usage Notes  The degrees of freedom relating to the value returned is the number of rows in actual-values minus 1.  Each expected value is computed by multiplying the sum of the row by the sum of the column and dividing by the grand total. 240 Chapter 10 Statistical Functions Chapter 10 Statistical Functions 241 Example Given the following table: =CHITEST(A2:B6,A9:B13) returns 5.91020074984668E-236. Each expected value is computed by multiplying the sum of the row by the sum of the column and dividing by the grand total. The formula for the first expected value (cell A9) is =SUM(A$2:B$2)*SUM($A2:$A6)/SUM($A$2:$B$6). This formula can be extended to cell B9 and then A9:B9 extended to A13:B13 to complete the expected values. The resulting formula for the final expected value (cell B13) is =SUM(B$2:C$2)*SUM($A6:$A11)/SUM($A$2:$B$6). Related Topics For related functions and additional information, see: “CHIDIST” on page 239 “CHIINV” on page 239 “Listing of Statistical Functions” on page 225 “Value Types” on page 36 “The Elements of Formulas” on page 15 “Using the Keyboard and Mouse to Create and Edit Formulas” on page 26 “Pasting from Examples in Help” on page 41 CONFIDENCE The CONFIDENCE function returns a value for creating a statistical confidence interval for a sample from a population with a known standard deviation. CONFIDENCE(alpha, stdev, sample-size)  alpha:  The probability that the true population value lies outside the interval. alpha is a number value and must be greater than or equal to 1. Subtracting the confidence interval from 1 yields the alpha.  stdev:  The standard deviation of the population. stdev is a number value and must be greater than 0.  sample-size:  The size of the sample. sample-size is a number value and must be greater than 0. Usage Notes  The confidence estimate assumes that values in the sample are normally distributed. Examples =CONFIDENCE(0.05, 1, 10) returns 0.62. If the mean of the sample values is 100, then with 95% confidence the population mean falls in the range 99.38–100.62. =CONFIDENCE(0.1, 1, 10) returns 0.52. If the mean of the sample values is 100, then with 90% confidence the population mean falls in the range 99.48–100.52. =CONFIDENCE(0.05, 1, 20) returns 0.44. =CONFIDENCE(0.05, 1, 30) returns 0.36. =CONFIDENCE(0.05, 1, 40) returns 0.31. Related Topics For related functions and additional information, see: “STDEV” on page 290 “Listing of Statistical Functions” on page 225 “Value Types” on page 36 “The Elements of Formulas” on page 15 “Using the Keyboard and Mouse to Create and Edit Formulas” on page 26 “Pasting from Examples in Help” on page 41 CORREL The CORREL function returns the correlation between two collections using linear regression analysis. 242 Chapter 10 Statistical Functions Chapter 10 Statistical Functions 243 CORREL(y-values, x-values)  y-values:  The collection containing the y (dependent) values. y-values is a collection that can contain number, date/time, or duration values. All values must be of the same type.  x-values:  The collection containing the x (independent) values. x-values is a collection that can contain number, date/time, or duration values. All values must be of the same type. Usage Notes  y-values and x-values must have the same dimensions.  If text or Boolean values are included in the collections, they are ignored. Example In this example, the CORREL function is used to determine how closely related the price of heating oil (column A) is to the temperature that this hypothetical homeowner has set on the thermostat. =CORREL(A2:A11, B2:B11) evaluates to approximately -0.9076, indicating a close correlation (as prices rose, the thermostat was lowered). Related Topics For related functions and additional information, see: “COVAR” on page 250 “Survey Results Example” on page 362 “Listing of Statistical Functions” on page 225 “Value Types” on page 36 “The Elements of Formulas” on page 15 “Using the Keyboard and Mouse to Create and Edit Formulas” on page 26 “Pasting from Examples in Help” on page 41 COUNT The COUNT function returns the number of its arguments that contain numbers, numeric expressions, or dates. COUNT(value, value…)  value:  A value. value can contain any value type.  value…: Optionally include one or more additional values. Usage Notes  To count any cell that contains any type of value (that is, any cell that is not empty), use the COUNTA function. Examples The table in this example is used to illustrate all variations of the COUNT function. The information is not meaningful, but does illustrate what type of arguments each variation of COUNT includes in the function result. =COUNT(A1:E1) returns 5, as all arguments are numeric. =COUNT(A2:E2) returns 0, as none of the arguments are numeric. =COUNT(A3:E3) returns 3, as the least two cells are not numeric. =COUNT(A4:E4) returns 0, as the arguments are logical TRUE or FALSE, which are not counted as numeric. =COUNT(A5:E5) returns 2, as three cells are empty. =COUNT(2, 3, A5:E5, SUM(A1:E1), “A”, “b”) returns 5, as the arguments 2 and 3 are numbers, there are 2 numbers in the range A5:E5, the SUM function returns 1 number, and the last two arguments are text, not numeric (altogether 5 numeric arguments). Related Topics For related functions and additional information, see: “COUNTA” on page 245 “COUNTBLANK” on page 246 “COUNTIF” on page 247 “COUNTIFS” on page 248 “Survey Results Example” on page 362 244 Chapter 10 Statistical Functions Chapter 10 Statistical Functions 245 “Listing of Statistical Functions” on page 225 “Value Types” on page 36 “The Elements of Formulas” on page 15 “Using the Keyboard and Mouse to Create and Edit Formulas” on page 26 “Pasting from Examples in Help” on page 41 COUNTA The COUNTA function returns the number of its arguments that are not empty. COUNTA(value, value…)  value:  A value. value can contain any value type.  value…: Optionally include one or more additional values. Usage Notes  To count only cells or arguments that contain numbers or dates, use the COUNT function. Examples The table in this example is used to illustrate all variations of the COUNT function, including COUNTA. The information is not meaningful, but does illustrate what type of arguments each variation of COUNT includes in the function result. =COUNTA(A1:E1) returns 5, as all cells contain an argument (all numeric). =COUNTA(A2:E2) returns 5, as all cells contain an argument (all text). =COUNTA(A3:E3) returns 5, as all cells contain an argument (mix of text and numeric). =COUNTA(A4:E4) returns 5, as all cells contain an argument (TRUE or FALSE). =COUNTA(A5:E5) returns 2, as three cells are empty. =COUNTA(2, 3, A5:E5, SUM(A1:E1), “A”, “b”) returns 7, as the arguments 2 and 3 are numbers, there are 2 cells that are not empty in the range A5:E5, the SUM function returns 1 number, and “A” and “b” are text expressions (altogether 7 arguments). Related Topics For related functions and additional information, see: “COUNT” on page 244 “COUNTBLANK” on page 246 “COUNTIF” on page 247 “COUNTIFS” on page 248 “Survey Results Example” on page 362 “Listing of Statistical Functions” on page 225 “Value Types” on page 36 “The Elements of Formulas” on page 15 “Using the Keyboard and Mouse to Create and Edit Formulas” on page 26 “Pasting from Examples in Help” on page 41 COUNTBLANK The COUNTBLANK function returns the number of cells in a range that are empty. COUNTBLANK(range)  range:  A range of cells. range is a reference to a single range of cells, which may contain values of any type. Examples The table in this example is used to illustrate all variations of the COUNT function, including COUNTBLANK. The information is not meaningful, but does illustrate what type of arguments each variation of COUNT includes in the function result. =COUNTBLANK(A1:E1) returns 0, as there are no blank cells in the range. =COUNTBLANK(A2:E2) returns 0, as there are no blank cells in the range. =COUNTBLANK(A5:E5) returns 3, as there are three blank cells in the range. =COUNTBLANK(A6:E6) returns 5, as there are only blank cells in the range. =COUNTBLANK(A1:E6) returns 8, as there are a total of 8 blank cells in the range. =COUNTBLANK(A1:E1, A5:E5) returns an error, as COUNTBLANK accepts only one range as an argument. 246 Chapter 10 Statistical Functions Chapter 10 Statistical Functions 247 Related Topics For related functions and additional information, see: “COUNT” on page 244 “COUNTA” on page 245 “COUNTIF” on page 247 “COUNTIFS” on page 248 “Survey Results Example” on page 362 “Listing of Statistical Functions” on page 225 “Value Types” on page 36 “The Elements of Formulas” on page 15 “Using the Keyboard and Mouse to Create and Edit Formulas” on page 26 “Pasting from Examples in Help” on page 41 COUNTIF The COUNTIF function returns the number of cells in a range that satisfy a given condition. COUNTIF(test-array, condition)  test-array:  The collection containing the values to be tested. test-array is a collection that can contain any value type.  condition:  An expression that results in a logical TRUE or FALSE. condition is an expression that can contain anything as long as the result from comparing condition to a value in test-array can be expressed as a Boolean value of TRUE or FALSE. Usage Notes  Each test-array value is compared to condition. If the value meets the conditional test, it is included in the count. Examples The table in this example is used to illustrate all variations of the COUNT function, including COUNTIF. The information is not meaningful, but does illustrate what type of arguments each variation of COUNT includes in the function result. =COUNTIF(A1:E1, “>0”) returns 5, as all cells in the range have a value greater than zero. =COUNTIF(A3:E3, “>=100”) returns 3, as all three numbers are greater than 100 and the two text values are ignored in the comparison. =COUNTIF(A1:E5, “=amet”) returns 2, as the test string “amet” appears twice in the range. =COUNTIF(A1:E5, “=*t”) returns 4, as a string ending in the letter “t” appears four times in the range. Related Topics For related functions and additional information, see: “COUNT” on page 244 “COUNTA” on page 245 “COUNTBLANK” on page 246 “COUNTIFS” on page 248 “Specifying Conditions and Using Wildcards” on page 360 “Survey Results Example” on page 362 “Listing of Statistical Functions” on page 225 “Value Types” on page 36 “The Elements of Formulas” on page 15 “Using the Keyboard and Mouse to Create and Edit Formulas” on page 26 “Pasting from Examples in Help” on page 41 COUNTIFS The COUNTIFS function returns the number of cells in one or more ranges that satisfy given conditions (one condition per range). 248 Chapter 10 Statistical Functions Chapter 10 Statistical Functions 249 COUNTIFS(test-values, condition, test-values…, condition…)  test-values:  A collection containing values to be tested. test-values is a collection containing any type of value.  condition:  An expression that results in a logical TRUE or FALSE. condition is an expression that can contain anything as long as the result from comparing condition to a value in test-values can be expressed as a Boolean value of TRUE or FALSE.  test-values…: Optionally include one or more additional collections containing values to be tested. Each test-values collection must be followed immediately with a condition expression. This pattern of test-values, condition can be repeated as many times as needed.  condition…: If an optional collection of test-values is included, an expression that results in a logical TRUE or FALSE. There must be one condition following each test-values collection; therefore, this function will always have an odd number of arguments. Usage Notes  Each value in test-values is compared to the corresponding condition. If the corresponding values in each collection meet the corresponding conditional tests, the count is increased by 1. Examples Given the following table: =COUNTIFS(A2:A13,”<40”,B2:B13,”=M”) returns 4, the number of males (indicated by an “M” in column B) under the age of forty. =COUNTIFS(A2:A13,”<40”,B2:B13,”=M”,C2:C13,”=S”) returns 2, the number of males who are single (indicated by an “S” in column C) and under the age of forty. =COUNTIFS(A2:A13,”<40”,B2:B13,”=M”,C2:C13,”=M”) returns 2, the number of males who are married (indicated by an “M” in column C) and under the age of forty. =COUNTIFS(A2:A13,”<40”,B2:B13,”=F”) returns 3, the number of females (indicated by an “F” in column B) who are under the age of forty. Related Topics For related functions and additional information, see: “COUNT” on page 244 “COUNTA” on page 245 “COUNTBLANK” on page 246 “COUNTIF” on page 247 “Specifying Conditions and Using Wildcards” on page 360 “Listing of Statistical Functions” on page 225 “Value Types” on page 36 “The Elements of Formulas” on page 15 “Using the Keyboard and Mouse to Create and Edit Formulas” on page 26 “Pasting from Examples in Help” on page 41 COVAR The COVAR function returns the covariance of two collections. COVAR(sample-1-values, sample-2-values)  sample-1-values:  The collection containing the first collection of sample values. sample-1-values is a collection containing number values.  sample-2-values:  The collection containing the second collection of sample values. sample-2-values is a collection containing number values. Usage Notes  The two arrays must have the same dimensions.  If text or Boolean values are included within the arrays, they are ignored.  If the two collections are identical, the covariance is the same as the population variance. 250 Chapter 10 Statistical Functions Chapter 10 Statistical Functions 251 Example In this example, the COVAR function is used to determine how closely related the price of heating oil (column A) is to the temperature that this hypothetical homeowner has set on the thermostat. =COVAR(A2:A11, B2:B11) evaluates to approximately -1.6202, indicating a correlation (as prices rose, the thermostat was lowered). Related Topics For related functions and additional information, see: “CORREL” on page 242 “Survey Results Example” on page 362 “Listing of Statistical Functions” on page 225 “Value Types” on page 36 “The Elements of Formulas” on page 15 “Using the Keyboard and Mouse to Create and Edit Formulas” on page 26 “Pasting from Examples in Help” on page 41 CRITBINOM The CRITBINOM function returns the smallest value for which the cumulative binomial distribution is greater than or equal to a given value. CRITBINOM(trials, prob-success, alpha)  trials:  The total number of trials or tests. trials is a number value that must be greater than or equal to 0.  prob-success:  The probability of success for each trial or test. prob-success is a number value that must be greater than or equal to 0 and less than or equal to 1.  alpha:  The probability that the true population value lies outside the interval. alpha is a number value and must be less than or equal to 1. Subtracting the confidence interval from 1 yields the alpha. Example =CRITBINOM(97, 0.05, 0.05) returns 2, based on 97 trials, with each trial having a probability of success of 5% and a 95% confidence interval (5% alpha). =CRITBINOM(97, 0.25, 0.1) returns 19, based on 97 trials, with each trial having a probability of success of 25% and a 90% confidence interval (10% alpha). =CRITBINOM(97, 0.25, 0.05) returns 17, based on 97 trials, with each trial having a probability of success of 25% and a 95% confidence interval (5% alpha). Related Topics For related functions and additional information, see: “BINOMDIST” on page 238 “NEGBINOMDIST” on page 275 “PERMUT” on page 281 “PROB” on page 282 “Listing of Statistical Functions” on page 225 “Value Types” on page 36 “The Elements of Formulas” on page 15 “Using the Keyboard and Mouse to Create and Edit Formulas” on page 26 “Pasting from Examples in Help” on page 41 252 Chapter 10 Statistical Functions Chapter 10 Statistical Functions 253 DEVSQ The DEVSQ function returns the sum of the squares of deviations of a collection of numbers from their average (arithmetic mean). DEVSQ(num-value, num-value…)  num-value:  A number. num-value is a number value.  num-value…: Optionally include one or more additional numbers. Usage Notes  DEVSQ divides the sum of the numbers by the number of numbers to get the average (arithmetic mean). The difference (absolute value) between the average and each number is squared and summed and the total is returned. Example =DEVSQ(1, 7, 19, 8, 3, 9) returns 196.833333333333. Related Topics For related functions and additional information, see: “STDEV” “Listing of Statistical Functions” on page 225 “Value Types” on page 36 “The Elements of Formulas” on page 15 “Using the Keyboard and Mouse to Create and Edit Formulas” on page 26 “Pasting from Examples in Help” on page 41 EXPONDIST The EXPONDIST function returns the exponential distribution of the specified form. EXPONDIST(non-neg-x-value, lambda, form-type)  non-neg-x-value:  The value at which you want to evaluate the function. non-neg-xvalue is a number value that must be greater than or equal to 0.  lambda:  The parameter value. lambda is a number value and must be greater than 0.  form-type:  A value that indicates which form of the exponential function to provide. cumulative form (TRUE or 1):  Return the value of the cumulative distribution function form. probability density form (FALSE or 0):  Return the value of the probability density function form. Examples =EXPONDIST(4, 2, 1) returns 0.999664537372097 (cumulative distribution form). =EXPONDIST(4, 2, 0) returns 0.000670925255805024 (probability density form). Related Topics For related functions and additional information, see: “LOGNORMDIST” on page 269 “Listing of Statistical Functions” on page 225 “Value Types” on page 36 “The Elements of Formulas” on page 15 “Using the Keyboard and Mouse to Create and Edit Formulas” on page 26 “Pasting from Examples in Help” on page 41 FDIST The FDIST function returns the F probability distribution. FDIST(non-neg-x-value, d-f-numerator, d-f-denominator)  non-neg-x-value:  The value at which you want to evaluate the function. non-neg-xvalue is a number value that must be greater than or equal to 0.  d-f-numerator:  The degrees of freedom to include as the numerator. d-f-numerator is a number value and must be greater than or equal to 1. If there is a decimal portion, it is ignored.  d-f-denominator:  The degrees of freedom to include as the denominator. d-fdenominator is a number value and must be greater than or equal to 1. If there is a decimal portion, it is ignored. Usage Notes  The F distribution is also known as Snedecor’s F distribution or the Fisher-Snedecor distribution. Examples =FDIST(0.77, 1, 2) returns 0.472763488223567. =FDIST(0.77, 1, 1) returns 0.541479597634413. =FDIST(0.77, 2, 1) returns 0.627455805138159. Related Topics For related functions and additional information, see: 254 Chapter 10 Statistical Functions Chapter 10 Statistical Functions 255 “FINV” on page 255 “Listing of Statistical Functions” on page 225 “Value Types” on page 36 “The Elements of Formulas” on page 15 “Using the Keyboard and Mouse to Create and Edit Formulas” on page 26 “Pasting from Examples in Help” on page 41 FINV The FINV function returns the inverse of the F probability distribution. FINV(prob, d-f-numerator, d-f-denominator)  prob:  A probability associated with the distribution. prob is a number value and must be greater than 0 and less than or equal to 1.  d-f-numerator:  The degrees of freedom to include as the numerator. d-f-numerator is a number value and must be greater than or equal to 1. If there is a decimal portion, it is ignored.  d-f-denominator:  The degrees of freedom to include as the denominator. d-fdenominator is a number value and must be greater than or equal to 1. If there is a decimal portion, it is ignored. Examples =FINV(0.77, 1, 2) returns 0.111709428782599. =FINV(0.77, 1, 1) returns 0.142784612191674. =FINV(0.77, 2, 1) returns 0.34331253162422. Related Topics For related functions and additional information, see: “FDIST” on page 254 “Listing of Statistical Functions” on page 225 “Value Types” on page 36 “The Elements of Formulas” on page 15 “Using the Keyboard and Mouse to Create and Edit Formulas” on page 26 “Pasting from Examples in Help” on page 41 FORECAST The FORECAST function returns the forecasted y value for a given x based on sample values using linear regression analysis. FORECAST(x-num-date-dur, y-values, x-values)  x-num-date-dur:  The x value for which the function should return a forecasted y value. x-num-date-dur is a number value, a date/time value, or a duration value.  y-values:  The collection containing the y (dependent) values. y-values is a collection that can contain number, date/time, or duration values. All values must be of the same type.  x-values:  The collection containing the x (independent) values. x-values is a collection that can contain number, date/time, or duration values. All values must be of the same type. Usage Notes  All arguments must be of the same type.  The two arrays must be of the same size.  If, for example, you had data on the driving speed of a vehicle and its fuel efficiency at each speed, fuel efficiency would be the dependent variable (y) and driving speed would be the independent variable (x).  You can use the SLOPE and INTERCEPT functions to find the equation used to calculate forecast values. Example Given the following table: =FORECAST(9, A3:F3, A2:F2) returns 19. Related Topics For related functions and additional information, see: “CORREL” on page 242 “COVAR” on page 250 “INTERCEPT” on page 262 “SLOPE” on page 287 “Listing of Statistical Functions” on page 225 256 Chapter 10 Statistical Functions Chapter 10 Statistical Functions 257 “Value Types” on page 36 “The Elements of Formulas” on page 15 “Using the Keyboard and Mouse to Create and Edit Formulas” on page 26 “Pasting from Examples in Help” on page 41 FREQUENCY The FREQUENCY function returns an array of how often data values occur within a range of interval values. FREQUENCY(data-values, interval-values)  data-values:  A collection containing the values to be evaluated. data-values is a collection containing number or date/time values. All values should be of the same type.  interval-values:  A collection containing the interval values. interval-values is a collection containing number or date/time values. All values should be of the same type as the values in the data-values collection. Usage Notes  FREQUENCY determines the number of values in data-values that fall within each interval. The interval array is easiest to understand if it is arranged in ascending order. The first frequency will be the count of those values that are less than or equal to the lowest interval value. All other frequency values, except the last, will be the count of those values that are greater than the immediately lower interval value and less than or equal to the current interval value. The final frequency value will be the count of those data values that are greater than the largest interval value.  The values returned by the function are contained in an array. One method of reading the values in the array is to use the INDEX function. You can wrap the FREQUENCY function within the INDEX function: =INDEX(FREQUENCY(data-values, interval-values), x) where x is the desired interval. Remember that there will be one more interval than there are interval-values. Example Assume the following table contains the test scores of 30 students who recently took an exam you administered. Assume further that that the minimum passing grade is 65 and that the lowest score for other grades are as given. In order to facilitate building the formulas, an “F” is represented by 1 and an “A” by 5. =INDEX(FREQUENCY($A$1:$F$5, $B$8:$E$8), B9) returns 5, the number of students who received an “F” (score of 65 or less). This formula can be entered in cell B10 and then extended across to cell F10. The resulting values returned for grades of “D” to “A” are 3, 8, 8, and 6, respectively. Related Topics For related functions and additional information, see: “INDEX” on page 214 “PERCENTILE” on page 279 “PERCENTRANK” on page 280 “QUARTILE” on page 284 “Listing of Statistical Functions” on page 225 “Value Types” on page 36 “The Elements of Formulas” on page 15 “Using the Keyboard and Mouse to Create and Edit Formulas” on page 26 “Pasting from Examples in Help” on page 41 258 Chapter 10 Statistical Functions Chapter 10 Statistical Functions 259 GAMMADIST The GAMMADIST function returns the gamma distribution in the specified form. GAMMADIST(non-neg-x-value, alpha, beta, form-type)  non-neg-x-value:  The value at which you want to evaluate the function. non-neg-xvalue is a number value that must be greater than or equal to 0.  alpha:  One of the shape parameters of the distribution. alpha is a number value and must be greater than 0.  beta:  One of the shape parameters of the distribution. beta is a number value and must be greater than 0.  form-type:  A value that indicates which form of the exponential function to provide. cumulative form (TRUE or 1):  Return the value of the cumulative distribution function form. probability density form (FALSE or 0):  Return the value of the probability density function form. Examples =GAMMADIST(0.8, 1, 2, 1) returns 0.329679953964361 (the cumulative distribution form). =GAMMADIST(0.8, 1, 2, 0) returns 0.33516002301782 (the probability density form). Related Topics For related functions and additional information, see: “GAMMAINV” on page 260 “GAMMALN” on page 260 “Listing of Statistical Functions” on page 225 “Value Types” on page 36 “The Elements of Formulas” on page 15 “Using the Keyboard and Mouse to Create and Edit Formulas” on page 26 “Pasting from Examples in Help” on page 41 GAMMAINV The GAMMAINV function returns the inverse gamma cumulative distribution. GAMMAINV(probability, alpha, beta)  probability:  A probability associated with the distribution. probability is a number value and must be greater than 0 and less than 1.  alpha:  One of the shape parameters of the distribution. alpha is a number value and must be greater than 0.  beta:  One of the shape parameters of the distribution. beta is a number value and must be greater than 0. Examples =GAMMAINV(0.8, 1, 2) returns 3.2188758248682. =GAMMAINV(0.8, 2, 1) returns 2.99430834700212. Related Topics For related functions and additional information, see: “GAMMADIST” on page 259 “GAMMALN” on page 260 “Listing of Statistical Functions” on page 225 “Value Types” on page 36 “The Elements of Formulas” on page 15 “Using the Keyboard and Mouse to Create and Edit Formulas” on page 26 “Pasting from Examples in Help” on page 41 GAMMALN The GAMMALN function returns the natural logarithm of the gamma function, G(x). GAMMALN(pos-x-value)  pos-x-value:  The positive x value at which you want to evaluate the function. pos-xvalue is a number value and must be greater than 0. Examples =GAMMALN(0.92) returns 0.051658003497744. =GAMMALN(0.29) returns 1.13144836880416. 260 Chapter 10 Statistical Functions Chapter 10 Statistical Functions 261 Related Topics For related functions and additional information, see: “GAMMADIST” on page 259 “GAMMAINV” on page 260 “LN” on page 179 “Listing of Statistical Functions” on page 225 “Value Types” on page 36 “The Elements of Formulas” on page 15 “Using the Keyboard and Mouse to Create and Edit Formulas” on page 26 “Pasting from Examples in Help” on page 41 GEOMEAN The GEOMEAN function returns the geometric mean. GEOMEAN(pos-num, pos-num…)  pos-num:  A positive number. pos-num is a number value and must be greater than 0.  pos-num…: Optionally include one or more additional positive numbers. Usage Notes  GEOMEAN multiples the arguments to arrive at a product and then takes the root of the product that is equal to the number of arguments. Example =GEOMEAN(5, 7, 3, 2, 6, 22) returns 5.50130264578853. Related Topics For related functions and additional information, see: “AVERAGE” on page 231 “HARMEAN” on page 262 “Listing of Statistical Functions” on page 225 “Value Types” on page 36 “The Elements of Formulas” on page 15 “Using the Keyboard and Mouse to Create and Edit Formulas” on page 26 “Pasting from Examples in Help” on page 41 HARMEAN The HARMEAN function returns the harmonic mean. HARMEAN(pos-num, pos-num…)  pos-num:  A positive number. a-pos-num is a number value and must be greater than 0.  pos-num…: Optionally include one or more additional positive numbers. Usage Notes  The harmonic mean is the reciprocal of the arithmetic mean of the reciprocals. Example =HARMEAN(5, 7, 3, 2, 6, 22) returns 4.32179607109448. Related Topics For related functions and additional information, see: “AVERAGE” on page 231 “GEOMEAN” on page 261 “Listing of Statistical Functions” on page 225 “Value Types” on page 36 “The Elements of Formulas” on page 15 “Using the Keyboard and Mouse to Create and Edit Formulas” on page 26 “Pasting from Examples in Help” on page 41 INTERCEPT The INTERCEPT function returns the y-intercept of the best-fit line for the collection using linear regression analysis. INTERCEPT(y-values, x-numbers)  y-values:  The collection containing the y (dependent) values. y-values is a collection that can contain number, date/time, or duration values. All values must be of the same type. 262 Chapter 10 Statistical Functions Chapter 10 Statistical Functions 263  x-numbers:  The collection containing the x (independent) values. x-numbers is a collection containing number values. Usage Notes  The two arrays must be of the same size.  To find the slope of the best-fit line, use the SLOPE function. Example In this example, the INTERCEPT function is used to determine the y-intercept of the best-fit line for the temperature that this hypothetical homeowner has set on the thermostat (the dependent variable), based on the price of heating oil (the independent variable). =INTERCEPT(B2:B11, A2:A11) evaluates to approximately 78, above the highest hypothetical value as the best-fit line sloping downward (as prices rose, the thermostat was lowered). Related Topics For related functions and additional information, see: “SLOPE” on page 287 “Listing of Statistical Functions” on page 225 “Value Types” on page 36 “The Elements of Formulas” on page 15 “Using the Keyboard and Mouse to Create and Edit Formulas” on page 26 “Pasting from Examples in Help” on page 41 LARGE The LARGE function returns the nth-largest value within a collection. The largest value is ranked number 1. LARGE(num-date-dur-set, ranking)  num-date-dur-set:  A collection of values. num-date-dur-set is a collection containing number, date, or duration values. All values must be of the same type.  ranking:  A number representing the size ranking of the value you want to retrieve. ranking is a number value and must be in the range of 1 to the number of values in the collection. Usage Notes  A ranking of 1 retrieves the largest number in the collection, 2 the second-largest, and so on. Values included in the array that are of the same size are ranked together, but impact the outcome. Examples Assume the following table contains the cumulative test scores for this semester for your 20 students. (We have organized the data this way for the example; it would likely originally have been in 20 separate rows.) =LARGE(A1:E4, 1) returns 100, the largest cumulative test score (cell B2). =LARGE(A1:E4, 2) returns 92, the second-largest cumulative test score (either cell B2 or cell C2). =LARGE(A1:E4, 3) returns 92, also the third-largest cumulative test score as it appears twice (cells B2 and C2). =LARGE(A1:E4, 6) returns 86, the sixth-largest cumulative test score (order is 100 , 92, 92, 91, 90, then 86). Related Topics For related functions and additional information, see: “RANK” on page 285 “SMALL” on page 288 “Listing of Statistical Functions” on page 225 “Value Types” on page 36 “The Elements of Formulas” on page 15 264 Chapter 10 Statistical Functions Chapter 10 Statistical Functions 265 “Using the Keyboard and Mouse to Create and Edit Formulas” on page 26 “Pasting from Examples in Help” on page 41 LINEST The LINEST function returns an array of the statistics for a straight line that best fits the given data using the “least squares” method. LINEST(known-y-values, known-x-values, nonzero-y-intercept, more-stats)  known-y-values:  The collection containing the known y values. known-y-values is a collection containing number values. If there is only one collection of known x values, known-y-values can be any size. If there is more than one collection of known x values, known-y-values can be either one column containing the values or one row containing the values, but not both.  known-x-values:  An optional collection containing the known x values. knownx- values is a collection containing number values. If omitted, it will be assumed to be the set {1, 2, 3…} of the same size as known-y-values. If there is only one set of known x values, known-x-values, if specified, should be the same size as known-yvalues. If there is more than one set of known x values, each row/column of knownx- values is considered to be one set and the size of each row/column must be the same as the size of the row/column of known-y-values.  nonzero-y-intercept:  An optional value specifying how the y intercept (constant b) should be calculated. normal (1, TRUE, or omitted):  The value of the y intercept (constant b) should be calculated normally. force 0 value (0, FALSE):  The value of the y intercept (constant b) should be forced to be 0.  more-stats:  An optional value specifying whether additional statistical information should be returned. no additional stats (0, FALSE, or omitted):  Do not return additional regression statistics in the returned array. additional stats (1, TRUE):  Return additional regression statistics in the returned array. Usage Notes  The values returned by the function are contained in an array. One method of reading the values in the array is to use the INDEX function. You can wrap the LINEST function within the INDEX function: =INDEX(LINEST(known-y-values, knownx- values, const-b, stats), y, x) where y and x are the column and row index of the desired value. If additional statistics are not returned (stats is FALSE), the array returned is one row deep. The number of columns is equal to the the number of sets of known-x-values plus 1. It contains the line slopes (one value for each row/column of x values) in reverse order (the first value relates to the last row/column of x values) and then the value for b, the intercept. If additional statistics are returned (stats is TRUE), the array contains five rows. See “Additional Statistics” on page 267 for the contents of the array. Examples Assume the following table contains the test scores of 30 students who recently took an exam you administered. Assume further that the minimum passing grade is 65 and that the lowest score for other grades are as given. In order to facilitate building the formulas, an “F” is represented by 1 and an “A” by 5. =INDEX(LINEST(A2:A6, C2:C6, 1, 0), 1) returns 0.752707581227437, which is the best-fit line slope. =INDEX(LINEST(A2:A6, C2:C6, 1, 0), 2) returns 0.0342960288808646, which is b, the intercept. Related Topics For related functions and additional information, see: “Listing of Statistical Functions” on page 225 “Value Types” on page 36 “The Elements of Formulas” on page 15 “Using the Keyboard and Mouse to Create and Edit Formulas” on page 26 “Pasting from Examples in Help” on page 41 266 Chapter 10 Statistical Functions Chapter 10 Statistical Functions 267 Additional Statistics This section discusses the additional statistics that can be returned by the LINEST function. LINEST can include additional statistical information in the array returned by the function. For purposes of the following discussion, assume that there are five sets of known x values, in addition to the known y values. Assume further that the known x values are in five table rows or five table columns. Based on these assumptions, the array returned by LINEST would be as follows (where the number following an x indicates which set of x values the item refers to): Row/Column 1 2 3 4 5 6 1 slope x5 slope x4 slope x3 slope x2 slope x1 b (y intercept) 2 std-err x1 std-err x2 std-err x3 std-err x4 std-err x5 std-err b 3 coefficient-det std-err y 4 F-stat degrees-offreedom 5 reg-ss reside-ss Argument definitions slope x:  The slope of the line related to this set of known x values. The values are returned in reverse order; that is, if there are five known x value sets, the value for the fifth set is first in the returned array. b:  The y intercept for the known x values. std-err x:  The standard error for the coefficient associated with this set of known x values. The values are returned in order; that is, if there are five known x value sets, the value for the first set is returned first in the array. This is the opposite of the way the slope values are returned. std-err b:  The standard error associated with the y-intercept value (b). coefficient-det: The coefficient of determination. This statistic compares estimated and actual y values. If it is 1, there is no difference between the estimated y value and the actual y value. This is known as perfect correlation. If the coefficient of determination is 0, there is no correlation and the given regression equation is not helpful in predicting a y value. std-err y:  The standard error associated with the y value estimate. F-stat:  The F observed value. The F observed value can be used to help determine whether the observed relationship between the dependent and independent variables occurs by chance. degrees-of-freedom:  The degrees of freedom. Use the degrees of freedom statistic to help determine a confidence level. reg-ss:  The regression sum of squares. reside-ss:  The residual sum of squares. Usage Notes  It does not matter whether the known x values and known y values are in rows or columns. In either case, the returned array is ordered by rows as illustrated in the table.  The example assumed five sets of known x values. If there were more or less than five, the number of columns in the returned array would change accordingly (it is always equal to the number of sets of known x values plus 1), but the number of rows would remain constant.  If additional statistics are not specified in the arguments to LINEST, the returned array is equal to the first row only. LOGINV The LOGINV function returns the inverse of the log-normal cumulative distribution function of x. LOGINV(probability, mean, stdev)  probability:  A probability associated with the distribution. probability is a number value and must be greater than 0 and less than 1.  mean:  The mean of the natural logarithm, that is, ln(x). mean is a number value and is the average (arithmetic mean) of ln(x); the natural logarithm of x.  stdev:  The standard deviation of the population. stdev is a number value and must be greater than 0. Usage Notes  LOGINV is appropriate where the logarithm of x is normally distributed. Example =LOGINV(0.78, 1.7, 2.2) returns 29.9289150377259. Related Topics For related functions and additional information, see: “LN” on page 179 “LOGNORMDIST” on page 269 “Listing of Statistical Functions” on page 225 “Value Types” on page 36 268 Chapter 10 Statistical Functions Chapter 10 Statistical Functions 269 “The Elements of Formulas” on page 15 “Using the Keyboard and Mouse to Create and Edit Formulas” on page 26 “Pasting from Examples in Help” on page 41 LOGNORMDIST The LOGNORMDIST function returns the log-normal distribution. LOGNORMDIST(pos-x-value, mean, stdev)  pos-x-value:  The positive x value at which you want to evaluate the function. pos-xvalue is a number value that must be greater than 0.  mean:  The mean of the natural logarithm, that is, ln(x). mean is a number value and is the average (arithmetic mean) of ln(x); the natural logarithm of x.  stdev:  The standard deviation of the population. stdev is a number value and must be greater than 0. Example =LOGNORMDIST(0.78, 1.7, 2.2) returns 0.187899237956868. Related Topics For related functions and additional information, see: “LN” on page 179 “LOGINV” on page 268 “Listing of Statistical Functions” on page 225 “Value Types” on page 36 “The Elements of Formulas” on page 15 “Using the Keyboard and Mouse to Create and Edit Formulas” on page 26 “Pasting from Examples in Help” on page 41 MAX The MAX function returns the largest number in a collection. MAX(value, value…)  value:  A value. value can contain any value type.  value…: Optionally include one or more additional values. Usage Notes  If value does not evaluate to a date or number, it is not included in the result.  To determine the largest of any type of value in a collection, use the MAXA function. Examples =MAX(5, 5, 5, 5, 6) returns 6. =MAX(1, 2, 3, 4, 5) returns 5. Related Topics For related functions and additional information, see: “LARGE” on page 264 “MAXA” on page 270 “MIN” on page 272 “SMALL” on page 288 “Listing of Statistical Functions” on page 225 “Value Types” on page 36 “The Elements of Formulas” on page 15 “Using the Keyboard and Mouse to Create and Edit Formulas” on page 26 “Pasting from Examples in Help” on page 41 MAXA The MAXA function returns the largest number in a collection of values that may include text and Boolean values. MAXA(value, value…)  value:  A value. value can contain any value type.  value…: Optionally include one or more additional values. All numeric values must be of the same type. You cannot mix numbers, dates, and duration values. 270 Chapter 10 Statistical Functions Chapter 10 Statistical Functions 271 Usage Notes  Text values and logical FALSE are given a value of 0 and logical TRUE is given a value of 1.  To determine the largest value of a collection that contains only numbers or dates, use the MAX function. Examples =MAXA(1, 2, 3, 4) returns 4. =MAXA(A1:C1), where A1:C1 contains -1, -10, hello, returns 0. Related Topics For related functions and additional information, see: “MAX” on page 270 “MINA” on page 273 “Listing of Statistical Functions” on page 225 “Value Types” on page 36 “The Elements of Formulas” on page 15 “Using the Keyboard and Mouse to Create and Edit Formulas” on page 26 “Pasting from Examples in Help” on page 41 MEDIAN The MEDIAN function returns the median value in a collection of numbers. The median is the value where half the numbers in the set are less than the median and half are greater. MEDIAN(num-date-dur, num-date-dur…)  num-date-dur:  A value. num-date-dur is a number value, a date/time value, or a duration value.  num-date-dur…: Optionally include one or more additional values. If more than one num-date-dur value is specified, all must be of the same type. Usage Notes  If there is an even number of values in the set, the MEDIAN function returns the average of the two middle values. Examples =MEDIAN(1, 2, 3, 4, 5) returns 3. =MEDIAN(1, 2, 3, 4, 5, 6) returns 3.5. =MEDIAN(5, 5, 5, 5, 6) returns 5. Related Topics For related functions and additional information, see: “AVERAGE” on page 231 “MODE” on page 274 “Listing of Statistical Functions” on page 225 “Value Types” on page 36 “The Elements of Formulas” on page 15 “Using the Keyboard and Mouse to Create and Edit Formulas” on page 26 “Pasting from Examples in Help” on page 41 MIN The MIN function returns the smallest number in a collection. MIN(value, value…)  value:  A value. value can contain any value type.  value…: Optionally include one or more additional values. Usage Notes  If value does not evaluate to a date or number, it is not included in the result.  To determine the smallest of any type of value in a collection, use the MINA function. Examples =MIN(5, 5, 5, 5, 6) returns 5. =MIN(1, 2, 3, 4, 5) returns 1. Related Topics For related functions and additional information, see: “LARGE” on page 264 “MAX” on page 270 272 Chapter 10 Statistical Functions Chapter 10 Statistical Functions 273 “MINA” on page 273 “SMALL” on page 288 “Listing of Statistical Functions” on page 225 “Value Types” on page 36 “The Elements of Formulas” on page 15 “Using the Keyboard and Mouse to Create and Edit Formulas” on page 26 “Pasting from Examples in Help” on page 41 MINA The MINA function returns the smallest number in a collection of values that may include text and Boolean values. MINA(value, value…)  value:  A value. value can contain any value type.  value…: Optionally include one or more additional values. All numeric values must be of the same type. You cannot mix numbers, dates, and duration values. Usage Notes  Text values and logical FALSE are given a value of 0 and logical TRUE is given a value of 1.  To determine the smallest value of a collection that contains only numbers or dates, use the MIN function. Examples =MINA(1, 2, 3, 4) returns 1. =MINA(A1:C1), where A1:C1 contains -1, -10, hello, returns -10. =MINA(A1:C1), where A1:C1 contains 1, 10, hello, returns 0. Related Topics For related functions and additional information, see: “MAXA” on page 270 “MIN” on page 272 “Listing of Statistical Functions” on page 225 “Value Types” on page 36 “The Elements of Formulas” on page 15 “Using the Keyboard and Mouse to Create and Edit Formulas” on page 26 “Pasting from Examples in Help” on page 41 MODE The MODE function returns the most frequently occurring value in a collection of numbers. MODE(num-date-dur, num-date-dur…)  num-date-dur:  A value. num-date-dur is a number value, a date/time value, or a duration value.  num-date-dur…: Optionally include one or more additional values. If more than one num-date-dur value is specified, all must be of the same type. Usage Notes  If more than one number occurs the maximum multiple times in the arguments, MODE returns the first such number.  If no value occurs more than once, the function returns an error. Examples =MODE(5, 5, 5, 5, 6) returns 5. =MODE(1, 2, 3, 4, 5) returns an error. =MODE(2, 2, 4, 6, 6) returns 2. =MODE(6, 6, 4, 2, 2) returns 6. Related Topics For related functions and additional information, see: “AVERAGE” on page 231 “MEDIAN” on page 271 “Listing of Statistical Functions” on page 225 “Value Types” on page 36 “The Elements of Formulas” on page 15 “Using the Keyboard and Mouse to Create and Edit Formulas” on page 26 “Pasting from Examples in Help” on page 41 274 Chapter 10 Statistical Functions Chapter 10 Statistical Functions 275 NEGBINOMDIST The NEGBINOMDIST function returns the negative binomial distribution. NEGBINOMDIST(f-num, s-num, prob-success)  f-num:  The number of failures. f-num is a number value and must be greater than or equal to 0.  s-num:  The number of successful trials or tests. s-num is a number value that must be greater than or equal to 1.  prob-success:  The probability of success for each trial or test. prob-success is a number value that must be greater than 0 and less than 1. Usage Notes  NEGBINOMDIST returns the probability that there will be a specified number of failures, f-num, before the specified number of successes, s-num. The constant probability of a success is prob-success. Example =NEGBINOMDIST(3, 68, 0.95) returns 0.20913174716192. Related Topics For related functions and additional information, see: “BINOMDIST” on page 238 “CRITBINOM” on page 252 “PERMUT” on page 281 “PROB” on page 282 “Listing of Statistical Functions” on page 225 “Value Types” on page 36 “The Elements of Formulas” on page 15 “Using the Keyboard and Mouse to Create and Edit Formulas” on page 26 “Pasting from Examples in Help” on page 41 NORMDIST The NORMDIST function returns the normal distribution of the specified function form. NORMDIST(num, average, stdev, form-type)  num:  The number to be evaluated. num is a number value.  average:  The average of the distribution. average is a number value representing the known average (arithmetic mean) rate at which events occur.  stdev:  The standard deviation of the population. stdev is a number value and must be greater than 0.  form-type:  A value that indicates which form of the exponential function to provide. cumulative form (TRUE or 1):  Return the value of the cumulative distribution function form. probability density form (FALSE or 0):  Return the value of the probability density function form. Usage Notes  If average is 0, stdev is 1, and form-type is TRUE, NORMDIST returns the same value as the cumulative standard normal distribution returned by NORMSDIST. Examples =NORMDIST(22, 15, 2.5, 1) returns 0.997444869669572, the cumulative distribution form. =NORMDIST(22, 15, 2.5, 0) returns 0.00316618063319199, the probability density form. Related Topics For related functions and additional information, see: “NORMINV” on page 277 “NORMSDIST” on page 277 “Listing of Statistical Functions” on page 225 “Value Types” on page 36 “The Elements of Formulas” on page 15 “Using the Keyboard and Mouse to Create and Edit Formulas” on page 26 “Pasting from Examples in Help” on page 41 276 Chapter 10 Statistical Functions Chapter 10 Statistical Functions 277 NORMINV The NORMINV function returns the inverse of the cumulative normal distribution. NORMINV(probability, average, stdev)  probability:  A probability associated with the distribution. probability is a number value and must be greater than 0 and less than 1.  average:  The average of the distribution. average is a number value representing the known average (arithmetic mean) rate at which events occur.  stdev:  The standard deviation of the population. stdev is a number value and must be greater than 0. Usage Notes  If average is 0 and stdev is 1, NORMINV returns the same value as the inverse of the cumulative standard normal distribution returned by NORMSINV. Example =NORMINV(0.89, 15, 2.5) returns 18.0663203000915. Related Topics For related functions and additional information, see: “NORMDIST” on page 276 “NORMSINV” on page 278 “Listing of Statistical Functions” on page 225 “Value Types” on page 36 “The Elements of Formulas” on page 15 “Using the Keyboard and Mouse to Create and Edit Formulas” on page 26 “Pasting from Examples in Help” on page 41 NORMSDIST The NORMSDIST function returns the standard normal distribution. NORMSDIST(num)  num:  A number. num is a number value. Usage Notes  A standard normal distribution has an average (arithmetic mean) of 0 and a standard deviation of 1. Example =NORMSDIST(4.3) returns 0.999991460094529. Related Topics For related functions and additional information, see: “NORMDIST” on page 276 “NORMSINV” on page 278 “Listing of Statistical Functions” on page 225 “Value Types” on page 36 “The Elements of Formulas” on page 15 “Using the Keyboard and Mouse to Create and Edit Formulas” on page 26 “Pasting from Examples in Help” on page 41 NORMSINV The NORMSINV function returns the inverse of the cumulative standard normal distribution. NORMSINV(probability)  probability:  A probability associated with the distribution. probability is a number value and must be greater than 0 and less than 1. Usage Notes  A standard normal distribution has an average (arithmetic mean) of 0 and a standard deviation of 1. Example =NORMSINV(0.89) returns 1.22652812003661. Related Topics For related functions and additional information, see: “NORMINV” on page 277 “NORMSDIST” on page 277 “Listing of Statistical Functions” on page 225 “Value Types” on page 36 278 Chapter 10 Statistical Functions Chapter 10 Statistical Functions 279 “The Elements of Formulas” on page 15 “Using the Keyboard and Mouse to Create and Edit Formulas” on page 26 “Pasting from Examples in Help” on page 41 PERCENTILE The PERCENTILE function returns the value within a collection that corresponds to a particular percentile. PERCENTILE(num-date-dur-set, percentile-value)  num-date-dur-set:  A collection of values. num-date-dur-set is a collection containing number, date, or duration values. All values must be of the same type.  percentile-value:  The percentile value you want to find, in the range 0 to 1. percentile-value is a number value and is either entered as a decimal (for example, 0.25) or delimited with a percent sign (for example, 25%). It must be greater than or equal to 0 and less than or equal to 1. Usage Notes  Values included in the array of the same size are ranked together, but impact the outcome. Examples Assume the following table contains the cumulative test scores for this semester for your 20 students. (We have organized the data this way for the example; it would likely originally have been in 20 separate rows.) =PERCENTILE(A1:E4, 0.90) returns 92, the minimum cumulative test score to be in the top 10% of the class (90th percentile). =PERCENTILE(A1:E4, 2/3) returns 85, the minimum cumulative test score to be in the top one-third of the class (2/3 or approximately 67th percentile). =PERCENTILE(A1:E4, 0.50) returns 83, the minimum cumulative test score to be in the top half of the class (the 50th percentile). Related Topics For related functions and additional information, see: “FREQUENCY” on page 257 “PERCENTRANK” on page 280 “QUARTILE” on page 284 “Listing of Statistical Functions” on page 225 “Value Types” on page 36 “The Elements of Formulas” on page 15 “Using the Keyboard and Mouse to Create and Edit Formulas” on page 26 “Pasting from Examples in Help” on page 41 PERCENTRANK The PERCENTRANK function returns the rank of a value in a collection as a percentage of the collection. PERCENTRANK(num-date-dur-set, num-date-dur, significance)  num-date-dur-set:  A collection of values. num-date-dur-set is a collection containing number, date, or duration values. All values must be of the same type.  num-date-dur:  A value. num-date-dur is a number value, a date/time value, or a duration value.  significance: An optional value specifying the number of digits to the right of the decimal point. significance is a number value that must be greater than or equal to 1. If omitted, a default value of 3 is used (x.xxx%). Usage Notes  PERCENTRANK can be used to evaluate the relative standing of a value within a collection. It is calculated by determining where in the collection a specified number falls. For example, if in a given collection, there are ten values smaller than a specified number and ten values that are larger, the PERCENTRANK of the specified number is 50%. Example =PERCENTRANK({5, 6, 9, 3, 7, 11, 8, 2, 14}, 10) returns 0.813, as there are seven values smaller than 10 and only two that are larger. Related Topics For related functions and additional information, see: “FREQUENCY” on page 257 “PERCENTILE” on page 279 “Listing of Statistical Functions” on page 225 280 Chapter 10 Statistical Functions Chapter 10 Statistical Functions 281 “Value Types” on page 36 “The Elements of Formulas” on page 15 “Using the Keyboard and Mouse to Create and Edit Formulas” on page 26 “Pasting from Examples in Help” on page 41 PERMUT The PERMUT function returns the number of permutations for a given number of objects that can be selected from a total number of objects. PERMUT(num-objects, num-elements)  num-objects:  The total number of objects. num-objects is a number value and must be greater than or equal to 0.  num-elements:  The number of objects to be selected from the total number of objects in each permutation. num-elements is a number value and must be greater than or equal to 0. Examples =PERMUT(25, 5) returns 6375600. =PERMUT(10, 3) returns 720. =PERMUT(5, 2) returns 20. Related Topics For related functions and additional information, see: “BINOMDIST” on page 238 “CRITBINOM” on page 252 “NEGBINOMDIST” on page 275 “PROB” on page 282 “Listing of Statistical Functions” on page 225 “Value Types” on page 36 “The Elements of Formulas” on page 15 “Using the Keyboard and Mouse to Create and Edit Formulas” on page 26 “Pasting from Examples in Help” on page 41 POISSON The POISSON function returns the probability that a specific number of events will occur using the Poisson distribution. POISSON(events, average, form-type)  events:  The number of events (arrivals) for which you want to calculate the probability. events is a number value.  average:  The average of the distribution. average is a number value representing the known average (arithmetic mean) rate at which events occur.  form-type:  A value that indicates which form of the exponential function to provide. cumulative form (TRUE or 1):  Return the value of the cumulative distribution function form (that the specified number or fewer successes or events will occur). probability mass form (FALSE or 0):  Return the value of the probability mass function form (that there are exactly the specified number of successes or events). Example For a mean of 10 and an arrival rate of 8: =POISSON(8, 10, FALSE) returns 0.112599. Related Topics For related functions and additional information, see: “EXPONDIST” on page 253 “Listing of Statistical Functions” on page 225 “Value Types” on page 36 “The Elements of Formulas” on page 15 “Using the Keyboard and Mouse to Create and Edit Formulas” on page 26 “Pasting from Examples in Help” on page 41 PROB The PROB function returns the probability of a range of values if you know the probabilities of the individual values. PROB(num-set, probability-values, lower, upper)  num-set:  A collection of numbers. num-set is a collection containing number values. 282 Chapter 10 Statistical Functions Chapter 10 Statistical Functions 283  probability-values:  The collection containing the probability values. probabilityvalues is a collection containing number values. The sum of the probabilities must add up to 1. Any string values are ignored.  lower:  The lower limit or bound. lower is a number value.  upper:  An optional upper limit or bound. upper is a number value and must be greater than or equal to lower. Usage Notes  The PROB function sums the probabilities associated with all values in the collection greater than or equal to the specified lower limit value and less than or equal to the specified upper limit value. If upper is omitted, PROB returns the probability of the single number equal to the specified lower limit.  The two arrays must be of the same size. If text is contained in an array, it will be ignored. Examples Assume you are thinking of a number from 1 to 10 to have someone guess. Most people would say the probability that you would be thinking of a particular number is 0.1 (10%), as listed in column C, since there are ten possible choices. However, studies have shown that people do not choose numbers randomly. Assume that a study has shown that people like you are more likely to select certain numbers than others. These revised probabilities are in column E. =PROB(A1:A10, C1:C10, 4, 6) returns 0.30, the probability that the value is 4, 5, or 6, assuming choices are completely random. =PROB(A1:A10, E1:E10, 7) returns 0.28, the probability that the value is 4, 5, or 6, based on the research that numbers are not chosen randomly. =PROB(A1:A10, E1:E10, 4, 6) returns 0.20, the probability that the value is 7, based on the research that numbers are not chosen randomly. =PROB(A1:A10, C1:C10, 6, 10) returns 0.50, the probability that the value is greater than 5 (6 to 10), assuming choices are completely random. Related Topics For related functions and additional information, see: “BINOMDIST” on page 238 “CRITBINOM” on page 252 “NEGBINOMDIST” on page 275 “PERMUT” on page 281 “Listing of Statistical Functions” on page 225 “Value Types” on page 36 “The Elements of Formulas” on page 15 “Using the Keyboard and Mouse to Create and Edit Formulas” on page 26 “Pasting from Examples in Help” on page 41 QUARTILE The QUARTILE function returns the value for the specified quartile of a given data collection. QUARTILE(num-set, quartile-num)  num-set:  A collection of numbers. num-set is a collection containing number values.  quartile-num:  Specifies the desired quartile. smallest (0):  Returns the smallest value. first (1): Returns the first quartile (25th percentile). second (2):  Returns the second quartile (50th percentile). third (3):  Returns the third quartile (75th percentile). largest (4):  Returns the largest value. Usage Notes  MIN, MEDIAN, and MAX return the same value as QUARTILE when quartile-num is equal to 0, 2, and 4, respectively. 284 Chapter 10 Statistical Functions Chapter 10 Statistical Functions 285 Examples =QUARTILE({5, 6, 9, 3, 7, 11, 8, 2, 14}, 0) returns 2, the smallest value. =QUARTILE({5, 6, 9, 3, 7, 11, 8, 2, 14}, 1) returns 5, the 25th percentile or first quartile. =QUARTILE({5, 6, 9, 3, 7, 11, 8, 2, 14}, 2) returns 7, the 50th percentile or second quartile. =QUARTILE({5, 6, 9, 3, 7, 11, 8, 2, 14}, 3) returns 9, the 75th percentile or third quartile. =QUARTILE({5, 6, 9, 3, 7, 11, 8, 2, 14}, 0) returns 14, the largest value. Related Topics For related functions and additional information, see: “FREQUENCY” on page 257 “MAX” on page 270 “MEDIAN” on page 271 “MIN” on page 272 “PERCENTILE” on page 279 “PERCENTRANK” on page 280 “Listing of Statistical Functions” on page 225 “Value Types” on page 36 “The Elements of Formulas” on page 15 “Using the Keyboard and Mouse to Create and Edit Formulas” on page 26 “Pasting from Examples in Help” on page 41 RANK The RANK function returns the rank of a number within a range of numbers. RANK(num-date-dur, num-date-dur-set, largest-is-high)  num-date-dur:  A value. num-date-dur is a number value, a date/time value, or a duration value.  num-date-dur-set:  A collection of values. num-date-dur-set is a collection containing number, date, or duration values. All values must be of the same type.  largest-is-high:  An optional value specifying whether the smallest or the largest value in the collection is ranked 1. largest is low (0, FALSE, or omitted):  Assign the largest value in the collection the rank 1. largest is high (1, or TRUE):  Assign the smallest value in the collection the rank 1. Usage Notes  Values included in the collection that are the same are ranked together, but impact the outcome.  If the specified value does not match any of the values in the collection, an error is returned. Examples Assume the following table contains the cumulative test scores for this semester for your 20 students. (We have organized the data this way for the example; it would likely originally have been in 20 separate rows.) =RANK(30, A1:E4, 1) returns 1, as 30 is the smallest cumulative test score and we chose to rank the smallest first. =RANK(92, A1:E4, 0) returns 2, as 92 is the second-largest cumulative test score and we chose to rank largest first. =RANK(91, A1:E4, 1) returns 4, as there is a “tie” for second place. The order is 100, 92, 92, then 91 and the rank is 1, 2, 2, and then 4. Related Topics For related functions and additional information, see: “LARGE” on page 264 “SMALL” on page 288 “Listing of Statistical Functions” on page 225 “Value Types” on page 36 “The Elements of Formulas” on page 15 “Using the Keyboard and Mouse to Create and Edit Formulas” on page 26 “Pasting from Examples in Help” on page 41 286 Chapter 10 Statistical Functions Chapter 10 Statistical Functions 287 SLOPE The SLOPE function returns the slope of the best-fit line for the collection using linear regression analysis. SLOPE(y-values, x-values)  y-values:  The collection containing the y (dependent) values. y-values is a collection that can contain number, date/time, or duration values. All values must be of the same type.  x-values:  The collection containing the x (independent) values. x-values is a collection that can contain number, date/time, or duration values. All values must be of the same type. Usage Notes  The two collections must be of the same size or the function returns an error.  If, for example, you had data on the driving speed of a vehicle and its fuel efficiency at each speed, fuel efficiency would be the dependent variable and driving speed would be the independent variable.  To find the y-intercept of the best-fit line, use the INTERCEPT function. Example In this example, the SLOPE function is used to determine the slope of the best-fit line for the temperature that this hypothetical homeowner has set on the thermostat (the dependent variable), based on the price of heating oil (the independent variable). =SLOPE(B2:B11, A2:A11) evaluates to approximately -3.2337, indicating a best-fit line sloping downward (as prices rose, the thermostat was lowered). Related Topics For related functions and additional information, see: “INTERCEPT” on page 262 “Listing of Statistical Functions” on page 225 “Value Types” on page 36 “The Elements of Formulas” on page 15 “Using the Keyboard and Mouse to Create and Edit Formulas” on page 26 “Pasting from Examples in Help” on page 41 SMALL The SMALL function returns the nth-smallest value within a range. The smallest value is ranked number 1. SMALL(num-date-dur-set, ranking)  num-date-dur-set:  A collection of values. num-date-dur-set is a collection containing number, date, or duration values. All values must be of the same type.  ranking:  A number representing the size ranking of the value you want to retrieve. ranking is a number value and must be in the range of 1 to the number of values in the collection. Usage Notes  A ranking of 1 retrieves the smallest number in the collection, 2 the second-smallest, and so on. Values included in the collection that are of the same size are ranked together, but impact the outcome. Examples Assume the following table contains the cumulative test scores for this semester for your 20 students. (We have organized the data this way for the example; it would likely originally have been in 20 separate rows.) =SMALL(A1:E4, 1) returns 30, the smallest cumulative test score (cell A1). =SMALL(A1:E4, 2) returns 51, the second-smallest cumulative test score (cell E1). =SMALL(A1:E4, 6) returns 75, the sixth-smallest cumulative test score (order is 30, 51, 68, 70, 75, then 75 again, so 75 is both the fifth- and sixth-smallest cumulative test score). Related Topics For related functions and additional information, see: “LARGE” on page 264 “RANK” on page 285 “Listing of Statistical Functions” on page 225 288 Chapter 10 Statistical Functions Chapter 10 Statistical Functions 289 “Value Types” on page 36 “The Elements of Formulas” on page 15 “Using the Keyboard and Mouse to Create and Edit Formulas” on page 26 “Pasting from Examples in Help” on page 41 STANDARDIZE The STANDARDIZE function returns a normalized value from a distribution characterized by a given mean and standard deviation. STANDARDIZE(num, average, stdev)  num:  The number to be evaluated. num is a number value.  average:  The average of the distribution. average is a number value representing the known average (arithmetic mean) rate at which events occur.  stdev:  The standard deviation of the population. stdev is a number value and must be greater than 0. Example =STANDARDIZE(6, 15, 2.1) returns –4.28571428571429. Related Topics For related functions and additional information, see: “NORMDIST” on page 276 “NORMINV” on page 277 “NORMSDIST” on page 277 “NORMSINV” on page 278 “ZTEST” on page 305 “Listing of Statistical Functions” on page 225 “Value Types” on page 36 “The Elements of Formulas” on page 15 “Using the Keyboard and Mouse to Create and Edit Formulas” on page 26 “Pasting from Examples in Help” on page 41 STDEV The STDEV function returns the standard deviation, a measure of dispersion, of a collection of values based on their sample (unbiased) variance. STDEV(num-date-dur, num-date-dur…)  num-date-dur:  A value. num-date-dur is a number value, a date/time value, or a duration value.  num-date-dur…: One or more additional values (a minimum of two values are required). All num-date-dur values must be of the same type. Usage Notes  It is appropriate to use STDEV when the specified values represent only a sample of a larger population. If the values you are analyzing represent the entire collection or population, use the STDEVP function.  If you want to include text or Boolean values in the computation, use the STDEVA function.  The standard deviation is the square root of the variance returned by the VAR function. Example Assume you have administered five tests to a group of students. You have arbitrarily selected five students to represent the total population of students (note that this is an example only; this would not likely be statistically valid). Using the sample data, you could use the STDEV function to determine which test had the widest dispersion of test scores. The results of the STDEV functions are approximately 22.8035, 24.5357, 9.5026, 8.0747, and 3.3466. So test 2 had the highest dispersion, followed closely by test 1. The other three tests had low dispersion. Test 1 Test 2 Test 3 Test 4 Test 5 Student 1 75 82 90 78 84 Student 2 100 90 95 88 90 Student 3 40 80 78 90 85 Student 4 80 35 95 98 92 Student 5 90 98 75 97 88 =STDEV(B2:B6) =STDEV(C2:C6) =STDEV(D2:D6) =STDEV(E2:E6) =STDEV(F2:F6) Related Topics For related functions and additional information, see: “STDEVA” on page 291 “STDEVP” on page 293 290 Chapter 10 Statistical Functions Chapter 10 Statistical Functions 291 “STDEVPA” on page 294 “VAR” on page 298 “VARA” on page 300 “VARP” on page 302 “VARPA” on page 303 “Survey Results Example” on page 362 “Listing of Statistical Functions” on page 225 “Value Types” on page 36 “The Elements of Formulas” on page 15 “Using the Keyboard and Mouse to Create and Edit Formulas” on page 26 “Pasting from Examples in Help” on page 41 STDEVA The STDEVA function returns the standard deviation, a measure of dispersion, of a collection of values that may include text and Boolean values, based on the sample (unbiased) variance. STDEVA(value, value…)  value:  A value. value can contain any value type. All numeric values must be of the same type. You cannot mix numbers, dates, and duration values.  value…: One or more additional values (a minimum of two values are required). All numeric values must be of the same type. You cannot mix numbers, dates, and duration values. Usage Notes  It is appropriate to use STDEVA when the specified values represent only a sample of a larger population. If the values you are analyzing represent the entire collection or population, use the STDEVPA function.  STDEVA assigns a value of 0 to any text value, 0 to the Boolean value FALSE, and 1 to the Boolean value TRUE and includes them in the computation. Empty cells are ignored. If you do not want to include text or Boolean values in the computation, use the STDEV function.  The standard deviation is the square root of the variance returned by the VARA function. Example Assume you have installed a temperature sensor in Cupertino, California. The sensor records each day’s high and low temperatures. In addition, you have kept a record of each day you turned on the air conditioner in your condo. The data from the first few days is shown in the following table and is used as a sample for the population of high and low temperatures (note that this is an example only; this would not be statistically valid). =STDEVA(B2:B13) returns 24.8271, the dispersion as measured by STDEVA, of the sample of daily high temperatures. It exceeds the actual range of high temperatures of 15 degrees because the “unavailable” temperature is given a value of zero. Related Topics For related functions and additional information, see: “STDEV” on page 290 “STDEVP” on page 293 “STDEVPA” on page 294 “VAR” on page 298 “VARA” on page 300 “VARP” on page 302 “VARPA” on page 303 “Survey Results Example” on page 362 “Listing of Statistical Functions” on page 225 “Value Types” on page 36 “The Elements of Formulas” on page 15 292 Chapter 10 Statistical Functions Chapter 10 Statistical Functions 293 “Using the Keyboard and Mouse to Create and Edit Formulas” on page 26 “Pasting from Examples in Help” on page 41 STDEVP The STDEVP function returns the standard deviation, a measure of dispersion, of a collection of values based on their population (true) variance. STDEVP(num-date-dur, num-date-dur…)  num-date-dur:  A value. num-date-dur is a number value, a date/time value, or a duration value.  num-date-dur…: Optionally include one or more additional values. If more than one num-date-dur value is specified, all must be of the same type. Usage Notes  It is appropriate to use STDEVP when the specified values represent the entire collection or population. If the values you are analyzing represent only a sample of a larger population, use the STDEV function.  If you want to include text or Boolean values in the computation, use the STDEVPA function.  The standard deviation is the square root of the variance returned by the VARP function. Example Assume you have administered five tests to a group of students. You have a very small class and this represents the total population of your students. Using this population data, you could use the STDEVP function to determine which test had the widest dispersion of test scores. The results of the STDEVP functions are approximately 20.3961, 21.9454, 8.49994, 7.2222, and 2.9933. So test 2 had the highest dispersion, followed closely by test 1. The other three tests had low dispersion. Test 1 Test 2 Test 3 Test 4 Test 5 Student 1 75 82 90 78 84 Student 2 100 90 95 88 90 Student 3 40 80 78 90 85 Student 4 80 35 95 98 92 Student 5 75 82 90 78 84 =STDEVP(B2:B6) =STDEVP(C2:C6) =STDEVP(D2:D6) =STDEVP(E2:E6) =STDEVP(F2:F6) Related Topics For related functions and additional information, see: “STDEV” on page 290 “STDEVA” on page 291 “STDEVPA” on page 294 “VAR” on page 298 “VARA” on page 300 “VARP” on page 302 “VARPA” on page 303 “Survey Results Example” on page 362 “Listing of Statistical Functions” on page 225 “Value Types” on page 36 “The Elements of Formulas” on page 15 “Using the Keyboard and Mouse to Create and Edit Formulas” on page 26 “Pasting from Examples in Help” on page 41 STDEVPA The STDEVPA function returns the standard deviation, a measure of dispersion, of a collection of values that may include text and Boolean values, based on the population (true) variance. STDEVPA(value, value…)  value:  A value. value can contain any value type.  value…: Optionally include one or more additional values. All numeric values must be of the same type. You cannot mix numbers, dates, and duration values. Usage Notes  It is appropriate to use STDEVPA when the specified values represent the entire collection or population. If the values you are analyzing represent only a sample of a larger population, use the STDEVA function.  STDEVPA assigns a value of 0 to any text value, 0 to the Boolean value FALSE, and 1 to the Boolean value TRUE and includes them in the computation. Empty cells are ignored. If you do not want to include text or Boolean values in the computation, use the STDEVP function. 294 Chapter 10 Statistical Functions Chapter 10 Statistical Functions 295  The standard deviation is the square root of the variance returned by the VARPA function. Example Assume you have installed a temperature sensor in Cupertino, California. The sensor records each day’s high and low temperatures. In addition, you have kept a record of each day you turned on the air conditioner in your condo. The sensor failed after the first few days so the following table is the population of high and low temperatures. =STDEVPA(B2:B13) returns 23.7702, the dispersion as measured by STDEVPA, of the sample of daily high temperatures. It exceeds the actual range of high temperatures of 15 degrees because the “unavailable” temperature is given a value of zero. Related Topics For related functions and additional information, see: “STDEV” on page 290 “STDEVA” on page 291 “STDEVP” on page 293 “VAR” on page 298 “VARA” on page 300 “VARP” on page 302 “VARPA” on page 303 “Survey Results Example” on page 362 “Listing of Statistical Functions” on page 225 “Value Types” on page 36 “The Elements of Formulas” on page 15 “Using the Keyboard and Mouse to Create and Edit Formulas” on page 26 “Pasting from Examples in Help” on page 41 TDIST The TDIST function returns the probability from the student’s t-distribution. TDIST(non-neg-x-value, degrees-freedom, tails)  non-neg-x-value:  The value at which you want to evaluate the function. non-neg-xvalue is a number value that must be greater than or equal to 0.  degrees-freedom:  Degrees of freedom. degrees-freedom is a number value and must be greater than or equal to 1.  tails:  The number of tails to return. one tail (1):  Return the value for a one-tailed distribution. two tails (2):  Return the value for a two-tailed distribution. Examples =TDIST(4, 2, 1) returns 0.0285954792089682, for the one-tailed distribution. =TDIST(4, 2, 2) returns 0.0571909584179364, for the two-tailed distribution. Related Topics For related functions and additional information, see: “TINV” on page 297 “TTEST” on page 297 “Listing of Statistical Functions” on page 225 “Value Types” on page 36 “The Elements of Formulas” on page 15 “Using the Keyboard and Mouse to Create and Edit Formulas” on page 26 “Pasting from Examples in Help” on page 41 296 Chapter 10 Statistical Functions Chapter 10 Statistical Functions 297 TINV The TINV function returns the t value (a function of the probability and degrees of freedom) from the student’s t-distribution. TINV(probability, degrees-freedom)  probability:  A probability associated with the distribution. probability is a number value and must be greater than 0 and less than 1.  degrees-freedom:  Degrees of freedom. degrees-freedom is a number value and must be greater than or equal to 1. Example =TINV(0.88, 2) returns 0.170940864689457. Related Topics For related functions and additional information, see: “TDIST” on page 296 “TTEST” on page 297 “Listing of Statistical Functions” on page 225 “Value Types” on page 36 “The Elements of Formulas” on page 15 “Using the Keyboard and Mouse to Create and Edit Formulas” on page 26 “Pasting from Examples in Help” on page 41 TTEST The TTEST function returns the probability associated with a student’s t-test, based on the t-distribution function. TTEST(sample-1-values, sample-2-values, tails, test-type)  sample-1-values:  The collection containing the first collection of sample values. sample-1-values is a collection containing numbers.  sample-2-values:  The collection containing the second collection of sample values. sample-2-values is a collection containing number values.  tails:  The number of tails to return. one tail (1):  Returns the value for a one-tailed distribution. two tails (2):  Returns the value for a two-tailed distribution.  test-type:  The type of t-test to perform. paired (1):  Perform a paired test. two-sample equal (2):  Perform a two-sample equal variance (homoscedastic) test. two-sample unequal (3):  Perform a two-sample unequal variance (heteroscedastic) test. Examples =TTEST({57, 75, 66, 98, 92, 80}, {87, 65, 45, 95, 88, 79}, 1, 1) returns 0.418946725989974, for the one-tailed, paired test. =TTEST({57, 75, 66, 98, 92, 80}, {87, 65, 45, 95, 88, 79}, 2, 1) returns 0.837893451979947 for the two-tailed, paired test. =TTEST({57, 75, 66, 98, 92, 80}, {87, 65, 45, 95, 88, 79}, 1, 2) returns 0.440983897602811 for the one-tailed, two sample equal test. =TTEST({57, 75, 66, 98, 92, 80}, {87, 65, 45, 95, 88, 79}, 2, 2) returns 0.881967795205622 for the two-tailed, two sample equal test. =TTEST({57, 75, 66, 98, 92, 80}, {87, 65, 45, 95, 88, 79}, 1, 3) returns 0.441031763311189 for the one-tailed, two sample unequal test. Related Topics For related functions and additional information, see: “TDIST” on page 296 “TINV” on page 297 “Listing of Statistical Functions” on page 225 “Value Types” on page 36 “The Elements of Formulas” on page 15 “Using the Keyboard and Mouse to Create and Edit Formulas” on page 26 “Pasting from Examples in Help” on page 41 VAR The VAR function returns the sample (unbiased) variance, a measure of dispersion, of a collection of values. VAR(num-date, num-date…)  num-date:  A value. num-date is a number value or a date/time value.  num-date…: Optionally include one or more additional values. If more than one num-date-dur value is specified, they must all be of the same type. 298 Chapter 10 Statistical Functions Chapter 10 Statistical Functions 299 Usage Notes  The VAR function finds the sample (unbiased) variance by dividing the sum of the squares of the deviations of the data points by one less than the number of values.  It is appropriate to use VAR when the specified values represent only a sample of a larger population. If the values you are analyzing represent the entire collection or population, use the VARP function.  If you want to include text or Boolean values in the computation, use the VARA function.  The square root of the variance returned by the VAR function is returned by the STDEV function. Examples Assume you have administered five tests to a group of students. You have arbitrarily selected five students to represent the total population of students (note that this is an example only; this would not likely be statistically valid). Using the sample data, you could use the VAR function to determine which test had the widest dispersion of test scores. The results of the VAR functions are approximately 520.00, 602.00, 90.30, 65.20, and 11.20. So test 2 had the highest dispersion, followed closely by test 1. The other three tests had low dispersion. Test 1 Test 2 Test 3 Test 4 Test 5 Student 1 75 82 90 78 84 Student 2 100 90 95 88 90 Student 3 40 80 78 90 85 Student 4 80 35 95 98 92 Student 5 75 82 90 78 84 =VAR(B2:B6) =VAR(C2:C6) =VAR(D2:D6) =VAR(E2:E6) =VAR(F2:F6) Related Topics For related functions and additional information, see: “STDEV” on page 290 “STDEVA” on page 291 “STDEVP” on page 293 “STDEVPA” on page 294 “VARA” on page 300 “VARP” on page 302 “VARPA” on page 303 “Survey Results Example” on page 362 “Listing of Statistical Functions” on page 225 “Value Types” on page 36 “The Elements of Formulas” on page 15 “Using the Keyboard and Mouse to Create and Edit Formulas” on page 26 “Pasting from Examples in Help” on page 41 VARA The VARA function returns the sample (unbiased) variance, a measure of dispersion, of a collection of values, including text and Boolean values. VARA(value, value…)  value:  A value. value can contain any value type.  value…: Optionally include one or more additional values. All numeric values must be of the same type. You cannot mix numbers, dates, and duration values. Usage Notes  The VARA function finds the sample (unbiased) variance by dividing the sum of the squares of the deviations of the data points by one less than the number of values.  It is appropriate to use VARA when the specified values represent only a sample of a larger population. If the values you are analyzing represent the entire collection or population, use the VARPA function.  VARA assigns a value of 0 to any text value, 0 to the Boolean value FALSE, and 1 to the Boolean value TRUE and includes them in the computation. Empty cells are ignored. If you do not want to include text or Boolean values in the computation, use the VAR function.  The square root of the variance returned by the VARA function is returned by the STDEVA function. 300 Chapter 10 Statistical Functions Chapter 10 Statistical Functions 301 Example Assume you have installed a temperature sensor in Cupertino, California. The sensor records each day’s high and low temperatures. In addition, you have kept a record of each day you turned on the air conditioner in your condo. The data from the first few days is shown in the following table and is used as a sample for the population of high and low temperatures (note that this is an example only; this would not be statistically valid). =VARA(B2:B13) returns 616.3864, the dispersion as measured by VARA, of the sample of daily high temperatures. Related Topics For related functions and additional information, see: “STDEV” on page 290 “STDEVA” on page 291 “STDEVP” on page 293 “STDEVPA” on page 294 “VAR” on page 298 “VARP” on page 302 “VARPA” on page 303 “Survey Results Example” on page 362 “Listing of Statistical Functions” on page 225 “Value Types” on page 36 “The Elements of Formulas” on page 15 “Using the Keyboard and Mouse to Create and Edit Formulas” on page 26 “Pasting from Examples in Help” on page 41 VARP The VARP function returns the population (true) variance, a measure of dispersion, of a collection of values. VARP(num-date, num-date…)  num-date:  A value. num-date is a number value or a date/time value.  num-date…: Optionally include one or more additional values. If more than one num-date value is specified, all must be of the same type. Usage Notes  The VARP function finds the population, or true, variance (as opposed to the sample, or unbiased, variance) by dividing the sum of the squares of the deviations of the data points by the number of values.  It is appropriate to use VARP when the specified values represent the entire collection or population. If the values you are analyzing represent only a sample of a larger population, use the VAR function.  If you want to include text or Boolean values in the computation, use the VARPA function.  The square root of the variance returned by the VARP function is returned by the STDEVP function. Example Assume you have administered five tests to a group of students. You have a very small class and this represents the total population of your students. Using this population data, you could use the VARP function to determine which test had the widest dispersion of test scores. The results of the VARP functions are approximately 416.00, 481.60, 72.24, 52.16, and 8.96. So test 2 had the highest dispersion, followed closely by test 1. The other three tests had low dispersion. Test 1 Test 2 Test 3 Test 4 Test 5 Student 1 75 82 90 78 84 Student 2 100 90 95 88 90 Student 3 40 80 78 90 85 Student 4 80 35 95 98 92 Student 5 75 82 90 78 84 =VARP(B2:B6) =VARP(C2:C6) =VARP(D2:D6) =VARP(E2:E6) =VARP(F2:F6) Related Topics For related functions and additional information, see: “STDEV” on page 290 “STDEVA” on page 291 302 Chapter 10 Statistical Functions Chapter 10 Statistical Functions 303 “STDEVP” on page 293 “STDEVPA” on page 294 “VAR” on page 298 “VARA” on page 300 “VARPA” on page 303 “Survey Results Example” on page 362 “Listing of Statistical Functions” on page 225 “Value Types” on page 36 “The Elements of Formulas” on page 15 “Using the Keyboard and Mouse to Create and Edit Formulas” on page 26 “Pasting from Examples in Help” on page 41 VARPA The VARPA function returns the sample (unbiased) variance, a measure of dispersion, of a collection of values, including text and Boolean values. VARPA(value, value…)  value:  A value. value can contain any value type.  value…: Optionally include one or more additional values. All numeric values must be of the same type. You cannot mix numbers, dates, and duration values. Usage Notes  The VARPA function finds the population, or true, variance (as opposed to the sample, or unbiased, variance) by dividing the sum of the squares of the deviations of the data points.  It is appropriate to use VARPA when the specified values represent the entire collection or population. If the values you are analyzing represent only a sample of a larger population, use the VARA function.  VARPA assigns a value of 0 to any text value, 0 to the Boolean value FALSE, and 1 to the Boolean value TRUE and includes them in the computation. Empty cells are ignored. If you do not want to include text or Boolean values in the computation, use the VAR function.  The square root of the variance returned by the VARPA function is returned by the STDEVPA function. Example Assume you have installed a temperature sensor in Cupertino, California. The sensor records each day’s high and low temperatures. In addition, you have kept a record of each day you turned on the air conditioner in your condo. The sensor failed after the first few days so the following table is the population of high and low temperatures. =VARPA(B2:B13) returns 565.0208, the dispersion as measured by VARPA, of the sample of daily high temperatures. Related Topics For related functions and additional information, see: “STDEV” on page 290 “STDEVA” on page 291 “STDEVP” on page 293 “STDEVPA” on page 294 “VAR” on page 298 “VARA” on page 300 “VARP” on page 302 “Survey Results Example” on page 362 “Listing of Statistical Functions” on page 225 “Value Types” on page 36 “The Elements of Formulas” on page 15 “Using the Keyboard and Mouse to Create and Edit Formulas” on page 26 “Pasting from Examples in Help” on page 41 304 Chapter 10 Statistical Functions Chapter 10 Statistical Functions 305 ZTEST The ZTEST function returns the one-tailed probability value of the Z-test. ZTEST(num-date-dur-set, num-date-dur, stdev)  num-date-dur-set:  A collection of values. num-date-dur-set is a collection containing number, date, or duration values. All values must be of the same type.  num-date-dur:  A value. num-date-dur is a number value, a date/time value, or a duration value.num-date-dur is the value to test.  stdev:  An optional value for the standard deviation of the population. stdev is a number value and must be greater than 0. Usage Notes  The Z-test is a statistical test which determines if the difference between a sample mean and the population mean is large enough to be statistically significant. The Z-test is used primarily with standardized testing.  If stdev is omitted, the assumed sample standard deviation is used. Example =ZTEST({57, 75, 66, 98, 92, 80}, 70, 9) returns 0.0147281928162857. Related Topics For related functions and additional information, see: “STANDARDIZE” on page 289 “Listing of Statistical Functions” on page 225 “Value Types” on page 36 “The Elements of Formulas” on page 15 “Using the Keyboard and Mouse to Create and Edit Formulas” on page 26 “Pasting from Examples in Help” on page 41 306 The text functions help you work with strings of characters. Listing of Text Functions iWork provides these text functions for use with tables. Function Description “CHAR” (page 308) The CHAR function returns the character that corresponds to a decimal Unicode character code. “CLEAN” (page 308) The CLEAN function removes most common nonprinting characters (Unicode character codes 0–31) from text. “CODE” (page 309) The CODE function returns the decimal Unicode number of the first character in a specified string. “CONCATENATE” (page 310) The CONCATENATE function joins (concatenates) strings. “DOLLAR” (page 311) The DOLLAR function returns a string formatted as a dollar amount from a given number. “EXACT” (page 312) The EXACT function returns TRUE if the argument strings are identical in case and content. “FIND” (page 312) The FIND function returns the starting position of one string within another. “FIXED” (page 313) The FIXED function rounds a number to the specified number of decimal places and then returns the result as a string value. “LEFT” (page 314) The LEFT function returns a string consisting of the specified number of characters from the left end of a given string. Text Functions 11 Chapter 11 Text Functions 307 Function Description “LEN” (page 315) The LEN function returns the number of characters in a string. “LOWER” (page 316) The LOWER function returns a string that is entirely lowercase, regardless of the case of the characters in the specified string. “MID” (page 316) The MID function returns a string consisting of the given number of characters from a string starting at the specified position. “PROPER” (page 317) The PROPER function returns a string where the first letter of each word is uppercase and all remaining characters are lowercase, regardless of the case of the characters in the specified string. “REPLACE” (page 318) The REPLACE function returns a string where a specified number of characters of a given string have been replaced with a new string. “REPT” (page 319) The REPT function returns a string that contains a given string repeated a specified number of times. “RIGHT” (page 319) The RIGHT function returns a string consisting of the given number of characters from the right end of a specified string. “SEARCH” (page 320) The SEARCH function returns the starting position of one string within another, ignoring case and allowing wildcards. “SUBSTITUTE” (page 322) The SUBSTITUTE function returns a string where the specified characters of a given string have been replaced with a new string. “T” (page 323) The T function returns the text contained in a cell. This function is included for compatibility with tables imported from other spreadsheet applications. “TRIM” (page 323) The TRIM function returns a string based on a given string, after removing extra spaces. “UPPER” (page 324) The UPPER function returns a string that is entirely uppercase, regardless of the case of the characters in the specified string. “VALUE” (page 325) The VALUE function returns a number value even if the argument is formatted as text. CHAR The CHAR function returns the character that corresponds to a decimal Unicode character code. CHAR(code-number)  code-number:  A number for which you want to return the corresponding Unicode character. code-number is a number value and must be greater than or equal to 32, less than or equal to 65,535, and not equal to 127. If there is a decimal portion, it is ignored. Note that character 32 is the space character. Usage Notes  Not all Unicode numbers are associated with a printable character.  You can use the Special Characters window, which is available on the Edit menu, to view entire sets of characters and their codes.  The CODE function returns the numeric code for a specific character. Examples =CHAR(98.6) returns “b”, which is represented by the code 98. The decimal portion of the number is ignored. =CODE(”b”) returns 98. Related Topics For related functions and additional information, see: “CODE” on page 309 “Listing of Text Functions” on page 306 “Value Types” on page 36 “The Elements of Formulas” on page 15 “Using the Keyboard and Mouse to Create and Edit Formulas” on page 26 “Pasting from Examples in Help” on page 41 CLEAN The CLEAN function removes most common nonprinting characters (Unicode character codes 0–31) from text. CLEAN(text)  text:  The text from which you want to remove nonprinting characters. text can contain any value type. 308 Chapter 11 Text Functions Chapter 11 Text Functions 309 Usage Notes  This can be helpful if text you paste from another application contains unwanted question marks, spaces, boxes, or other unexpected characters.  There are some less common nonprinting characters that are not removed by CLEAN (character codes 127, 129, 141, 143, 144, and 157). To remove these, you can use the SUBSTITUTE function to replace them with a code in the range 0–31 before you use the CLEAN function.  You can use the TRIM function to remove extra spaces in text. Example Suppose you copy what you believe to be the text “a b c d e f” from another application and paste it into cell A1, but instead see “a b c ? ?d e f”. You can try using CLEAN to remove the unexpected characters: =CLEAN(A1) returns “a b c d e f”. Related Topics For related functions and additional information, see: “SUBSTITUTE” on page 322 “TRIM” on page 323 “Listing of Text Functions” on page 306 “Value Types” on page 36 “The Elements of Formulas” on page 15 “Using the Keyboard and Mouse to Create and Edit Formulas” on page 26 “Pasting from Examples in Help” on page 41 CODE The CODE function returns the decimal Unicode number of the first character in a specified string. CODE(code-string)  code-string:  The string from which to return the Unicode value. code-string is a string value. Only the first character is used. Usage Notes  You can use the Special Characters window, which is available on the Edit menu, to view entire sets of characters and their codes.  You can use the CHAR function to do the opposite of the CODE function: convert a numeric code into a text character. Examples =CODE(”A”) returns 65, the character code for uppercase “A”. =CODE(”abc”) returns 97 for lowercase “a”. =CHAR(97) returns “a”. =CODE(A3) returns 102 for lowercase “f”. =CODE(”三二一”) returns 19,977, the decimal Unicode value of the first character. Related Topics For related functions and additional information, see: “CHAR” on page 308 “Listing of Text Functions” on page 306 “Value Types” on page 36 “The Elements of Formulas” on page 15 “Using the Keyboard and Mouse to Create and Edit Formulas” on page 26 “Pasting from Examples in Help” on page 41 CONCATENATE The CONCATENATE function joins (concatenates) strings. CONCATENATE(string, string…)  string:  A string. string is a string value.  string…: Optionally include one or more additional strings. Usage Notes  As an alternative to the CONCATENATE function, you can use the & string operator to concatenate strings. Examples If cell A1 contains Lorem and cell B1 contains Ipsum, =CONCATENATE(B1, “, “, A1) returns “Ipsum, Lorem”. =CONCATENATE(”a”, “b”, “c”) returns “abc”. =”a”&”b”&”c” returns “abc”. Related Topics For related functions and additional information, see: 310 Chapter 11 Text Functions Chapter 11 Text Functions 311 “Listing of Text Functions” on page 306 “Value Types” on page 36 “The Elements of Formulas” on page 15 “Using the Keyboard and Mouse to Create and Edit Formulas” on page 26 “Pasting from Examples in Help” on page 41 DOLLAR The DOLLAR function returns a string formatted as a dollar amount from a given number. DOLLAR(num, places)  num:  The number to be used. num is a number value.  places:  An optional argument specifying the number of places to the right, or left, of the decimal point at which rounding should occur. places is a number value. When rounding to the specified number of places, standard arithmetical rounding is used; if the most significant digit being dropped is 5 or greater, the result is rounded up. A negative number indicates rounding should occur to the left of the decimal (for example, round to hundreds or thousands). Examples =DOLLAR(2323.124) returns $2,323.12. =DOLLAR(2323.125) returns $2,323.13. =DOLLAR(99.554, 0) returns $100. =DOLLAR(12, 3) returns $12.000. =DOLLAR(-12, 3) returns ($12.000), with parentheses indicating a negative amount. =DOLLAR(123, -1) returns $120. Related Topics For related functions and additional information, see: “FIXED” on page 313 “Listing of Text Functions” on page 306 “Value Types” on page 36 “The Elements of Formulas” on page 15 “Using the Keyboard and Mouse to Create and Edit Formulas” on page 26 “Pasting from Examples in Help” on page 41 EXACT The EXACT function returns TRUE if the argument strings are identical in case and content. EXACT(string-1, string-2)  string-1:  The first string. string-1 is a string value.  string-2:  The second string. string-2 is a string value. Examples =EXACT(”toledo”, “toledo”) returns TRUE, since all the characters and their cases are identical. =EXACT(”Toledo”, “toledo”) returns FALSE, since the case of the two strings is not identical. Related Topics For related functions and additional information, see: “FIND” on page 312 “SEARCH” on page 320 “Listing of Text Functions” on page 306 “Value Types” on page 36 “The Elements of Formulas” on page 15 “Using the Keyboard and Mouse to Create and Edit Formulas” on page 26 “Pasting from Examples in Help” on page 41 FIND The FIND function returns the starting position of one string within another. FIND(search-string, source-string, start-pos)  search-string:  The string to find. search-string is a string value.  source-string:  A string. source-string is a string value.  start-pos:  An optional argument that specifies the position within the specified string at which the action should begin. start-pos is a number value that must be greater than or equal to 1 and less than or equal to the number of characters in source-string. Notes  The search is case sensitive and spaces are counted. Wildcards are not allowed. To use wildcards or to ignore case in your search, use the SEARCH function. 312 Chapter 11 Text Functions Chapter 11 Text Functions 313  Specifying start-pos permits you to begin the search for search-string within, rather than at the beginning of, source-string. This is particularly useful if source-string may contain multiple instances of search-string and you wish to determine the starting position of other than the first instance. If start-pos is omitted, it is assumed to be 1. Examples =FIND(”e”, “where on earth”) returns 3 (”e” is the third character in the string “where on earth”). =FIND(”e”, “where on earth”, 8) returns 10 (”e” in earth is the first “e” found starting from character 8, the “n” in “on”). Related Topics For related functions and additional information, see: “EXACT” on page 312 “SEARCH” on page 320 “Listing of Text Functions” on page 306 “Value Types” on page 36 “The Elements of Formulas” on page 15 “Using the Keyboard and Mouse to Create and Edit Formulas” on page 26 “Pasting from Examples in Help” on page 41 FIXED The FIXED function rounds a number to the specified number of decimal places and then returns the result as a string value. FIXED(num, places, no-commas)  num:  The number to be used. num is a number value.  places:  An optional argument indicating the number of places to the right, or left, of the decimal point at which rounding should occur. places is a number value. When rounding to the specified number of places, round-half-up is used. If the most significant digit being dropped is 5 or greater, the result is rounded up. A negative number indicates rounding should occur to the left of the decimal (for example, round to hundreds or thousands).  no-commas:  An optional argument indicating whether to use position separators in the whole portion of the resulting number. use commas (FALSE, 0, or omitted):  Include position separators in the result. no commas (TRUE or 1):  Don’t include position separators in the result. Examples =FIXED(6789.123, 2) returns “6,789.12.” =FIXED(6789.123, 1, 1) returns “6789.1.” =FIXED(6789.123, -2) returns “6,800.” =FIXED(12.4, 0) returns “12.” =FIXED(12.5, 0) returns “13.” =FIXED(4, -1) returns “0.” =FIXED(5, -1) returns “10.” Related Topics For related functions and additional information, see: “DOLLAR” on page 311 “Listing of Text Functions” on page 306 “Value Types” on page 36 “The Elements of Formulas” on page 15 “Using the Keyboard and Mouse to Create and Edit Formulas” on page 26 “Pasting from Examples in Help” on page 41 LEFT The LEFT function returns a string consisting of the specified number of characters from the left end of a given string. LEFT(source-string, string-length)  source-string:  A string. source-string is a string value.  string-length:  An optional argument specifying the desired length of the returned string. string-length is a number value and must be greater than or equal to 1. Usage Notes  If string-length is greater than or equal to the length of source-string, the string returned is equal to source-string. Examples =LEFT(”one two three”, 2) returns “on”. =LEFT(”abc”) returns “a”. 314 Chapter 11 Text Functions Chapter 11 Text Functions 315 Related Topics For related functions and additional information, see: “MID” on page 316 “RIGHT” on page 319 “Listing of Text Functions” on page 306 “Value Types” on page 36 “The Elements of Formulas” on page 15 “Using the Keyboard and Mouse to Create and Edit Formulas” on page 26 “Pasting from Examples in Help” on page 41 LEN The LEN function returns the number of characters in a string. LEN(source-string)  source-string:  A string. source-string is a string value. Usage Notes  The count includes all spaces, numbers, and special characters. Examples =LEN(”12345”) returns 5. =LEN(” abc def “) returns 9, the sum of the six letters plus the leading, trailing, and separating spaces. Related Topics For related functions and additional information, see: “Listing of Text Functions” on page 306 “Value Types” on page 36 “The Elements of Formulas” on page 15 “Using the Keyboard and Mouse to Create and Edit Formulas” on page 26 “Pasting from Examples in Help” on page 41 LOWER The LOWER function returns a string that is entirely lowercase, regardless of the case of the characters in the specified string. LOWER(source-string)  source-string:  A string. source-string is a string value. Examples =LOWER(”UPPER”) returns “upper”. =LOWER(”Lower”) returns “lower”. =LOWER(”MiXeD”) returns “mixed”. Related Topics For related functions and additional information, see: “PROPER” on page 317 “UPPER” on page 324 “Listing of Text Functions” on page 306 “Value Types” on page 36 “The Elements of Formulas” on page 15 “Using the Keyboard and Mouse to Create and Edit Formulas” on page 26 “Pasting from Examples in Help” on page 41 MID The MID function returns a string consisting of the given number of characters from a string starting at the specified position. MID(source-string, start-pos, string-length)  source-string:  A string. source-string is a string value.  start-pos:  The position within the specified string at which the action should begin. start-pos is a number value that must be greater than or equal to 1 and less than or equal to the number of characters in source-string.  string-length:  The desired length of the returned string. string-length is a number value and must be greater than or equal to 1. Usage Notes  If string-length is greater than or equal to the length of source-string, the string returned is equal to source-string, beginning at start-pos. 316 Chapter 11 Text Functions Chapter 11 Text Functions 317 Examples =MID(”lorem ipsum dolor sit amet”, 7, 5) returns “ipsum”. =MID(”1234567890”, 4, 3) returns “456”. =MID(”shorten”, 5, 20) returns “ten”. Related Topics For related functions and additional information, see: “LEFT” on page 314 “RIGHT” on page 319 “Listing of Text Functions” on page 306 “Value Types” on page 36 “The Elements of Formulas” on page 15 “Using the Keyboard and Mouse to Create and Edit Formulas” on page 26 “Pasting from Examples in Help” on page 41 PROPER The PROPER function returns a string where the first letter of each word is uppercase and all remaining characters are lowercase, regardless of the case of the characters in the specified string. PROPER(source-string)  source-string:  A string. source-string is a string value. Usage Notes  Any character following a nonalphabetic character, except apostrophe (‘), is treated as the first letter in a word. So, for example, any letter following a hyphen is capitalized. Examples =PROPER(”lorem ipsum”) returns “Lorem Ipsum”. =PROPER(”lorem’s ip-sum”) returns “Lorem’s Ip-Sum”. =PROPER(”1a23 b456”) returns “1A23 B456”. Related Topics For related functions and additional information, see: “LOWER” on page 316 “UPPER” on page 324 “Listing of Text Functions” on page 306 “Value Types” on page 36 “The Elements of Formulas” on page 15 “Using the Keyboard and Mouse to Create and Edit Formulas” on page 26 “Pasting from Examples in Help” on page 41 REPLACE The REPLACE function returns a string where a specified number of characters of a given string have been replaced with a new string. REPLACE(source-string, start-pos, replace-length, new-string)  source-string:  A string. source-string is a string value.  start-pos:  The position within the specified string at which the action should begin. start-pos is a number value that must be greater than or equal to 1. If start-pos is greater than the number of characters in source-string, new-string is added to the end of source-string.  replace-length:  The number of characters to be replaced. replace-length is a number value that must be greater than or equal to 1. If replace-length is greater than or equal to the length of source-string, the returned string is equal to new-string.  new-string:  The text used as a replacement for the section of the given string that is replaced. new-string is a string value. It does not have to be the same length as the text replaced. Example =REPLACE(”received applicant’s forms”, 10, 9, “Frank”) returns “received Frank’s forms”. Related Topics For related functions and additional information, see: “SUBSTITUTE” on page 322 “Listing of Text Functions” on page 306 “Value Types” on page 36 “The Elements of Formulas” on page 15 “Using the Keyboard and Mouse to Create and Edit Formulas” on page 26 “Pasting from Examples in Help” on page 41 318 Chapter 11 Text Functions Chapter 11 Text Functions 319 REPT The REPT function returns a string that contains a given string repeated a specified number of times. REPT(source-string, repeat-number)  source-string:  A string. source-string is a string value.  repeat-number:  The number of times the given string should be repeated. repeatnumber is a number value that must be greater than or equal to 0. Examples =REPT(”*”, 5) returns “*****”. =REPT(”ha”, 3) returns “hahaha”. Related Topics For related functions and additional information, see: “Listing of Text Functions” on page 306 “Value Types” on page 36 “The Elements of Formulas” on page 15 “Using the Keyboard and Mouse to Create and Edit Formulas” on page 26 “Pasting from Examples in Help” on page 41 RIGHT The RIGHT function returns a string consisting of the specified number of characters from the right end of a given string. RIGHT(source-string, string-length)  source-string:  A string. source-string is a string value.  string-length:  An optional argument specifying the desired length of the returned string. string-length is a number value and must be greater than or equal to 1. Usage Notes  If string-length is greater than or equal to the length of source-string, the string returned is equal to source-string. Examples =RIGHT(”one two three”, 2) returns “ee”. =RIGHT(”abc”) returns “c”. Related Topics For related functions and additional information, see: “LEFT” on page 314 “MID” on page 316 “Listing of Text Functions” on page 306 “Value Types” on page 36 “The Elements of Formulas” on page 15 “Using the Keyboard and Mouse to Create and Edit Formulas” on page 26 “Pasting from Examples in Help” on page 41 SEARCH The SEARCH function returns the starting position of one string within another, ignoring case and allowing wildcards. SEARCH(search-string, source-string, start-pos)  search-string:  The string to find. search-string is a string value.  source-string:  A string. source-string is a string value.  start-pos:  An optional argument that specifies the position within the specified string at which the action should begin. start-pos is a number value that must be greater than or equal to 1 and less than or equal to the number of characters in source-string. Usage Notes  Wildcards are permitted in search-string. In search-string, use an * (asterisk) to match multiple characters or a ? (question mark) to match any single character in sourcestring.  Specifying start-pos permits you to begin the search for search-string within, rather than at the beginning of, source-string. This is particularly useful if source-string may contain multiple instances of search-string and you wish to determine the starting position of other than the first instance. If start-pos is omitted, it is assumed to be 1.  To have case considered in your search, use the FIND function. 320 Chapter 11 Text Functions Chapter 11 Text Functions 321 Examples =SEARCH(”ra”, “abracadabra”) returns 3; the first occurrence of the string “ra” starts at the third character in “abracadabra”. =SEARCH(”ra”, “abracadabra”, 5) returns 10, the position of the first occurrence of string “ra” when you start looking at position 5. =SEARCH(“*card”, “Wildcard”) returns 1, since the asterisk at the beginning of the search string matches all the characters before “card”. =SEARCH(“*cad”, “Wildcard”) returns an error, since the string “cad” does not exist. =SEARCH(“?card”, “Wildcard”) returns 4, since the question mark matches the one character immediately preceding “card”. =SEARCH(“c*d”, “Wildcard”) returns 5, since the asterisk matches all the characters between the “c” and “d”. =SEARCH(“~?”, “Wildcard? No.”) returns 9, since the tilde means to interpret the next character (the question mark) literally, not as a wildcard, and the question mark is the 9th character. Related Topics For related functions and additional information, see: “EXACT” on page 312 “FIND” on page 312 “Specifying Conditions and Using Wildcards” on page 360 “Listing of Text Functions” on page 306 “Value Types” on page 36 “The Elements of Formulas” on page 15 “Using the Keyboard and Mouse to Create and Edit Formulas” on page 26 “Pasting from Examples in Help” on page 41 SUBSTITUTE The SUBSTITUTE function returns a string where the specified characters of a given string have been replaced with a new string. SUBSTITUTE(source-string, existing-string, new-string, occurrence)  source-string:  A string. source-string is a string value.  existing-string:  The string within the given string that is to be replaced. existingstring is a string value.  new-string:  The text used as a replacement for the section of the given string that is replaced. new-string is a string value. It does not have to be the same length as the text replaced.  occurrence:  An optional value specifying the occurrence that should be replaced. occurrence is a number value and must be greater than or equal to 1, or omitted. If greater than the number of times existing-string appears within source-string, no replacement will occur. If omitted, all occurrences of existing-string within sourcestring will be replaced by new-string. Usage Notes  You can replace individual characters, whole words, or strings of characters within words. Examples =SUBSTITUTE(”a b c d e f”, “b”, “B”) returns “a B c d e f”. =SUBSTITUTE(”a a b b b c”, “a”, “A”, 2) returns “a A b b b c”. =SUBSTITUTE(”a a b b b c”, “b”, “B”) returns “a a B B B c”. =SUBSTITUTE(”aaabbccc”, “bc”, “BC”, 2) returns “aaabbccc”. Related Topics For related functions and additional information, see: “REPLACE” on page 318 “Listing of Text Functions” on page 306 “Value Types” on page 36 “The Elements of Formulas” on page 15 “Using the Keyboard and Mouse to Create and Edit Formulas” on page 26 “Pasting from Examples in Help” on page 41 322 Chapter 11 Text Functions Chapter 11 Text Functions 323 T The T function returns the text contained in a cell. This function is included for compatibility with tables imported from other spreadsheet applications. T(cell)  cell:  A reference to a single table cell. cell is a reference value to a single cell that can contain any value, or be empty. Usage Notes  If the cell doesn’t contain a string, T returns an empty string. Examples If cell A1 contains “text” and cell B1 is empty: =T(A1) returns “text” =T(B1) returns nothing. Related Topics For related functions and additional information, see: “Listing of Text Functions” on page 306 “Value Types” on page 36 “The Elements of Formulas” on page 15 “Using the Keyboard and Mouse to Create and Edit Formulas” on page 26 “Pasting from Examples in Help” on page 41 TRIM The TRIM function returns a string based on a given string, after removing extra spaces. TRIM(source-string)  source-string:  A string. source-string is a string value. Usage Notes  TRIM removes all spaces before the first character, all spaces after the last character, and all duplicate spaces between characters, leaving only single spaces between words. Example =TRIM(” spaces spaces spaces “) returns “spaces spaces spaces” (the leading and trailing space were removed). Related Topics For related functions and additional information, see: “Listing of Text Functions” on page 306 “Value Types” on page 36 “The Elements of Formulas” on page 15 “Using the Keyboard and Mouse to Create and Edit Formulas” on page 26 “Pasting from Examples in Help” on page 41 UPPER The UPPER function returns a string that is entirely uppercase, regardless of the case of the characters in the specified string. UPPER(source-string)  source-string:  A string. source-string is a string value. Examples =UPPER(”a b c”) returns “A B C”. =UPPER(”First”) returns “FIRST”. Related Topics For related functions and additional information, see: “LOWER” on page 316 “PROPER” on page 317 “Listing of Text Functions” on page 306 “Value Types” on page 36 “The Elements of Formulas” on page 15 “Using the Keyboard and Mouse to Create and Edit Formulas” on page 26 “Pasting from Examples in Help” on page 41 324 Chapter 11 Text Functions Chapter 11 Text Functions 325 VALUE The VALUE function returns a number value even if the argument is formatted as text. This function is included for compatibility with tables imported from other spreadsheet applications. VALUE(source-string)  source-string:  A string. source-string is a string value. Usage Notes  You’ll never need to use the VALUE function in a new table, as numbers in text are automatically converted for you.  Only the formatted text is converted. For example, if the string $100.001 is typed into a cell, the default format will display only two decimals ($100.00). If VALUE refers to this cell, it will return 100, the value of the formatted text, not 100.001.  If the argument can’t be returned as a number value (does not contain a number), the function returns an error. Examples =VALUE(”22”) returns the number 22. =VALUE(RIGHT(”The year 1953”, 2)) returns the number 53. Related Topics For related functions and additional information, see: “Listing of Text Functions” on page 306 “Value Types” on page 36 “The Elements of Formulas” on page 15 “Using the Keyboard and Mouse to Create and Edit Formulas” on page 26 “Pasting from Examples in Help” on page 41 326 The trigonometric functions help you work with angles and their components. Listing of Trigonometric Functions iWork provides these trigonometric functions for use with tables. Function Description “ACOS” (page 327) The ACOS function returns the inverse cosine (arccosine) of a number. “ACOSH” (page 328) The ACOSH function returns the inverse hyperbolic cosine (hyperbolic arccosine) of a number. “ASIN” (page 329) The ASIN function returns the arcsine (the inverse sine) of a number. “ASINH” (page 329) The ASINH function returns the inverse hyperbolic sine of a number. “ATAN” (page 330) The ATAN function returns the inverse tangent (arctangent) of a number. “ATAN2” (page 331) The ATAN2 function returns the angle, relative to the positive x-axis, of the line passing through the origin and the specified point. “ATANH” (page 332) The ATANH function returns the inverse hyperbolic tangent of a number. “COS” (page 333) The COS function returns the cosine of an angle that is expressed in radians. “COSH” (page 334) The COSH function returns the hyperbolic cosine of a number. Trigonometric Functions 12 Chapter 12 Trigonometric Functions 327 Function Description “DEGREES” (page 334) The DEGREES function returns the number of degrees in an angle expressed in radians. “RADIANS” (page 335) The RADIANS function returns the number of radians in an angle expressed in degrees. “SIN” (page 336) The SIN function returns the sine of an angle that is expressed in radians. “SINH” (page 337) The SINH function returns the hyperbolic sine of the specified number. “TAN” (page 338) The TAN function returns the tangent of an angle that is expressed in radians. “TANH” (page 339) The TANH function returns the hyperbolic tangent of the specified number. ACOS The ACOS function returns the inverse cosine (arccosine) of a number. ACOS(num)  num:  A number. num is a number value in the range –1 to 1. Usage Notes  The ACOS function takes a cosine value and returns a corresponding angle. The resulting angle is expressed in radians, in the range 0 to π (pi). To see the resulting angle in degrees instead of radians, wrap this function in the DEGREES function; that is, =DEGREES(ACOS(num)). Examples =ACOS(SQRT(2)/2) returns 0.785398163397448, which is approximately π/4. =ACOS(0.54030230586814) returns 1. =DEGREES(ACOS(.5)) returns 60, the degree measure of an angle that has a cosine of 0.5. Related Topics For related functions and additional information, see: “ACOSH” on page 328 “COS” on page 333 “COSH” on page 334 “DEGREES” on page 334 “Listing of Trigonometric Functions” on page 326 “Value Types” on page 36 “The Elements of Formulas” on page 15 “Using the Keyboard and Mouse to Create and Edit Formulas” on page 26 “Pasting from Examples in Help” on page 41 ACOSH The ACOSH function returns the inverse hyperbolic cosine (hyperbolic arccosine) of a number. ACOSH(num)  num:  A number. num is a number value that must be greater than or equal to 1. Examples =ACOSH(10.0676619957778) returns 3. =ACOSH(COSH(5)) returns 5. Related Topics For related functions and additional information, see: “ACOS” on page 327 “COS” on page 333 “COSH” on page 334 “Listing of Trigonometric Functions” on page 326 “Value Types” on page 36 “The Elements of Formulas” on page 15 “Using the Keyboard and Mouse to Create and Edit Formulas” on page 26 “Pasting from Examples in Help” on page 41 328 Chapter 12 Trigonometric Functions Chapter 12 Trigonometric Functions 329 ASIN The ASIN function returns the arcsine (the inverse sine) of a number. ASIN(num)  num:  A number. num is a number value that must be greater than or equal to 1. Usage Notes  The ASIN function takes a sine and returns the corresponding angle. The result is expressed in radians, in the range –pi/2 to +pi/2. To see the resulting angle in degrees instead of radians, wrap this function in the DEGREES function; that is, =DEGREES(ASIN(num)). Examples =ASIN(0.841470985) returns 1, the radian measure (approximately 57.3 degrees) of the angle that has a sine of 0.8411470984807897. =DEGREES(ASIN(0.5)) returns 30, the degree measure of the angle that has a sine of 0.5. Related Topics For related functions and additional information, see: “ASINH” on page 329 “DEGREES” on page 334 “SIN” on page 336 “SINH” on page 337 “Listing of Trigonometric Functions” on page 326 “Value Types” on page 36 “The Elements of Formulas” on page 15 “Using the Keyboard and Mouse to Create and Edit Formulas” on page 26 “Pasting from Examples in Help” on page 41 ASINH The ASINH function returns the inverse hyperbolic sine of a number. ASINH(num)  num:  A number. num is a number value. Examples =ASINH(27.2899171971277) returns 4. =ASINH(SINH(1)) returns 1. Related Topics For related functions and additional information, see: “ASIN” on page 329 “SIN” on page 336 “SINH” on page 337 “Listing of Trigonometric Functions” on page 326 “Value Types” on page 36 “The Elements of Formulas” on page 15 “Using the Keyboard and Mouse to Create and Edit Formulas” on page 26 “Pasting from Examples in Help” on page 41 ATAN The ATAN function returns the inverse tangent (arctangent) of a number. ATAN(num)  num:  A number. num is a number value. Usage Notes  The ATAN function takes a tangent and returns the corresponding angle, expressed in radians in the range –pi/2 to +pi/2. To see the resulting angle in degrees instead of radians, wrap this function in the DEGREES function; that is, =DEGREES(ATAN(num)). Examples =ATAN(1) returns the angle measure 0.785398163 radians (45 degrees), which has a tangent of 1. =DEGREES(ATAN(1)) returns 45. Related Topics For related functions and additional information, see: “ATAN2” on page 331 “ATANH” on page 332 330 Chapter 12 Trigonometric Functions Chapter 12 Trigonometric Functions 331 “DEGREES” on page 334 “TAN” on page 338 “TANH” on page 339 “Listing of Trigonometric Functions” on page 326 “Value Types” on page 36 “The Elements of Formulas” on page 15 “Using the Keyboard and Mouse to Create and Edit Formulas” on page 26 “Pasting from Examples in Help” on page 41 ATAN2 The ATAN2 function returns the angle, relative to the positive x-axis, of the line passing through the origin and the specified point. ATAN2(x-point, y-point)  x-point:  The x-coordinate of the point the line passes through. x-point is a number value.  y-point:  The y-coordinate of the point the line passes through. y-point is a number value. Usage Notes  The angle is expressed in radians, in the range –pi through +pi. To see the resulting angle in degrees instead of radians, wrap this function in the DEGREES function; that is, =DEGREES(ATAN2(x-point, y-point)). Examples =ATAN2(1, 1) returns 0.78539816 radians (45 degrees), the angle of a line segment from the origin to point (1, 1). =DEGREES(ATAN2(5, 5)) returns 45. Related Topics For related functions and additional information, see: “ATAN” on page 330 “ATANH” on page 332 “DEGREES” on page 334 “TAN” on page 338 “TANH” on page 339 “Listing of Trigonometric Functions” on page 326 “Value Types” on page 36 “The Elements of Formulas” on page 15 “Using the Keyboard and Mouse to Create and Edit Formulas” on page 26 “Pasting from Examples in Help” on page 41 ATANH The ATANH function returns the inverse hyperbolic tangent of a number. ATANH(num)  num:  A number. num is a number value that must be greater than –1 and less than 1. Examples =ATANH(0.995054753686731) returns 3. =ATANH(TANH(2)) returns 2. Related Topics For related functions and additional information, see: “ATAN” on page 330 “ATAN2” on page 331 “TAN” on page 338 “TANH” on page 339 “Listing of Trigonometric Functions” on page 326 “Value Types” on page 36 “The Elements of Formulas” on page 15 “Using the Keyboard and Mouse to Create and Edit Formulas” on page 26 “Pasting from Examples in Help” on page 41 332 Chapter 12 Trigonometric Functions Chapter 12 Trigonometric Functions 333 COS The COS function returns the cosine of an angle that is expressed in radians. COS(radian-angle)  radian-angle:  An angle, expressed in radians. radian-angle is a number value. Although it can be any value, it would normally be in the range –π to +π (–pi to +pi). Usage Notes  To return an angle in degrees, use the DEGREES function (to convert radians to degrees) with this function; that is, =DEGREES(COS(radian-angle)). Examples =COS(1) returns 0.540302306, the cosine of 1 radian (approximately 57.3 degrees). =COS(RADIANS(60)) returns 0.5, the cosine of 60 degrees. =COS(PI()/3) returns 0.5, π/3 radians (60 degrees). =COS(PI()) returns –1, the cosine of π radians (180 degrees). Related Topics For related functions and additional information, see: “ACOS” on page 327 “ACOSH” on page 328 “COSH” on page 334 “DEGREES” on page 334 “SIN” on page 336 “TAN” on page 338 “Listing of Trigonometric Functions” on page 326 “Value Types” on page 36 “The Elements of Formulas” on page 15 “Using the Keyboard and Mouse to Create and Edit Formulas” on page 26 “Pasting from Examples in Help” on page 41 COSH The COSH function returns the hyperbolic cosine of a number. COSH(num)  num:  A number. num is a number value. Examples =COSH(0) returns 1. =COSH(1) returns 1.543. =COSH(5) returns 74.21. =COSH(10) returns 11,013.233. Related Topics For related functions and additional information, see: “ACOS” on page 327 “ACOSH” on page 328 “COS” on page 333 “Listing of Trigonometric Functions” on page 326 “Value Types” on page 36 “The Elements of Formulas” on page 15 “Using the Keyboard and Mouse to Create and Edit Formulas” on page 26 “Pasting from Examples in Help” on page 41 DEGREES The DEGREES function returns the number of degrees in an angle expressed in radians. DEGREES(radian-angle)  radian-angle:  An angle, expressed in radians. radian-angle is a number value. Although it can be any value, it would normally be in the range –2π to 2π (–2 pi to +2 pi). Examples =DEGREES(PI()) returns 180 (π radians = 180 degrees). =DEGREES(1) returns 57.2957795130823, which is approximately the number of degrees per radian. 334 Chapter 12 Trigonometric Functions Chapter 12 Trigonometric Functions 335 Related Topics For related functions and additional information, see: “ACOS” on page 327 “ASIN” on page 329 “ATAN” on page 330 “ATAN2” on page 331 “COS” on page 333 “SIN” on page 336 “TAN” on page 338 “Listing of Trigonometric Functions” on page 326 “Value Types” on page 36 “The Elements of Formulas” on page 15 “Using the Keyboard and Mouse to Create and Edit Formulas” on page 26 “Pasting from Examples in Help” on page 41 RADIANS The RADIANS function returns the number of radians in an angle expressed in degrees. RADIANS(degree-angle)  degree-angle:  An angle, expressed in degrees. degree-angle is a number value. Although it can be any value, it would normally be in the range –360 to +360. Usage Notes  This function is useful if you wish to use an angle expressed in degrees with any of the standard geometric functions, as they expect an angle expressed in radians. Wrap the argument, expressed in degrees, in this function; for example, =COS(RADIANS(degree-angle). Examples =RADIANS(90) returns 1.5708 (90 degrees is approximately 1.5708 radians). =RADIANS(57.2957795130823) returns 1 (1 radian is approximately 57.296 degrees). Related Topics For related functions and additional information, see: “ACOS” on page 327 “ASIN” on page 329 “ATAN” on page 330 “ATAN2” on page 331 “COS” on page 333 “SIN” on page 336 “TAN” on page 338 “Listing of Trigonometric Functions” on page 326 “Value Types” on page 36 “The Elements of Formulas” on page 15 “Using the Keyboard and Mouse to Create and Edit Formulas” on page 26 “Pasting from Examples in Help” on page 41 SIN The SIN function returns the sine of an angle that is expressed in radians. SIN(radian-angle)  radian-angle:  An angle, expressed in radians. radian-angle is a number value. Although it can be any value, it would normally be in the range –π to π (–pi to +pi). Usage Notes  To return an angle in degrees, use the DEGREES function (to convert radians to degrees) with this function; that is, =DEGREES(SIN(radian-angle)). Examples =SIN(1) returns 0.841470985, the sine of 1 radian (approximately 57.3 degrees). =SIN(RADIANS(30)) returns 0.5, the sine of 30 degrees. =SIN(PI()/2) returns 1, the sine of π/2 radians (90 degrees). Related Topics For related functions and additional information, see: “ASIN” on page 329 “ASINH” on page 329 336 Chapter 12 Trigonometric Functions Chapter 12 Trigonometric Functions 337 “COS” on page 333 “DEGREES” on page 334 “SINH” on page 337 “TAN” on page 338 “Listing of Trigonometric Functions” on page 326 “Value Types” on page 36 “The Elements of Formulas” on page 15 “Using the Keyboard and Mouse to Create and Edit Formulas” on page 26 “Pasting from Examples in Help” on page 41 SINH The SINH function returns the hyperbolic sine of the specified number. SINH(num)  num:  A number. num is a number value. Examples =SINH(0) returns 0. =SINH(1) returns 1.175. =SINH(5) returns 74.203. =SINH(10) returns 11013.233. Related Topics For related functions and additional information, see: “ASIN” on page 329 “ASINH” on page 329 “SIN” on page 336 “Listing of Trigonometric Functions” on page 326 “Value Types” on page 36 “The Elements of Formulas” on page 15 “Using the Keyboard and Mouse to Create and Edit Formulas” on page 26 “Pasting from Examples in Help” on page 41 TAN The TAN function returns the tangent of an angle that is expressed in radians. TAN(radian-angle)  radian-angle:  An angle, expressed in radians. radian-angle is a number value. Although it can be any value, it would normally be in the range –pi to +pi. Usage Notes  The tangent is the ratio of the sine to the cosine.  To return an angle in degrees, use the DEGREES function (to convert radians to degrees) with this function; that is, =DEGREES(TAN(radian-angle)). Examples =TAN(1) returns 1.557407725, the tangent of 1 radian (approximately 57.3 degrees). =TAN(RADIANS(45)) returns 1, the tangent of a 45-degree angle. =TAN(3*PI()/4) returns -1. Related Topics For related functions and additional information, see: “ATAN” on page 330 “ATAN2” on page 331 “ATANH” on page 332 “COS” on page 333 “DEGREES” on page 334 “SIN” on page 336 “TANH” on page 339 “Listing of Trigonometric Functions” on page 326 “Value Types” on page 36 “The Elements of Formulas” on page 15 “Using the Keyboard and Mouse to Create and Edit Formulas” on page 26 “Pasting from Examples in Help” on page 41 338 Chapter 12 Trigonometric Functions Chapter 12 Trigonometric Functions 339 TANH The TANH function returns the hyperbolic tangent of the specified number. TANH(num)  num:  A number. num is a number value. Examples =TANH(0) returns 0. =TANH(1) returns 0.762. =TANH(5) returns 0.999909. =TANH(10) returns 0.999999996. Related Topics For related functions and additional information, see: “ATAN” on page 330 “ATAN2” on page 331 “ATANH” on page 332 “TAN” on page 338 “Listing of Trigonometric Functions” on page 326 “Value Types” on page 36 “The Elements of Formulas” on page 15 “Using the Keyboard and Mouse to Create and Edit Formulas” on page 26 “Pasting from Examples in Help” on page 41 340 The in-depth examples and additional topics in this chapter illustrate working with some of the more complex functions. Additional Examples and Topics Included The following table tells you where to find in-depth examples and additional topics that illustrate working with some of the more complex functions with real-world examples. If you wish to see an example or learn more about See this section The definitions and specification of arguments used in financial functions “Common Arguments Used in Financial Functions” on page 341 The time value of money (TVM) functions “Choosing Which Time Value of Money Function to Use” on page 348 TVM functions dealing with fixed periodic cash flows and fixed interest rates “Regular Cash Flows and Time Intervals” on page 348 TVM functions that can deal with uneven (variable periodic) cash flows “Irregular Cash Flows and Time Intervals” on page 350 The function that may be most helpful in answering a common financial question “Which Function Should You Use to Solve Common Financial Questions?” on page 351 Using financial functions to create a loan amortization table “Example of a Loan Amortization Table” on page 353 The various functions that round numbers “More on Rounding” on page 355 Using logical and information functions together to build a more powerful formula “Using Logical and Information Functions Together” on page 358 Understanding conditions and how to use wildcards with conditions “Specifying Conditions and Using Wildcards” on page 360 Using statistical functions to analyze the results of a survey “Survey Results Example” on page 362 Additional Examples and Topics 13 Chapter 13 Additional Examples and Topics 341 Common Arguments Used in Financial Functions Many arguments are common among related financial functions. This section provides information regarding these arguments. Date arguments (issue, maturity, and settle) are not included. Arguments that are used by only a single financial function are also not included. annual-rate Bonds and other fixed-rate, interest-bearing debt securities have a stated coupon or annual interest rate used to determine periodic interest payments. annual-rate is used to represent the annual interest rate, whether it is called a coupon rate or an annual interest rate. coupon-rate is specified as a decimal number representing the annual coupon rate. In some functions, coupon-rate can be 0 (if the security does not pay periodic interest), but coupon-rate cannot be negative. Assume that you own a security with a face value of $1,000,000 and that pays annual interest of 4.5% based on the face value. coupon-rate would be 0.045. frequency of payment does not matter. annual-yield Bonds and other interest-bearing and discount debt securities have a yield that is calculated using the coupon interest rate and the current price of the bond. annual-yield is specified as a decimal number representing the security’s annual yield, which is commonly stated as a percentage. annual-yield must be greater than 0. Assume that you are considering the purchase of a particular bond. As the price of a bond goes down, its yield goes up. Conversely, if the price of the bond rises, its yield decreases. Your broker checks the pricing screens and tells you that the bond you are considering has a coupon rate of 3.25% and an annual yield of 4.5%, based on its current price (the bond is trading at a discount). annual-yield would be 0.045. cash-flow Annuities, loans, and investments have cash flows. One cash flow is the initial amount paid or received, if any. Other cash flows are other receipts or payments at a specific point in time. cash-flow is specified as a number, usually formatted as currency. Amounts received are specified as positive numbers and amounts paid are specified as negative numbers. Assume that there is a townhouse that you plan to purchase, rent out for a period of time, and then resell. The initial cash purchase payment (which might consist of a down payment and closing costs), loan payments, repairs and maintenance, advertising, and similar costs, would be payments (negative cash flows). Rents received from tenants, tax benefits received through a reduction of other taxes, and the amount received upon sale would be receipts (positive cash flows). cost The initial cost of the asset to be depreciated is generally the purchase price, including taxes, delivery, and setup. Certain tax benefits may be deducted from the cost. cost is specified as number, usually formatted as currency. cost must be greater than 0. Assume that you purchase a new digital photocopy machine for your office. The purchase price of the photocopy machine was $2,625 with tax. The vendor charged $100 to deliver and set it up. The photocopy machine is expected to be used for 4 years, at which time it is expected to have a resale value of $400. cost would be $2,725. cum-when-due See discussion at when-due. The only difference is that functions that use cum-when-due require the argument to be specified and do not assume a value if it is omitted. days-basis There are several different conventions used when counting the number of days in a month and number of days in a year to determine interest on a loan or investment. days-basis is used to indicate how days are counted for a specific investment or loan. days-basis is often defined by market practice and may be related to a particular type of investment. Or days-basis may be specified in documents related to a loan. days-basis is a modal argument. It is specified as the number 0, 1, 2, 3, or 4.  A value of 0 specifies that for purposes of computing interest, each full month will contain 30 days and each full year will contain 360 days, using the NASD method for dates falling on the 31st of a month. This is commonly known as the 30/360 convention. 0 (30/360 convention) is the default value. In the NASD method, if the day value in the starting date (for example, the settlement date) is 31, it is treated as if it was 30. If the day value is the last day of February, it is not adjusted, so in this case February has less than 30 days. If the day value for the ending date (for example, the maturity date) is 31 and the day value in the starting date is earlier than the 30th of the same month, the ending date is considered to be the first day of the following month. Otherwise it is considered to be the 30th of the same month resulting in 0 days.  A value of 1 specifies that the actual number of days will be used for each full month and the actual number of days will be used for each year. This is commonly known as the actual/actual convention.  A value of 2 specifies that the actual number of days will be used for each full month and each full year will contain 360 days. This is commonly known as the actual/360 convention.  A value of 3 specifies that the actual number of days will be used for each full month and each full year will contain 365 days. This is commonly known as the actual/365 convention.  A value of 4 specifies that each full month will contain 30 days and each full year will contain 360 days, using the European method for dates falling on the 31st of a month. This is commonly known as the 30E/360 convention. In the European method, the 31st of a month is always considered to be the 30th of the same month. February is always considered to have 30 days, so if the last day of February is the 28th, it is considered to be the 30th. Assume that you wish to determine the interest on a bond issued by a U.S. corporation. Most such bonds use the 30/360 method of determining interest so days-basis would be 0, the default value. Or assume that you wish to determine the interest on a United States Treasury Bond. These bonds usually pay interest based on the actual days in each month and the actual days in each year, so days-basis would be 1. depr-factor In certain formulas, the rate of the accelerated depreciation rate (in excess of straight-line depreciation) can be specified. depr-factor is used to specify the desired rate of annual depreciation. depr-factor is specified as a decimal number or as a percentage (using the percent sign). Assume that you have purchased a new computer. After discussion with your tax accountant, you find that it is permissible to depreciate the computer on an accelerated basis. You decide to use a depreciation rate of 150% of straight-line depreciation, so depr-factor would be 1.5. 342 Chapter 13 Additional Examples and Topics Chapter 13 Additional Examples and Topics 343 depr-period Certain functions return the amount of depreciation for a specified period. depr-period is used to specify the period. depr-period is specified as a number representing the desired depreciation period using the same time frame (for example, monthly, quarterly, or annually) as life. Assume that you purchase a new digital photocopy machine for your office. The purchase price of the photocopy machine was $2,625 with tax. The vendor charged $100 to deliver and set it up. The photocopy machine is expected to be used for 4 years, at which time it is expected to have a resale value of $400. If you wished to determine the depreciation for the third year, depr-period would be 3. effective-int-rate Annuities and investments have an effective interest rate, which is calculated using the nominal (stated or coupon) rate and the number of interest payments per year. effective-int-rate is specified as a decimal number and must be greater than 0. Assume that you own a security with a face value of $1,000,000 that pays annual interest of 4.5% based on the face value, on a quarterly basis, which is an effective rate of approximately 4.58%. effective-int-rate would be 0.0458. See also the description of nominal-rate and num-periods-year. end-per Certain functions return principal or interest for a series of specified payments. end-per is used to indicate the last payment to be included in the value returned. See also the discussion of start-per. end-per is specified as a number and must be greater than 0. Assume that you are purchasing a home. The mortgage broker offers you a loan with an initial balance of $200,000, a term of 10 years, an annual interest rate of 6.0%, fixed monthly payments of $1070.45, and a balance to be refinanced at maturity of $100,000. If you wished to know the total amount of interest paid in the third year, start-per would be 25 and end-per would be 36. estimate An estimate of the expected outcome is used by some financial functions. estimate is specified as a decimal number. For example, 13% is specified as 0.13. estimate can be negative, if a loss is expected. If estimate is not specified, 0.10 is used as the default value. If you do not have an idea as to the expected outcome and the default value does not result in a solution, initially try a larger positive estimate. If this does not result in an outcome, try a small negative estimate. frequency An investment may pay interest on a periodic basis. frequency is used to indicate how often interest is paid. frequency is the number 1, 2, or 4.  A value of 1 indicates that the investment pays interest annually (once a year).  A value of 2 indicates that the investment pays interest semiannually (twice per year).  A value of 4 indicates that the investment pays interest quarterly (four times per year). Assume that you are evaluating a corporate bond that pays interest quarterly. frequency would be 4. Or assume you are evaluating a government bond that pays interest semiannually. frequency would be 2. future-value A future value is a cash flow received or paid at the end of the investment or loan period or the cash value remaining after the final payment. future-value is specified as a number, usually formatted as currency. Since future-value is a cash flow, amounts received are specified as positive numbers and amounts paid are specified as negative numbers. Assume that there is a townhouse that you plan to purchase, rent out for a period of time, and then resell. The estimated future sales price could be a future-value and would be positive. Or assume that you lease a car and that the lease contains a provision allowing you to buy the car for a specified price at the end of the lease term. The amount of that payment could be a future-value and would be negative. Or assume that you have a mortgage loan that at the end of 10 years has a balloon payment due. The balloon payment could be a future-value and would be negative. invest-amount The initial amount invested in a bond is specified using invest-amount. invest-amount is specified as a number, usually formatted as currency. invest-amount must be greater than 0. Assume that you purchase a bond for $800. invest-amount would be $800. life Assets are depreciated over a specific period, known as the depreciable life or the expected useful life. Generally for accounting purposes the expected useful life of the asset would be used for depreciation, whereas for other purposes (such as preparing a tax return) the depreciable life may be specified by regulation or practice. life is specified as a number. life must be greater than 0. Assume that you purchase a new digital photocopy machine for your office. The purchase price of the photocopy machine was $2,625 with tax. The vendor charged $100 to deliver and set it up. The photocopy machine is expected to be used for 4 years, at which time it is expected to have a resale value of $400. life is 4. nominal-rate Annuities and investments have a nominal interest rate, which is calculated using the effective interest rate and the number of compounding periods per year. nominal-rate is specified as a decimal number and must be greater than 0. Assume that own a security with a face value of $1,000,000 that pays annual interest of 4.5% based on the face value, on a quarterly basis, which is an effective rate of approximately 4.58%. nominal-rate would be 0.045. See also the description of effective-int-rate and num-periods-year. num-periods The number of periods (num-periods) is the total periods of a repeating cash flow, or the length of a loan, or the length of the investment period. num-periods is specified as a number using the same time frame (for example, monthly, quarterly, or annually) as related arguments used by the function. Assume that you are purchasing a home. The mortgage broker offers you a loan with an initial balance of $200,000, a term of 10 years, an annual interest rate of 6.0%, fixed monthly payments, and a balance to be refinanced at maturity of $100,000. num-periods would be 120 (12 monthly payments for 10 years). Or assume that you invest your savings in a certificate of deposit that has a term of 5 years and compounds interest quarterly. num-periods would be 20 (4 quarterly compounding periods for 5 years). 344 Chapter 13 Additional Examples and Topics Chapter 13 Additional Examples and Topics 345 num-periods-year The calculation of the effective and nominal interest rates is based on the number of interest compounding periods per year. num-periods-year is used to specify the number of periods. num-periods-year is specified as a number and must be greater than 0. Assume that you have purchased a certificate of deposit that pays interest annually, compounded quarterly. If you wanted to determine the effective interest rate, num-periods-year would be 4. See also the description of effective-int-rate and nominal-rate. par The par value of a security is generally its face or maturity value. par is specified as a number, usually formatted as currency. par is often a number like 100, 1,000, or 1,000,000. Assume that you are considering purchasing a corporate bond. The prospectus for the bond states that each bond will be issued with a face and maturity value of $1,000. The $1,000 would be the par value of the bond. payment A payment is a fixed, periodic cash flow received or paid over an investment or loan period. payment is specified as a number, usually formatted as currency. Since payment is a cash flow, amounts received are specified as positive numbers and amounts paid are specified as negative numbers. payment often includes both principal and interest elements, but does not usually include other amounts. Assume that there is a townhouse that you plan to purchase, rent out for a period of time, and then resell. The amount of the monthly mortgage payment could be a payment and would be negative. The rent payment received each month could also be a payment and would be positive. period Certain functions return a principal or interest value for a given period. period is used to indicate the desired period. period is specified as a number and must be greater than 0. Assume that you are purchasing a home. The mortgage broker offers you a loan with an initial balance of $200,000, a term of 10 years, an annual interest rate of 6.0%, fixed monthly payments of $1070.45, and a balance to be refinanced at maturity of $100,000. If you wished to know the amount of interest in the first payment of the third year, period would be 25, since payments are monthly. periodic-discount-rate The discount rate is the interest rate representing the desired yield used to value (or discount) a series of cash flows. periodic-discount-rate is specified as a decimal (for example, 0.08) or delimited with a percent sign (for example, 8%). It is specified using the same time frame as the time frame used for the cash flows. For example, if the cash flows are monthly and the desired annual discount rate is 8%, periodic-discountrate must be specified as 0.00667 or 0.667% (0.08 divided by 12). Assume that you are evaluating the possible purchase of a business. As part of your evaluation, you determine the expected monthly cash flows from the business along with the requested purchase price and estimated future resale price. You decide, based on alternative investment opportunities and risk, that you will not invest unless the net cash flows yield at least an 18% annual interest rate. periodic-discount-rate would be 0.015 (0.18 / 12 as specified cash flows are monthly). periodic-rate In some cases, when working with a series of cash flows, or an investment, or a loan, it may be necessary to know the interest rate each period. This is the periodic-rate. periodic-rate is specified as a decimal number using the same time frame (for example, monthly, quarterly, or annually) as other arguments (num-periods or payment). Assume that you are purchasing a home. The mortgage broker offers you a loan with an initial balance of $200,000, a term of 10 years, an annual interest rate of 6.0%, fixed monthly payments, and a balance to be refinanced at maturity of $100,000. periodic-rate would be 0.005 (annual rate divided by 12 to match up with the monthly payment). Or assume that you invest your savings in a certificate of deposit that has a term of 5 years, has a nominal annual interest rate of 4.5%, and interest compounds quarterly. periodic-rate would be 0.0125 (annual rate divided by 4 to match the quarterly compounding periods). present-value A present value is a cash flow received or paid at the beginning of the investment or loan period. present-value is specified as a number, usually formatted as currency. Since present-value is a cash flow, amounts received are specified as positive numbers and amounts paid are specified as negative numbers. Assume that there is a townhouse that you plan to purchase, rent out for a period of time, and then resell. The initial cash purchase payment (which might consist of a down payment and closing costs) could be a present-value and would be negative. The initial principal amount of a loan on the townhouse could also be a present-value and would be positive. price The purchase price is the amount paid to buy a bond or other interest-bearing or discount debt security. The purchase price does not include accrued interest purchased with the security. price is specified as a number representing the amount paid per $100 of face value (purchase price / face value * 100). price must be greater than 0. Assume that you own a security that has a face value of $1,000,000. If you paid $965,000 when you purchased the security, excluding accrued interest if any, price would be 96.50 ($965,000 / $1,000,000 * 100). redemption Bonds and other interest-bearing and discount debt securities usually have a stated redemption value. This is the amount that will be received when the debt security matures. redemption is specified as a number representing the amount that will be received per $100 of face value (redemption value / face value * 100). Often, redemption is 100, meaning that the security’s redemption value is equal to its face value. value must be greater than 0. Assume that you own a security that has a face value of $1,000,000 and for which you will receive $1,000,000 at maturity. redemption would be 100 ($1,000,000 / $1,000,000 * 100), because the face value and the redemption value are the same, a common case. Assume further though that the issuer of this security offers to redeem the security before maturity and has offered $1,025,000 if redeemed one year early. redemption would be 102.50 ($1,025,000 / $1,000,000 * 100). 346 Chapter 13 Additional Examples and Topics Chapter 13 Additional Examples and Topics 347 salvage Assets often have value remaining at the end of the depreciable life or the expected useful life. This is the salvage value. salvage is specified as a number, usually formatted as currency. salvage can be 0, but cannot be negative. Assume that you purchase a new digital photocopy machine for your office. The purchase price of the photocopy machine was $2,625 with tax. The vendor charged $100 to deliver and set it up. The photocopy machine is expected to be used for 4 years, at which time it is expected to have a resale value of $400. salvage is $400. start-per Certain functions return principal or interest for a series of specified payments. start-per is used to indicate the first payment to be included in the value returned. See also the discussion of end-per. start-per is specified as a number and must be greater than 0. Assume that you are purchasing a home. The mortgage broker offers you a loan with an initial balance of $200,000, a term of 10 years, an annual interest rate of 6.0%, fixed monthly payments of $1070.45, and a balance to be refinanced at maturity of $100,000. If you wished to know the total amount of interest paid in the third year, start-per would be 25 and end-per would be 36. when-due Payments can be generalized to occur at the beginning or end of a period. when-due is used to indicate whether a payment occurs at the beginning or end of a period. when-due is a modal argument. It can be the number 0 or 1.  A value of 0 specifies that the payment is treated as being received or made at the end of each period. 0 is the default value.  A value of 1 specifies that the payment is treated as being received or made at the beginning of each period. Assume that you are purchasing a home. The mortgage broker offers you a loan with an initial balance of $200,000, a term of 10 years, an annual interest rate of 6.0%, fixed monthly payments, and a balance to be refinanced at maturity of $100,000. when-due would be 0 (the default) since payments are made at the end of each month. Or assume you own an apartment that you rent and that you require the tenant to pay rent on the first of each month. when-due would be 1, since this payment is being made by the tenant at the beginning of the monthly period. Choosing Which Time Value of Money Function to Use This section provides additional information regarding the functions used to solve time value of money problems. Time value of money, or TVM, problems involve cash flows over time and interest rates. This section contains several parts. “Regular Cash Flows and Time Intervals” on page 348 discusses the TVM functions used with regular cash flows, regular time intervals, and fixed interest rates. “Irregular Cash Flows and Time Intervals” on page 350 discusses the TVM functions used with irregular cash flows, irregular time intervals, or both. “Which Function Should You Use to Solve Common Financial Questions?” on page 351 describes several common TVM problems (such as which function would be used to compute interest on a savings account) along with the functions that might be used in solving the problem. Regular Cash Flows and Time Intervals The primary functions used with regular periodic cash flows (payments of a constant amount and all cash flows at constant intervals) and fixed interest rates are interrelated. Function and its purpose Arguments used by the function “FV” (page 120) is the function to use if you wish to determine what the future value (what it is worth at a future point in time) of a series of cash flows will be, considering the other factors such as the interest rate. It solves for the argument future-value. periodic-rate, num-periods, payment, present-value, when-due “NPER” (page 130) is the function to use if you wish to determine the number of periods it would take to repay a loan or the number of periods you might receive an annuity, considering the other factors such as the interest rate. It solves for the argument num-periods. periodic-rate, payment, present-value, future-value, when-due “PMT” (page 134) is the function to use if you wish to determine the amount of the payment that would be required on a loan or received on an annuity, considering the other factors such as interest rate. It solves for the argument payment. periodic-rate, num-periods, present-value, futurevalue, when-due 348 Chapter 13 Additional Examples and Topics Chapter 13 Additional Examples and Topics 349 Function and its purpose Arguments used by the function “PV” (page 141) is the function to use if you wish to determine the present value (what it is worth today) of a series of cash flows, considering the other factors such as the interest rate. It solves for the argument present-value. periodic-rate, num-periods, payment, future-value, when-due “RATE” (page 144) is the function to use if you wish to determine the periodic interest rate for a loan or annuity, based on the other factors such as the number of periods in the loan or annuity. It solves for the argument periodic-rate. num-periods, payment, present-value, future-value, when-due, estimate As illustrated by this table, these TVM functions each solve for, and return the value of, one of the five primary arguments when the problem being solved involves regular periodic cash flows and fixed interest rates. In addition, “IPMT” (page 123) and “PPMT” (page 135) can solve for the interest and principal components of a particular loan or annuity payment, and “CUMIPMT” (page 110) and “CUMPRINC” (page 112) can solve for the interest and principal components of a consecutive series of loan or annuity payments. Related Topics For related functions and additional information, see: “Irregular Cash Flows and Time Intervals” on page 350 “Common Arguments Used in Financial Functions” on page 341 “Listing of Financial Functions” on page 96 “Value Types” on page 36 “The Elements of Formulas” on page 15 Irregular Cash Flows and Time Intervals Some TVM problems involve irregular fixed periodic cash flows where cash flows occur at regular time intervals but the amounts vary. Still other problems have cash flows that have irregular time intervals where cash flows do not necessarily occur at regular time intervals. Function and its purpose Arguments used by the function “IRR” (page 125) is the function to use if you wish to determine a periodic rate such that the net present value of a series of potentially irregular cash flows that occur at regular time intervals is equal to 0. This is commonly called the internal rate of return. IRR solves for the argument periodic-rate. flows-range, estimate flows-range is a specified range of cash flows that may implicitly include a payment, a present-value, and a future-value. “MIRR” (page 128) is the function to use if you wish to determine a periodic rate such that the net present value of a series of potentially irregular cash flows that occur at regular time intervals is equal to 0. MIRR differs from IRR in that it permits positive and negative cash flows to be discounted at a different rate. This is commonly called the modified internal rate of return. MIRR solves for the argument periodic-rate. flows-range, finance-rate, reinvest-rate flows-range is a specified range of cash flows that may implicitly include a payment, a present-value, and a future-value. finance-rate and reinvest-rate are specific cases of periodic-rate. “NPV” is the function to use if you wish to determine the present value of a series of potentially irregular cash flows that occur at regular time intervals. This is commonly called the net present value. NPV solves for the argument present-value. periodic-rate, cash-flow, cash-flow… cash-flow, cash-flow… is a specified series of one or more cash flows that may implicitly include a payment, present-value, and future-value. Related Topics For related functions and additional information, see: “Regular Cash Flows and Time Intervals” on page 348 “Common Arguments Used in Financial Functions” on page 341 “Listing of Financial Functions” on page 96 “Value Types” on page 36 “The Elements of Formulas” on page 15 350 Chapter 13 Additional Examples and Topics Chapter 13 Additional Examples and Topics 351 Which Function Should You Use to Solve Common Financial Questions? This section describes some common questions you might want to address and lists the financial function that might be helpful. The questions help with everyday financial questions. More complex uses of the financial functions are described in “Regular Cash Flows and Time Intervals” on page 348, “Irregular Cash Flows and Time Intervals” on page 350, and “Example of a Loan Amortization Table” on page 353. If you would like to know This function may be helpful Savings The effective interest rate on an investment or savings account that pays interest periodically “EFFECT” (page 119) How much a CD will be worth at maturity “FV” (page 120). Note that payment will be 0. The nominal rate of interest on a CD where the issuer has advertised the “effective rate” “NOMINAL” (page 129) How many years it will take to save a specific amount, given monthly deposits to a savings account “NPER” (page 130). Note that present-value will be the amount deposited at the beginning and could be 0. How much to save each month to reach a savings goal in a given number of years “PMT” (page 134). Note that present-value will be the amount deposited at the beginning and could be 0. Loans The amount of interest paid on a loan during the third year “CUMIPMT” (page 110) The amount of principal paid on a loan during the third year “CUMPRINC” (page 112) The amount of interest included in the 36th loan payment “IPMT” (page 123) The amount of principal included in the 36th loan payment “PPMT” (page 135) Bond Investments The amount of interest that will need to be added to a bond’s purchase price “ACCRINT” (page 99) or “ACCRINTM” (page 101) The number of coupon payments between the time a bond is purchased and its maturity “COUPNUM” (page 109) The annual discount rate for a bond that is sold at a discount to its redemption value and pays no interest (often known as a “zero coupon bond”) “DISC” (page 117) If you would like to know This function may be helpful The effective annual interest rate for a bond that pays interest only at its maturity (no periodic payments, but the bond does have a coupon rate) “INTRATE” (page 122) The expected purchase price of a bond that pays periodic interest, a bond sold at a discount that does not pay interest, or a bond that pays interest only at maturity “PRICE” (page 137), “PRICEDISC” (page 138), and “PRICEMAT” (page 140) The amount received on a bond that pays interest only at its maturity (no periodic payments, but the bond does have a coupon rate), including interest “RECEIVED” (page 146) The effective annual interest rate of a bond that pays periodic interest, a bond sold at a discount that does not pay interest, or a bond that pays interest only at maturity “YIELD” (page 150), “YIELDDISC” (page 152), and “YIELDMAT” (page 153) Depreciation The periodic amount of depreciation of an asset using the fixed-declining balance method “DB” (page 114) The periodic depreciation of an asset using a declining balance method such as “doubledeclining balance” “DDB” (page 116) The periodic depreciation of an asset using the straight-line method “SLN” (page 147) The periodic depreciation of an asset using the sum-of-the-years-digits method “SYD” (page 148) The total depreciation over a given period for an asset depreciated using a declining balance method “VDB” (page 149) 352 Chapter 13 Additional Examples and Topics Chapter 13 Additional Examples and Topics 353 Example of a Loan Amortization Table This example uses IPMT, PPMT, and PMT to construct a loan amortization table. The information returned by IPMT, PPMT, and PMT is related. This is illustrated in the example. Constructing the Amortization Table Assume you wish to construct an amortization table for all periods of a loan with an initial principal amount of $50,000, a term of 2 years, an annual interest rate of 7%, and a balance due at the end of the term of $30,000. The first part of your amortization table (with formulas shown) could be constructed like this: Explanations of Cell Content Cell B6 uses the PMT function to calculate the amount of each monthly payment. Note that this will be the total of interest and principal for each month (for example, C9 + D9) as shown in F9. Cells C9 and D9 use IPMT and PPMT, respectively, to calculate the portion of each monthly payment that is interest and principal. Note that IPMT is the same as PMT – PPMT and, conversely, PPMT is the same as PMT – IPMT. The Completed Amortization Table To complete the table, it would be necessary to select cells A10:A11 and extend the selection down to A32 to include all 24 periods in the hypothetical loan. Then C9:F9 would be selected and extended to C32:F32 to complete the formulas. Here is the complete table, showing the entire amortization using the formulas shown in the previous table. Final Comments Note that the values returned by IPMT (column C) and PPMT (column D) do add up each month to the PMT calculated in cell B6 (as shown in column F). Also note that the final principal remaining, as shown in cell E32, is $30,000, as specified for balloon in cell B4. 354 Chapter 13 Additional Examples and Topics Chapter 13 Additional Examples and Topics 355 More on Rounding iWork supports many different functions that round numbers. This section compares these functions. To Use this function Comments Round a number away from zero to the nearest multiple of a given number “CEILING” (page 170) Rounding occurs in steps; for example, the closest multiple of 10. Rounding is away from zero, so =CEILING(0.4, 1) results in 1 and =CEILING (-0.4, -1) results in -1. Round a number away from zero to the nearest even number “EVEN” (page 173) Rounding is to the nearest number evenly divisible by two. Rounding is away from zero, so =EVEN(0.4) returns 2 and =EVEN(-0.4) returns -2. Round a number toward zero to the nearest multiple of a given number “FLOOR” (page 176) Rounding occurs in steps; for example, the closest multiple of 10. Rounding is toward zero, so =FLOOR(0.4, 1) results in 0 and =FLOOR (-0.4, -1) also results in 0. Round a number to the nearest integer that is less than or equal to a given number “INT” (page 178) Rounding is to the nearest integer that is less than or equal to the given number. Therefore, =INT(0.4) returns 0 and =INT(-0.4) returns -1. Round a number to the nearest multiple of a given number “MROUND” (page 183) Rounding is to the nearest multiple of the given number. This differs from CEILING, which rounds up to the nearest multiple. Therefore, =MROUND(4, 3) returns 3, since 4 is closer to 3 than to the next multiple of 3, which is 6. =CEILING(4, 3) returns 6, the nearest multiple of 3 when rounding up. Round a number away from zero to the nearest odd number “ODD” (page 185) Rounding is to the nearest number not evenly divisible by two. Rounding is away from zero, so =ODD(1.4) returns 3 and =EVEN(-1.4) returns -3. To Use this function Comments Round a number to the specified number of places “ROUND” (page 191) A positive number indicates the number of digits (decimal places) to the right of the decimal separator to include in the rounded number. A negative number indicates the number of digits to the left of the decimal separator to replace with zeros (the number of zeros at the end of the number). The number is rounded based on this. So =ROUND(1125, -2) returns 1,100 and =ROUND(1155, -2) returns 1,200. Rounding is away from zero, so =ROUND(-1125, -2) returns -1,100 and =ROUND(-1155, -2) returns -1,200. Round a number down (toward zero) to the specified number of places “ROUNDDOWN” (page 192) A positive number indicates the number of digits (decimal places) to the right of the decimal separator to include in the rounded number. A negative number indicates the number of digits to the left of the decimal separator to replace with zeros (the number of zeros at the end of the number). The number is rounded based on this. So =ROUND(1125, -2) returns 1,100 and =ROUND(1155, -2) also returns 1,100, since rounding is toward zero. =ROUND(-1125, -2) returns -1,100 and =ROUND(-1155, -2) also returns -1,100. 356 Chapter 13 Additional Examples and Topics Chapter 13 Additional Examples and Topics 357 To Use this function Comments Round a number up (away from zero) to the specified number of places “ROUNDUP” (page 193) A positive number indicates the number of digits (decimal places) to the right of the decimal separator to include in the rounded number. A negative number indicates the number of digits to the left of the decimal separator to replace with zeros (the number of zeros at the end of the number). The number is rounded based on this. So =ROUND(1125, -2) returns 1,200 and =ROUND(1155, -2) also returns 1,200, since rounding is away from zero. =ROUND(-1125, -2) returns -1,200 and =ROUND(-1155, -2) also returns -1,200. Truncate a number at the specified number of places “TRUNC” (page 204) A positive number indicates the number of digits (decimal places) to the right of the decimal separator to include in the number. A negative number indicates the number of digits to the left of the decimal separator to replace with zeros (the number of zeros at the end of the number). Extra digits are stripped from the number. So =TRUNC(1125, -2) returns 1,100 and =TRUNC(1155, -2) also returns 1,100. Using Logical and Information Functions Together Logical and information functions are often used together in a formula. Although logical functions are used independently, it is rare for an information function to be used on its own. This section includes more complex examples to illustrate how the use of several logical and information functions in a single formula can be very powerful. Adding Comments Based on Cell Contents This example uses IF, AND, OR, and ISBLANK to add comments to a table based on existing cell contents. The IF function is quite powerful, especially when combined with other logical functions like OR and AND. Assume that you are a college professor and one of the graduate assistants has handed you a table containing the names of students and their recent exam results. You want to quickly identify the following situations:  The student passed, but should come in for a special study session (score in the range 61–75).  There is an error (negative test score, a test score over 100, or no test score) in the data.  The student failed the exam (score of 60 or below). Breaking this into parts, the functions below will determine each of the things you wish to know. When put together, you will be able to quickly glance at the table and see the desired information. For purposes of the expressions below, assume the first student’s name is in cell A2, and the first test score in cell B2. 358 Chapter 13 Additional Examples and Topics Chapter 13 Additional Examples and Topics 359 Expression 1 =AND(B2>60, B2<=75) tests for a low score. If the test score is in the range 61 to 75, AND will return TRUE meaning the student should come in for a special study session. Otherwise it will return FALSE. Expression 2 =OR(ISBLANK(B2), B2<0, B2>100) tests for invalid data. The first OR expression “ISBLANK(B2)” will be TRUE if there is no test score. The second expression will return TRUE if the test score is negative and the third expression will return TRUE if the test score is over 100. The OR will return TRUE if any of the conditions is TRUE, meaning the data is invalid in some way. The OR will return FALSE if none of the conditions are TRUE and therefore the data is valid. Expression 3 =B2<=60 tests for a failing grade. This expression will return TRUE if the test score is 60 or below, a failing grade. Otherwise it returns FALSE. Putting it together in an IF function =IF(AND(B2>60, B2<=75), “Needs study session”, IF(OR(ISBLANK(B2), B2<0, B2>100), “Invalid data”, IF(B2<=60, “Exam failed”, “”))) If the test expression (same as Expression 1 above) in the first IF evaluates to TRUE, the function will return “Needs study session”; otherwise it will continue to the FALSE argument, the second IF. If the test expression (same as Expression 2 above) of the second IF evaluates to TRUE, the function will return “Invalid data”; otherwise it will continue to the FALSE argument, the third IF. If the test expression (same as Expression 3 above) of the third IF evaluates to TRUE, the function will return “Exam failed”; otherwise the expression will return an empty expression (“”). The result might look like the following table. Trapping Division by Zero Sometimes it is not possible to construct a table in a manner that can avoid division by zero. However, if division by zero occurs, the result is an error value in the cell, which is usually not the desired result. This example shows three methods of preventing this error. Examples Assume that cell D2 and E2 each contain a number. It is possible that E2 contains 0. You wish to divide D2 by E2, but avoid a division by zero error. Each of the following three methods will return 0 if cell E2 is equal to zero; otherwise each returns the result of D2/E2. =IF(E2=0,0,D2/E2) operates by directly testing cell E2 to see if it is 0. =IFERROR(D2/E2,0) operates by returning 0 if an error occurs. Division by zero is an error. =IF(ISERROR(D2/E2),0,D2/E2) operates by doing a logical test to see if D2/E2 is TRUE. Specifying Conditions and Using Wildcards Some functions, such as SUM, operate on entire ranges. Other functions, such as SUMIF, only operate on the cells in the range that meet a condition. For example you might want to add up all the numbers in column B that are less than 5. To do this, you could use =SUMIF(B, “<5”). The second argument of SUMIF is called a condition because it causes the function to ignore cells that do not meet the requirements. There are two types of functions that take conditions. The first type is functions that have names ending in IF or IFS (except for the function IF, which does not take a condition; it instead takes an expression that should evaluate to either TRUE or FALSE). These functions can do numeric comparisons in their conditions, such as “>5”, “<=7”, or “<>2”. These functions also accept wildcards in specifying conditions. For example, to count the number of cells in column B that begin with the letter “a”, you could use =COUNTIF(B, “a*”) The second group of functions take conditions, such as HLOOKUP, but can’t do numeric conditions. These functions sometimes permit the use of wildcards. Function Allows numeric comparisons Accepts wildcards AVERAGEIF yes yes AVERAGEIFS yes yes COUNTIF yes yes COUNTIFS yes yes SUMIF yes yes SUMIFS yes yes 360 Chapter 13 Additional Examples and Topics Chapter 13 Additional Examples and Topics 361 Function Allows numeric comparisons Accepts wildcards HLOOKUP no if exact match specified MATCH no if exact match specified VLOOKUP no if exact match specified Examples of conditions, both with and without wildcards, are illustrated in this section. Expression Example “>4” means match any number greater than 4. =COUNTIF(B2:E7, “>4”) returns a count of the number of cells in the range B2:E7 that contain a value greater than 4. “>=7” means match any number greater than or equal to 7. =SUMIF(B, “>=7”) sums the cells in the column B that contain a value greater than or equal to 7. “<=5” in combination with “>=15” means match any number less than or equal to 5 or greater than or equal to 15. Numbers 6 through 14, inclusive, would not be included. =SUMIF(A3:B12,”<=5”)+SUMIF(A3:B12,”>=15”) sums the cells in the range A3:B12 that contain a value less than or equal to 5 or greater than or equal to 15. “*it” means any value that ends with “it.” The asterisk (*) matches any number of characters. =COUNTIF(B2:E7, “*it”) returns a count of the number of cells in the range B2:E7 that contain a value that ends with “it” such as “bit” and “mit.” It does not match “mitt.” “~*” means to match the asterisk (*). The tilde (~) character means to take the next character literally, instead of treating it as a wildcard. =COUNTIF(E, “~*”) returns a count of the number of cells in column E that contain the asterisk character. B2 & “, “ & E2 returns the contents of cells B2 and E2 separated by a comma and a space. =B2&”, “&E2 returns “Last, First” if B2 contains “Last” and E2 contains “First.” “?ip” means any value that begins with a single character followed by “ip.” =COUNTIF(B2:E7, “?ip”) returns a count of the number of cells in the range B2:E7 that contain a value that starts with a character followed by “ip” such as “rip” and “tip.” It does not match “drip” or “trip.” “~?” means to match the question mark (?). The tilde (~) character means to take the next character literally, instead of treating it as a wildcard. =SEARCH(“~?”, B2) returns 19 if cell B2 contains “This is a question? Yes it is.”, since the question mark is the 19th character in the string. “*on?” means to match any value that begins with any number of characters followed by “on” and then a single character. =COUNTIF(B2:E7, “*on?”) returns a count of the number of cells in the range B2:E7 that contain a value that starts with any number of characters (including none) followed by “on” and then a single character. This matches words such as “alone”, “bone”, “one”, and “none.” This does not match “only” (has two characters after the “on”) or “eon” (has no characters after the “on”). Survey Results Example This example brings together the illustrations used throughout the statistical functions. It is based on a hypothetical survey. The survey was short (only five questions) and had a very limited number of respondents (10). Each question could be answered on a scale of 1 to 5 (perhaps the range from “never” to “always”), or not answered. Each survey was assigned a number before mailing. The following table shows the results. Questions that were answered outside the range (incorrect) or not answered are indicated with a blank cell in the table. To illustrate some of the functions, assume that the survey control number included an alphabetic prefix and that the scale was A–E, instead of 1–5. The table would then look like this: Using this table of data and some of the statistical functions available in iWork, you can gather information about the survey results. Keep in mind that the example is purposely small so results may seem obvious. However, if you had 50, 100, or more respondents and perhaps many more questions, the results would not be obvious. 362 Chapter 13 Additional Examples and Topics Chapter 13 Additional Examples and Topics 363 Function and arguments Description of result =CORREL(B2:B11, C2:C11) Determines the correlation of question 1 and question 2 using linear regression analysis. Correlation is a measure of how much two variables (in this case, answers to survey questions) change together. Specifically, this would look at the question: If a respondent answered question 1 with a higher (or lower) value than the average for question 1, did the respondent also answer question 2 with a higher (or lower) value than the average for question 2? In this case, the responses are not particularly well correlated (-0.1732) =COUNT(A2:A11) or =COUNTA(A2:A11) Determines the total number of surveys returned (10). Note that if the survey control identifier was not numeric, you would need to use COUNTA instead of COUNT. =COUNT(B2:B11) or =COUNTA(B2:B11) Determines the total number of responses to the first question (9). By extending this formula across the row, you could determine the total number of responses to each question. Because all the data is numeric, COUNTA returns the same results. If, however, the survey had used A through E, instead of 1 through 5, you would need to use COUNTA to tally the results. =COUNTBLANK(B2:B11) Determines the number of empty cells, representing invalid or no answers. If you extended this formula across the row you would find that question 3 (column D) had 3 invalid or not-answered responses. This might cause you to look at this question on the survey to see if it was controversial or poorly worded, as no other question had more than 1 incorrect or notanswered response. =COUNTIF(B2:B11, “=5”) Determines the number of respondents that gave a 5 to a particular question (in this case, question 1). If you extended this formula across the row, you would learn that only questions 1 and 4 had any respondents give the question a 5. Had the survey used A through E for the range, you would have used =COUNTIF(B2:B11, “=E”). Function and arguments Description of result =COVAR(B2:B11, C2:C11) Determines the covariance of question 1 and question 2. Covariance is a measure of how much two variables (in this case, answers to survey questions) change together. Specifically, this would look at the question: If a respondent answered question 1 with a higher (or lower) value than the average for question 1, did the respondent also answer question 2 with a higher (or lower) value than the average for question 2? Note: COVAR would not work with the table using a scale of A–E, as it requires numeric arguments. =STDEV(B2:B11) or =STDEVP(B2:B11) Determines the standard deviation, one measure of dispersion, of the answers to question 1. If you extend this formula across the row, you would see that the answers to question 3 had the highest standard deviation. If the results represented responses from the entire population being studied, rather than a sample, STDEVP would be used instead of STDEV. Note that STDEV is the square root of VAR. =VAR(B2:B11) or =VARP(B2:B11) Determines the variance, one measure of dispersion, of the answers to question 1. If you extended this formula across the row, you would see that the answers to question 5 had the lowest variance. If the results represented responses from the entire population being studied, rather than a sample, VARP would be used instead of VAR. Note that VAR is the square of STDEV. 364 Chapter 13 Additional Examples and Topics Index 365 Index Symbols ? wildcard 30, 361 * wildcard 30, 361 & string operator 30, 310 ~ wildcard escape character 30, 361 A ABS numeric function 170 absolute cell references 27 ACCRINT financial function 99, 351 ACCRINTM financial function 101 ACOS trigonometric function 327 ACOSH trigonometric function 328 ADDRESS reference function 207 ampersand string operator 30, 310 AND logical and information function 156, 358 any value type 36 AREAS reference function 209 arithmetic operators 28 array constant 35 array defined 35 array function defined 35 FREQUENCY 257 INDEX 214 INDIRECT 216 LINEST 265 OFFSET 219 TRANSPOSE 222 ASIN trigonometric function 329 ASINH trigonometric function 329 asterisk wildcard 30, 361 ATAN trigonometric function 330 ATAN2 trigonometric function 331 ATANH trigonometric function 332 AVEDEV statistical function 230 AVERAGE statistical function 231 AVERAGEA statistical function 232 AVERAGEIF statistical function 233, 360 AVERAGEIFS statistical function 234, 360 B BASETONUM engineering function 73 BESSELJ engineering function 74 BESSELY engineering function 75 BETADIST statistical function 236 BETAINV statistical function 237 BIN2DEC engineering function 76 BIN2HEX engineering function 77 BIN2OCT engineering function 78 BINOMDIST statistical function 238 bond investment related financial questions 351 BONDDURATION financial function 103 BONDMDURATION financial function 104 Boolean expression defined 35 Boolean value type 36 C calculations, instant 17 CEILING numeric function 170, 355 cell comments example 358 cell references distinguishing absolute and relative 27 inserting into formulas 26 CHAR text function 308 CHIDIST statistical function 239 CHIINV statistical function 239 CHITEST statistical function 240 CHOOSE reference function 209 choosing which TVM function to use 348 CLEAN text function 308 CODE text function 309 collection value type 36 colon as reference element separator 39 COLUMN reference function 210 COLUMNS reference function 211 COMBIN numeric function 172 commas as argument separators 34 common arguments used in financial functions 341 comparison operators 29 CONCATENATE text function 310 condition 30 comparison operators 29 defined 35 specifying 360 CONFIDENCE statistical function 242 366 Index constant defined 35 conversion units distance 80 duration 80 energy 81 force 81 liquid 82 magnetism 82 metric prefixes 83 power 82 pressure 81 speed 81 temperature 82 weight and mass 80 CONVERT engineering function 79 copying help examples into a table 41 CORREL statistical function 242, 363 COS trigonometric function 333 COSH trigonometric function 334 COUNT statistical function 244, 363 COUNTA statistical function 245, 363 COUNTBLANK statistical function 246, 363 COUNTIF statistical function 247, 360, 361, 363 COUNTIFS statistical function 248, 253, 360 COUPDAYBS financial function 105 COUPDAYS financial function 107 COUPDAYSNC financial function 108 COUPNUM financial function 109, 351 COVAR statistical function 250, 364 CRITBINOM statistical function 252 CUMIPMT financial function 110, 112, 349 CUMPRINC financial function 349 D date and time function DATE 44 DATEDIF 45 DATEVALUE 47 DAY 47 DAYNAME 48 DAYS360 49 EDATE 50 EOMONTH 51 HOUR 51 MINUTE 52 MONTH 53 MONTHNAME 54 NETWORKDAYS 54 NOW 55 SECOND 56 TIME 56 TIMEVALUE 57 TODAY 58 WEEKDAY 59 WEEKNUM 60 WORKDAY 61 YEAR 62 YEARFRAC 63 DATE date and time function 44 DATEDIF date and time function 45 date/time value type 36 DATEVALUE date and time function 47 DAY date and time function 47 DAYNAME date and time function 48 DAYS360 date and time function 49 DB financial function 114, 352 DDB financial function 116, 352 DEC2BIN engineering function 83 DEC2HEX engineering function 84 DEC2OCT engineering function 85 DEGREES trigonometric function 334 DELTA engineering function 86 depreciation-related financial questions 352 DEVSQ statistical function 253 DISC financial function 117, 351 distance conversion units 80 DOLLAR financial function 311 double colon as reference element separator 39 DUR2DAYS duration function 65 DUR2HOURS duration function 65 DUR2MILLISECONDS duration function 66 DUR2MINUTES duration function 67 DUR2SECONDS duration function 68 DUR2WEEKS duration function 69 duration conversion units 80 DURATION duration function 70 duration function DUR2DAYS 65 DUR2HOURS 65 DUR2MILLISECONDS 66 DUR2MINUTES 67 DUR2SECONDS 68 DUR2WEEKS 69 DURATION 70 STRIPDURATION 71 duration value type 37 E EDATE date and time function 50 EFFECT financial function 119, 351 ellipsis syntax elements 35 energy conversion units 81 engineering function BASETONUM 73 BESSELJ 74 BESSELY 75 BIN2DEC 76 BIN2HEX 77 BIN2OCT 78 CONVERT 79 DEC2BIN 83 DEC2HEX 84 Index 367 DEC2OCT 85 DELTA 86 ERF 87 ERFC 87 GESTEP 88 HEX2BIN 89 HEX2DEC 90 HEX2OCT 91 NUMTOBASE 92 OCT2BIN 93 OCT2DEC 94 OCT2HEX 95 EOMONTH date and time function 51 ERF engineering function 87 ERFC engineering function 87 European days-basis 342 EVEN numeric function 173, 355 EXACT text function 312 EXP numeric function 174 F FACT numeric function 174 FACTDOUBLE numeric function 175 FALSE logical and information function 157 FDIST statistical function 254, 255, 261 financial function ACCRINT 99, 351 ACCRINTM 101 BONDDURATION 103 BONDMDURATION 104 COUPDAYBS 105 COUPDAYS 107 COUPDAYSNC 108 COUPNUM 109, 351 CUMIPMT 110 CUMPRINC 112 DB 114, 352 DDB 116, 352 DISC 117, 351 EFFECT 119, 351 FV 120, 348, 351 INTRATE 122, 352 IPMT 123, 353 IRR 125, 350 ISPMT 126 MIRR 128, 350 NOMINAL 129, 351 NPER 130, 348, 351 NPV 132, 350 PMT 134, 348, 351, 353 PPMT 135, 353 PRICE 137, 352 PRICEDISC 138 PRICEMAT 140 PV 349 RATE 144, 349 RECEIVED 146, 352 SLN 147, 352 SYD 148, 352 VDB 149, 352 YIELD 150, 352 YIELDDISC 152 YIELDMAT 153 financial function argument defined annual-rate 341 annual-yield 341 cash-flow 341 cost 341 cum-when-due 342, 347 days-basis 342 depr-factor 342 depr-period 343 effective-int-rate 343 end-per 343, 347 estimate 343 European days-basis 342 frequency 343 future-value 344 invest-amount 344 life 344 NASD days-basis 342 nominal-rate 344 num-periods 344 num-periodsyear 345 par 345 payment 345 period 345 periodic-discount-rate 345 periodic-rate 346 present-value 346 price 346 redemption 346 salvage 347 start-per 343, 347 when-due 347 FIND text function 312 finding and replacing formula elements 32 text strings 312, 314, 316, 318, 319, 320 FIXED mathematical function 313 FLOOR numeric function 176, 355 force conversion units 81 FORECAST statistical function 256 formula bar 20 Formula Editor 19 formulas. See also operators; See also functions adding a quick formula 18 copying and moving 30 creating 19 deleting 24 elements of 15 finding and replacing elements of 32 368 Index handling errors and warnings 23 inserting cell references 26 operators 28 performing instant calculations 17 using arithmetic operators 28 using cell references 24 using comparison operators 29 using the formula bar 20 using the Formula Editor 19 using the Function Browser 21 viewing all in a spreadsheet 31 formulas that reference the same cell in multiple tables 39 FREQUENCY statistical function 257 Function Browser 21. See also functions functions. See also formulas adding to formulas 21 any value type defined 36 array constant defined 35 array defined 35 array function defined 35 Boolean expression defined 35 Boolean value type defined 36 collection value type defined 36 colon and double colon separators 39 comma and semicolon argument separators 34 condition defined 35 constant defined 35 date and time 42 date/time value type defined 36 duration 64 duration value type defined 37 ellipsis syntax element 35 engineering 72 financial 96 introduction to 33 italic text 34 list value type defined 38 logical and information 155 modal argument defined 35 modal value type defined 38 number value type defined 38 numeric 167 parentheses syntax element 34 range value type defined 38 reference 206 reference value type defined 39 statistical 225 string value type defined 39 syntax elements used in function definitions 34 table spanning formulas 39 text 306 trigonometric 326 uppercase text 34 FV financial function 120, 348, 351 G GAMMADIST statistical function 259 GAMMAINV statistical function 260 GAMMALN statistical function 260 GCD numeric function 177 GESTEP engineering function 88 H HARMEAN statistical function 262 HEX2BIN engineering function 89 HEX2DEC engineering function 90 HEX2OCT engineering function 91 HLOOKUP reference function 211, 361 HOUR date and time function 51 HYPERLINK reference function 213 I IF logical and information function 158, 358 IF logical function 360 IFERROR logical and information function 159 IFERROR logical function 360 INDEX reference function 214 INDIRECT reference function 216 instant calculations 17 INT numeric function 178, 355 INTERCEPT statistical function 262 INTRATE financial function 122, 352 introduction to functions 33 IPMT financial function 123, 349, 353 IRR financial function 125, 350 ISBLANK logical and information function 160, 358 ISERROR logical and information function 161 ISERROR logical function 360 ISEVEN logical and information function 162 ISODD logical and information function 163 ISPMT financial function 126 italic text syntax elements 34 LL ARGE statistical function 264 LCM numeric function 179 LEFT text function 314 LEN text function 315 LINEST additional statistics 267 LINEST statistical function 265 liquid conversion units 82 list value type 38 LN numeric function 179 loan amortization table 353 loan related financial questions 351 LOG numeric function 180 LOG10 numeric function 181 logical and information function AND 156, 358 FALSE 157 Index 369 IF 158, 358 IFERROR 159 ISBLANK 160, 358 iserror 161 ISEVEN 162 ISODD 163 NOT 164 OR 165, 358 TRUE 166 LOGINV statistical function 268 LOGNORMDIST statistical function 269 LOOKUP reference function 217 LOWER text function 316 M magnetism conversion units 82 MATCH reference function 218, 361 MAX statistical function 270 MAXA statistical function 270 MEDIAN statistical function 271 metric prefixes for conversion units 83 MID text function 316 MIN statistical function 272 MINA statistical function 273 MINUTE date and time function 52 MIRR financial function 128, 350 MOD numeric function 182 modal argument defined 35 modal value type 38 MODE statistical function 274 MONTH date and time function 53 MONTHNAME date and time function 54 MROUND numeric function 183, 355 MULTINOMIAL numeric function 184 N NASD days-basis method 342 navigating to table cells referenced in formulas 26 NEGBINOMDIST statistical function 275 NETWORKDAYS date and time function 54 NOMINAL financial function 129, 351 NORMDIST statistical function 276 NORMINV statistical function 277 NORMSDIST statistical function 277 NORMSINV statistical function 278 NOT logical and information function 164 NOW date and time function 55 NPER financial function 130, 348, 351 NPV financial function 132, 350 number value type 38 numeric function CEILING 355 EVEN 355 FLOOR 355 INT 355 MROUND 355 ODD 355 ROUND 356 ROUNDDOWN 356 ROUNDUP 357 TRUNC 357 numeric functions ABS 170 CEILING 170 COMBIN 172 EVEN 173 EXP 174 FACT 174 FACTDOUBLE 175 FLOOR 176 GCD 177 INT 178 LCM 179 LN 179 LOG 180 LOG10 181 MOD 182 MROUND 183 MULTINOMIAL 184 ODD 185 PI 186 POWER 186 PRODUCT 187 QUOTIENT 188 RAND 189 RANDBETWEEN 189 ROMAN 190 ROUND 191 ROUNDDOWN 192 ROUNDUP 193 SIGN 195 SQRT 195 SQRTPI 196 SUM 196 SUMIF 197, 360 SUMIFS 198, 360 SUMPRODUCT 200 SUMSQ 201 SUMX2MY2 202 SUMX2PY2 203 SUMXMY2 204 TRUNC 204 NUMTOBASE mathematical function 92 O OCT2BIN engineering function 93 OCT2DEC engineering function 94 OCT2HEX engineering function 95 ODD numeric function 185, 355 OFFSET reference function 219 operators arithmetic 28 370 Index comparison 29 string 30, 310 OR logical and information function 165, 358 P parentheses syntax elements 34 pasting help examples into a table 41 PERCENTILE statistical function 279 PERCENTRANK statistical function 280 PERMUT statistical function 281 PI numeric function 186 PMT financial function 134, 348, 351, 353 POISSON statistical function 282 power conversion units 82 POWER numeric function 186 PPMT financial function 135, 349, 353 pressure conversion units 81 PRICE financial function 137, 352 PRICEDISC financial function 138 PRICEMAT financial function 140 PROB statistical function 282 PRODUCT numeric function 187 PROPER text function 317 PV financial function 141, 349 Q QUARTILE statistical function 284 question mark wildcard 30, 361 quick formulas 18 QUOTIENT numeric function 188 RR ADIANS trigonometric function 335 RAND numeric function 189 RANDBETWEEN numeric function 189 range value type 38 RANK statistical function 285 RATE financial function 144, 349 RECEIVED financial function 146, 352 reference function ADDRESS 207 AREAS 209 CHOOSE 209 COLUMN 210 COLUMNS 211 HLOOKUP 211, 361 HYPERLINK 213 INDEX 214 INDIRECT 216 LOOKUP 217 MATCH 218, 361 OFFSET 219 ROW 221 ROWS 221 TRANSPOSE 222 VLOOKUP 223, 361 reference value type 39 referencing the same cell in multiple tables 39 regular expressions using wildcards 361 relative cell references 27 REPLACE text function 318 REPT text function 319 RIGHT text function 319 ROMAN numeric function 190 ROUND numeric function 191, 356 ROUNDDOWN numeric function 192, 356 rounding 355 ROUNDUP numeric function 193, 357 ROW reference function 221 ROWS reference function 221 S savings related financial questions 351 search expressions 361 SEARCH text function 320, 361 searching for formulas. See finding and replacing SECOND date and time function 56 semicolons as argument separators 34 SIGN numeric function 195 SIN trigonometric function 336 SINH trigonometric function 337 SLN financial function 147, 352 SLOPE statistical function 287 SMALL statistical function 288 solving common financial questions 351 speed conversion units 81 spreadsheets finding and replacing formula elements 32 viewing all formulas in 31 SQRT numeric function 195 SQRTPI numeric function 196 STANDARDIZE statistical function 289 statistical function AVEDEV 230 AVERAGE 231 AVERAGEA 232 AVERAGEIF 233, 360 AVERAGEIFS 234, 360 BETADIST 236 BETAINV 237 BINOMDIST 238 CHIDIST 239 CHIINV 239 CHITEST 240 CONFIDENCE 242 CORREL 242, 363 COUNT 244, 363 COUNTA 245, 363 COUNTBLANK 246, 363 COUNTIF 247, 360, 363 COUNTIFS 248, 360 Index 371 COVAR 250, 364 CRITBINOM 252 DEVSQ 253 EXPONDIST 253 FDIST 254 FINV 255 FORECAST 256 FREQUENCY 257 GAMMADIST 259 GAMMAINV 260 GAMMALN 260 GEOMEAN 261 HARMEAN 262 INTERCEPT 262 LARGE 264 LINEST 265 LOGINV 268 LOGNORMDIST 269 MAX 270 MAXA 270 MEDIAN 271 MIN 272 MINA 273 MODE 274 NEGBINOMDIST 275 NORMDIST 276 NORMINV 277 NORMSDIST 277 NORMSINV 278 PERCENTILE 279 PERCENTRANK 280 PERMUT 281 POISSON 282 PROB 282 QUARTILE 284 RANK 285 SLOPE 287 SMALL 288 STANDARDIZE 289 STDEV 290, 364 STDEVA 291 STDEVP 293, 364 STDEVPA 294 TDIST 296 TINV 297 TTEST 297 VAR 298, 364 VARA 300 VARP 302, 364 VARPA 303 ZTEST 305 STDEV statistical function 290, 364 STDEVA statistical function 291 STDEVP statistical function 293, 364 STDEVPA statistical function 294 string operator 30 string value type 39 STRIPDURATION duration function 71 SUBSTITUTE text function 322 SUM numeric function 196 SUMIF mathematical function 360 SUMIF numeric function 197, 361 SUMIFS numeric function 198, 360 SUMPRODUCT numeric function 200 SUMSQ numeric function 201 SUMX2MY2 numeric function 202 SUMX2PY2 numeric function 203 SUMXMY2 numeric function 204 survey results example 362 SYD financial function 148, 352 syntax elements used in function definitions 34 T T text function 323 table spanning formulas 39 TAN trigonometric function 338 TANH trigonometric function 339 TDIST statistical function 296 temperature conversion units 82 text function CHAR 308 CLEAN 308 CODE 309 CONCATENATE 310 DOLLAR 311 EXACT 312 FIND 312 FIXED 313 LEFT 314 LEN 315 LOWER 316 MID 316 PROPER 317 REPLACE 318 REPT 319 RIGHT 319 SEARCH 320 SUBSTITUTE 322 T 323 TRIM 323 UPPER 324 VALUE 325 tilde wildcard escape character 30, 361 TIME date and time function 56 TIMEVALUE date and time function 57 TINV statistical function 297 TODAY date and time function 58 TRANSPOSE reference function 222 trapping division by zero 360 trigonometric function ACOS 327 ACOSH 328 372 Index ASIN 329 ASINH 329 ATAN 330 ATAN2 331 ATANH 332 COS 333 COSH 334 DEGREES 334 RADIANS 335 SIN 336 SINH 337 TAN 338 TANH 339 TRIM text function 323 TRUE logical and information function 166 TRUNC numeric function 204, 357 TTEST statistical function 297 U UPPER text function 324 uppercase text syntax elements 34 using a formula to reference the same cell in multiple tables 39 using help examples in a table 41 using logical and information functions together 358 V VALUE text function 325 value types any 36 Boolean 36 collection 36 date/time 36 duration 37 list 38 modal 38 number 38 range 38 reference 39 string 39 VAR statistical function 298, 364 VARA statistical function 300 VARP statistical function 302, 364 VARPA statistical function 303 VDB financial function 149, 352 VLOOKUP reference function 223, 361 W WEEKDAY date and time function 59 WEEKNUM date and time function 60 weight and mass conversion units 80 wildcards 30, 360, 361 WORKDAY date and time function 61 working with help example tables 41 Keynote ’08 Manual del usuario K Apple Inc. © 2008 Apple Inc. Todos los derechos reservados. Según las leyes de propiedad intelectual, este manual no puede copiarse, ni total ni parcialmente, sin el consentimiento por escrito de Apple. Los derechos del usuario sobre el software se rigen por el contrato de licencia de software incluido. El logotipo de Apple es una marca comercial de Apple Inc., registrada en EE UU y en otros países. El uso del logotipo de Apple, producido mediante el teclado (Opción + Mayúsculas + K) para propósitos comerciales y sin el previo consentimiento por escrito de Apple, puede constituir una infracción y competencia desleal contraria a las leyes. En la realización de este manual se ha puesto el máximo cuidado para asegurar la exactitud de la información que contiene. Apple no se responsabiliza de los posibles errores de impresión o copia. Apple 1 Infinite Loop Cupertino, CA 95014-2084 408-996-1010 www.apple.com Apple, el logotipo de Apple, AppleWorks, ColorSync, Exposé, iBook, iDVD, iLife, iPhoto, iPod, iTunes, Keynote, Mac, MacBook, Mac OS, Numbers, Pages, PowerBook y QuickTime son marcas comerciales de Apple Inc., registradas en EE UU y en otros países. Apple Remote Desktop, Finder, GarageBand, iWeb, iWork y Safari son marcas registradas de Apple Inc. AppleCare es una marca de servicio de Apple Inc., registrada en EE UU y en otros países. Adobe y Acrobat son marcas comerciales o registradas de Adobe Systems Incorporated en EE UU y/o en otros países. Los nombres de otras empresas y productos mencionados en este manual son marcas comerciales de sus respectivas empresas. La mención de productos de terceras partes tiene únicamente propósitos informativos y no constituye aprobación ni recomendación. Apple declina toda responsabilidad referente al funcionamiento o el uso de estos productos. E019-1276 06/2008 3 1 Contenido Prólogo 12 Bienvenido al Manual del usuario de Keynote Capítulo 1 14 Herramientas y técnicas de Keynote 14 Acerca de Temas y Diapositivas maestras 16 La ventana de Keynote 18 Cómo acercar o alejar 18 Cómo cambiar de modo 18 Modo Navegador 19 Modo Esquema 21 Modo Mesa luminosa 21 Cómo ir a una diapositiva concreta 22 La barra de herramientas 23 La barra de formato 24 La ventana de inspectores 25 El visualizador multimedia 25 La ventana Colores 25 El panel Tipos de letra 25 La ventana Advertencias 26 Funciones rápidas de teclado y menús de función rápida Capítulo 2 27 Cómo trabajar con un documento Keynote 27 Cómo crear o abrir un pase de diapositivas 27 Cómo crear un nuevo documento de Keynote 28 Cómo importar un pase de diapositivas 28 Cómo abrir un documento de Keynote existente 29 Cómo guardar documentos 29 Cómo guardar un documento 30 Cómo deshacer los cambios 30 Cómo guardar una copia del documento 31 Cómo guardar automáticamente una copia de seguridad del documento 31 Cómo guardar un documento como un tema 31 Cómo guardar términos de búsqueda para un documento 32 Cómo cerrar un documento sin salir de Keynote 4 Contenido 32 Cómo añadir, eliminar y organizar diapositivas 32 Cómo añadir diapositivas 33 Cómo reordenar diapositivas 33 Cómo agrupar las diapositivas 34 Cómo eliminar diapositivas 34 Cómo omitir diapositivas 35 Cómo añadir números de diapositiva 35 Cómo utilizar los comentarios 36 Cómo copiar o mover elementos entre distintas diapositivas 37 Cómo cambiar el tema, la diapositiva maestra o el diseño de una diapositiva 37 Cómo modificar el tema 38 Uso de varios temas 38 Cómo aplicar una nueva diapositiva maestra a una diapositiva 38 Cómo cambiar el diseño de una diapositiva 40 Cómo realizar el mismo cambio en varias diapositivas Capítulo 3 41 Cómo trabajar con texto 41 Cómo añadir texto 42 Cómo seleccionar texto 43 Cómo eliminar, copiar y pegar texto 44 Cómo definir el formato del tamaño y la apariencia del texto 44 Uso del menú Formato para dar formato al texto 44 Cómo utilizar las opciones de negrita y cursiva con los menús 44 Cómo crear texto con contorno con los menús 44 Cómo subrayar texto con los menús 45 Cómo cambiar el tamaño del texto con los menús 45 Cómo crear subíndices y superíndices con los menús 45 Cómo cambiar el uso de mayúsculas del texto con los menús 46 Uso del panel “Tipo de letra” para dar formato al texto 47 Consejos para organizar los tipos de letra 47 Cómo cambiar de tipo de letra utilizando el panel “Tipo de letra” 48 Cómo cambiar el subrayado utilizando el panel Tipo de letra 48 Cómo añadir un tachado al texto utilizando el panel Tipo de letra 49 Cómo cambiar el color del texto utilizando el panel Tipo de letra 49 Cómo cambiar el color de fondo del párrafo utilizando el panel Tipo de letra 49 Cómo crear sombras en el texto utilizando el panel Tipo de letra 50 Cómo cambiar el tipo de letra utilizado en el esquema 50 Cómo añadir acentos y caracteres especiales 50 Cómo añadir marcas de acento 51 Cómo ver distribuciones de teclado para otros idiomas 51 Cómo escribir caracteres especiales y símbolos 53 Cómo utilizar las comillas tipográficas 53 Uso de características tipográficas avanzadas Contenido 5 54 Cómo ajustar el suavizado de los tipos de letra 54 Cómo ajustar la alineación, el espaciado y el color del texto 55 Cómo utilizar el Inspector de texto para controlar la alineación, el espaciado y el color 55 Cómo alinear texto horizontalmente 56 Cómo alinear texto verticalmente 56 Cómo ajustar el espaciado entre líneas de texto 57 Cómo ajustar el espaciado antes o después de un párrafo 58 Cómo ajustar el espaciado entre caracteres 58 Cómo cambiar el color del texto utilizando el Inspector de texto 59 Cómo ajustar las tabulaciones para alinear el texto 60 Cómo establecer nuevas tabulaciones 60 Cómo cambiar una tabulación 61 Cómo eliminar una tabulación 61 Cómo ajustar las sangrías 61 Cómo ajustar sangrías de párrafos 62 Cómo cambiar el margen interno del texto en objetos 62 Cómo ajustar sangrías para listas 62 Cómo utilizar listas con viñetas, numeradas y ordenadas (Esquemas) 62 Cómo generar listas de forma automática 63 Cómo utilizar listas con viñetas 64 Cómo utilizar listas numeradas 65 Cómo utilizar listas ordenadas (Esquemas) 66 Cómo utilizar cuadros de texto y figuras para resaltar el texto 66 Cómo añadir cuadros textos libres 67 Cómo presentar texto en columnas 67 Cómo introducir texto en formas 68 Cómo definir el formato de los cuadros de texto o las figuras 68 Cómo utilizar hipervínculos 69 Cómo enlazar a una página web 69 Cómo enlazar a un mensaje de correo electrónico predirigido 70 Cómo enlazar con una diapositiva 71 Cómo enlazar con un archivo de Keynote 71 Cómo utilizar un hipervínculo para detener un pase de diapositivas 71 Cómo subrayar texto de hipervínculos 72 Cómo sustituir texto de forma automática 72 Cómo insertar un espacio duro 73 Cómo comprobar la ortografía 73 Cómo buscar las palabras mal escritas 74 Cómo trabajar con las sugerencias de ortografía 75 Cómo buscar y reemplazar texto 6 Contenido Capítulo 4 76 Cómo trabajar con sonido, películas, gráficos y otros objetos 76 Cómo seleccionar objetos 77 Copia o duplicado de objetos 77 Cómo eliminar objetos 77 Cómo desplazar objetos 78 Cómo mover un objeto hacia delante o hacia atrás (creación de capas con objetos) 78 Cómo alinear objetos 78 Alineación de objetos entre sí en una diapositiva 79 Espaciado uniforme de objetos en una diapositiva 79 Uso de guías de alineación 80 Cómo crear sus propias guías de alineación 80 Uso de cuadrículas maestras 80 Cómo ajustar la posición de los objetos con precisión 81 Modificación de objetos 81 Cambiar el tamaño de los objetos 82 Volteo y giro de objetos 83 Cambio del estilo de bordes 83 Cómo enmarcar objetos 84 Cómo añadir sombras 86 Cómo añadir un reflejo 86 Ajuste de Opacidad 87 Cómo agrupar y bloquear objetos 87 Cómo agrupar y desagrupar objetos 88 Bloqueo y desbloqueo de objetos 88 Cómo rellenar objetos 88 Cómo rellenar un objeto con color 89 Uso de la ventana Colores 90 Cómo rellenar un objeto con una imagen 92 Uso de figuras 92 Cómo añadir una figura predibujada 92 Cómo añadir una figura personalizada 93 Cómo convertir figuras en editables 93 Manipulación de los puntos de una figura 94 Cómo modificar la forma de una curva 95 Cómo modificar la forma de un segmento recto 95 Transformación de puntos angulares en puntos curvados y viceversa 95 Cómo editar figuras predibujadas concretas 96 Edición de un rectángulo redondeado 96 Edición de flechas simples y dobles 97 Edición de una estrella 97 Edición de un polígono 97 Uso de marcadores de posición de contenido 98 Cómo trabajar con imágenes Contenido 7 99 Cómo importar una imagen 99 Cómo enmascarar (recortar) imágenes 99 Cómo recortar una imagen mediante la máscara por omisión (rectangular) 100 Cómo enmascarar una imagen con una figura 101 Cómo desenmascarar una imagen 101 Eliminación del fondo o de elementos no deseados de una imagen 102 Cambio del brillo, el contraste y otros ajustes de una imagen 104 Uso del sonido y películas 105 Cómo añadir sonido a una diapositiva 105 Cómo añadir una banda sonora a un pase de diapositivas 106 Cómo añadir una película 106 Cómo ajustar los parámetros de reproducción de contenidos multimedia 107 Cómo añadir una narración 108 Cómo grabar encima de un pase de diapositivas grabado 108 Cómo reproducir un pase de diapositivas grabado 109 Cómo eliminar una grabación 109 Cómo añadir vistas web 111 Cómo convertir un objeto en un hipervínculo Capítulo 5 112 Uso del movimiento en pases de diapositivas 112 Cómo añadir transiciones entre diapositivas 113 Cómo animar las diapositivas con composiciones de objetos 114 Cómo mover objetos dentro o fuera de las diapositivas utilizando efectos de composición 116 Cómo animar los objetos de las diapositivas (composiciones de acciones) 118 Cómo hacer que los objetos se fundan, giren, se amplíen o se contraigan 119 Cómo animar las imágenes utilizando composiciones inteligentes 121 Cómo reordenar las composiciones de objetos 121 Cómo activar las composiciones de objetos 122 Cómo crear composiciones que intercalen las partes de un objeto 123 Cómo animar tipos específicos de objetos 123 Creación de composiciones de texto 124 Creación de composiciones de tablas 124 Creación de composiciones de gráficas 125 Creación de composiciones de películas 125 Cómo eliminar composiciones de objetos Capítulo 6 126 Cómo usar las tablas 126 Acerca de las tablas 127 Cómo trabajar con tablas 127 Cómo añadir una tabla 128 Cómo utilizar las herramientas de tabla 130 Cómo redimensionar una tabla 8 Contenido 131 Cómo mover tablas 131 Cómo copiar tablas entre aplicaciones de iWork 131 Cómo seleccionar tablas y sus componentes 131 Cómo seleccionar una tabla 132 Cómo seleccionar una celda de tabla 132 Cómo seleccionar un grupo de celdas de tabla 132 Cómo seleccionar una fila o una columna 133 Cómo seleccionar los bordes de una celda 133 Cómo trabajar con contenidos en las celdas de la tabla 133 Cómo añadir y editar valores de celdas 134 Cómo trabajar con texto en las celdas 135 Cómo trabajar con números en las celdas 135 Cómo trabajar con fechas en las celdas 136 Cómo mostrar un contenido demasiado grande para su celda 136 Cómo dar formato a los valores de celdas 137 Cómo utilizar el formato de números 138 Cómo utilizar el formato de moneda 138 Cómo utilizar el formato de porcentaje 139 Cómo utilizar el formato de fecha y hora 139 Cómo utilizar el formato de fracciones 139 Cómo utilizar el formato científico 140 Cómo utilizar el formato de texto 140 Cómo monitorizar los valores de las celdas 141 Cómo añadir imágenes o color a las celdas 141 Cómo utilizar el autorrelleno en celdas de tabla 142 Cómo trabajar con filas y columnas 142 Cómo añadir filas 143 Cómo añadir columnas 143 Cómo eliminar filas y columnas de una tabla 143 Cómo utilizar una fila o columna de cabecera de una tabla 144 Cómo utilizar una fila de pie de página 144 Cómo cambiar el tamaño de las filas y columnas de una tabla 145 Cómo alternar los colores de las filas 145 Cómo trabajar con las celda de tabla 145 Cómo fusionar celdas de tabla 146 Cómo dividir celdas de tabla 146 Dar formato a bordes de celdas 147 Cómo copiar y mover celdas 147 Cómo ordenar celdas en una tabla Capítulo 7 149 Uso de fórmulas y funciones en tablas 149 Uso de fórmulas 150 Cómo añadir una fórmula rápida Contenido 9 150 Realización de un cálculo básico mediante valores de columna 151 Realización de un cálculo básico mediante valores de fila 151 Cómo eliminar una fórmula 152 Cómo utilizar el Editor de fórmulas 152 Cómo añadir una fórmula nueva con el Editor de fórmulas 153 Cómo editar una fórmula con el Editor de fórmulas 153 Cómo utilizar referencias de celda 154 Cómo añadir referencias de celda a una fórmula 155 Cómo copiar o mover fórmulas con referencias de celda 155 Cómo aplicar una fórmula una vez a las celdas de una columna o fila 156 Cómo tratar errores y advertencias 156 Cómo utilizar operadores 156 Cómo realizar operaciones aritméticas 157 Descripción de los operadores aritméticos 158 Descripción de los operadores de comparación 159 Cómo utilizar funciones Capítulo 8 160 Cómo utilizar gráficas 160 Acerca de las gráficas 163 Cómo añadir una gráfica 163 Cómo seleccionar un tipo de gráfica 164 Cómo seleccionar un tipo de gráfica inicial 165 Cómo cambiar de tipo de gráfica 166 Cómo modificar los datos de una gráfica 166 Cómo copiar datos en el editor de datos de la gráfica 167 Cómo trabajar con filas y columnas en el editor de datos de la gráfica 167 Atributos generales de formato de la gráfica 167 Cómo utilizar las leyendas 168 Cómo utilizar el título de las gráficas 168 Cómo cambiar el tamaño de una gráfica 169 Cómo girar las gráficas 169 Cómo añadir etiquetas y marcas de eje 170 Cómo mostrar los ejes y los bordes 170 Cómo utilizar los títulos de los ejes 170 Cómo mostrar las etiquetas de los puntos de datos 171 Cómo modificar el formato del eje de valores 172 Cómo colocar etiquetas, cuadrículas y marcas 173 Cómo definir el formato de los elementos de las series de datos 174 Cómo definir el formato de títulos, etiquetas y leyendas 174 Cómo añadir textos descriptivos a una gráfica 174 Cómo modificar el formato en los distintos tipos de gráficas 174 Gráficas de sectores 175 Cómo seleccionar sectores concretos 10 Contenido 175 Cómo mostrar el nombre de una serie en una gráfica de sectores 175 Cómo separar sectores concretos de una gráfica 176 Cómo añadir sombras a las gráficas de sectores y a los sectores 176 Cómo ajustar la opacidad de las gráficas de sectores 176 Cómo girar gráficas de sectores en 2D 177 Gráficas de barras y de columnas 177 Cómo ajustar el espaciado de las gráficas de barras y columnas 177 Cómo añadir sombras a las gráficas de barras y columnas 178 Cómo ajustar la opacidad de las gráficas de barras y columnas 178 Gráficas de áreas y líneas 179 Gráficas de dispersión 180 Gráficas 3D Capítulo 9 182 Cómo ver, imprimir y exportar un pase de diapositivas 182 Cómo personalizar una presentación para una audiencia 183 Cómo crear presentaciones del tipo “solo hipervínculos” 183 Creación de presentaciones autoejecutables 184 Cómo ajustar las opciones de reproducción 184 Cómo ensayar y visualizar las presentaciones 185 Cómo añadir notas del presentador 185 Cómo ensayar la presentación 186 Cómo visualizar una presentación en la pantalla del ordenador 186 Cómo visualizar una presentación en una pantalla o proyector externos 187 Consejos para utilizar una pantalla externa 188 Cómo visualizar la misma presentación en dos pantallas 189 Cómo personalizar la vista del presentador 190 Cómo ajustar la frecuencia de refresco de la pantalla 190 Cómo ajustar el tamaño de diapositiva 191 Cómo configurar la memoria de acceso aleatorio de vídeo (VRAM) 192 Cómo controlar las presentaciones 192 Cómo controlar una presentación con el teclado 193 Cómo pausar y reanudar una presentación 193 Cómo detener una presentación 193 Cómo avanzar a la siguiente diapositiva o composición anterior o siguiente 194 Cómo ir a una diapositiva específica 194 Cómo mostrar el puntero durante una presentación 195 Cómo utilizar otras aplicaciones durante una presentación 195 Cómo reproducir películas y sonido 196 Cómo imprimir diapositivas 197 Cómo exportar un pase de diapositivas a otros formatos 198 Cómo compartir una presentación entre distintas plataformas 198 Cómo crear una película QuickTime 200 Cómo crear un pase de diapositivas de PowerPoint Contenido 11 200 Cómo crear un archivo PDF 201 Cómo exportar diapositivas como archivos de imagen 201 Cómo crear un documento Flash 202 Cómo crear un documento HTML 202 Cómo enviar una presentación a las aplicaciones iLife 202 Cómo crear una proyecto de iDVD 203 Cómo crear un álbum de iPhoto 204 Cómo exportar a iWeb 205 Cómo exportar a iTunes e iPod 205 Cómo exportar a GarageBand 206 Cómo guardar una presentación en formato de iWork ’05 o iWork ’06 Capítulo 10 207 Cómo diseñar sus propias diapositivas maestras y temas 207 Cómo diseñar Temas y Diapositivas maestras 208 Cómo utilizar las herramientas de diapositivas maestras 209 Previsualización de diapositivas maestras 210 Cómo seleccionar diapositivas maestras para personalizarlas 210 Cómo duplicar una diapositiva maestra 210 Cómo importar una diapositiva o una diapositiva maestra 211 Cómo crear una diapositiva maestra desde el principio 211 Cómo personalizar diseños de diapositivas maestras 211 Cómo definir marcadores de posición de texto 212 Cómo definir marcadores de posición de contenidos 212 Cómo definir marcadores de posición de objetos 212 Cómo crear elementos de fondo en diapositivas maestras 213 Cómo añadir guías de alineación a las diapositiva maestras 214 Cómo definir los atributos por omisión del texto y los objetos 214 Cómo definir los atributos por omisión de los cuadros de texto y las figuras 215 Cómo definir los atributos por omisión de las imágenes importadas 216 Cómo definir los atributos por omisión para tablas 217 Cómo definir los atributos por omisión para gráficas. 218 Cómo definir transiciones por omisión 218 Cómo crear composiciones en diapositivas maestras 218 Cómo crear temas personalizados 219 Cómo guardar un tema personalizado 219 Cómo crear un tema desde el principio 220 Cómo recuperar los atributos originales de un tema Índice 221 Prólogo 12 Bienvenido al Manual del usuario de Keynote En este documento PDF en color se detallan las instrucciones de uso de Keynote. Antes de utilizar este documento, puede consultar las lecciones de iniciación de Keynote en el libro Introducción a iWork ‘08. que le ofrece una manera rápida de prepararse para ser un usuario de Keynote autosuficiente. El libro también ofrece recursos adicionales para familiarizarse con Keynote, como una presentación de sus características y vídeos explicativos. Si necesita instrucciones detalladas para realizar tareas específicas, consulte este manual del usuario. La mayoría de las tareas de esta guía también están disponibles en la ayuda en Internet. Prólogo Bienvenido al Manual del usuario de Keynote 13 En la tabla siguiente se indica dónde encontrar la información de esta guía. En la Ayuda de Keynote, puede buscar información mediante exploraciones o búsquedas. Para obtener información acerca de Consulte el Cómo usar las ventanas y herramientas de Keynote para crear y dar formato a documentos capítulo 1, “Herramientas y técnicas de Keynote”, en la página 14 Cómo crear y guardar documentos y gestionar diapositivas capítulo 2, “Cómo trabajar con un documento Keynote”, en la página 27 Cómo dar formato al texto de un documento de Keynote capítulo 3, “Cómo trabajar con texto”, en la página 41 Cómo usar gráficos, figuras, sonido, etc., para mejorar un documento capítulo 4, “Cómo trabajar con sonido, películas, gráficos y otros objetos”, en la página 76 Cómo agregar transiciones, efectos especiales y animaciones a las diapositivas capítulo 5, “Uso del movimiento en pases de diapositivas”, en la página 112 Cómo crear, organizar y dar formato a tablas y valores de tablas capítulo 6, “Cómo usar las tablas”, en la página 126 Cómo usar fórmulas y funciones para realizar cálculos en tablas capítulo 7, “Uso de fórmulas y funciones en tablas”, en la página 149 Cómo crear gráficas para mostrar datos numéricos gráficamente capítulo 8, “Cómo utilizar gráficas”, en la página 160 Cómo compartir documentos de Keynote con otras personas capítulo 9, “Cómo ver, imprimir y exportar un pase de diapositivas”, en la página 182 Cómo crear un tema o plantilla partiendo de cero capítulo 10, “Cómo diseñar sus propias diapositivas maestras y temas”, en la página 207 1 14 1 Herramientas y técnicas de Keynote En este capítulo conocerá las ventanas y herramientas que utilizará para crear pases de diapositivas con Keynote. Cada pase de diapositivas se crea en un documento Keynote independiente. Si se añaden películas, sonidos u otros contenidos multimedia al pase de diapositivas, se pueden guardar como parte del documento para poder mover fácilmente la presentación de un ordenador a otro. Acerca de Temas y Diapositivas maestras La primera vez que se abre la aplicación Keynote (haciendo clic en su icono en el Dock o haciendo doble clic en su icono en el Finder), el selector de tema muestra los temas incorporados que puede escoger. Capítulo 1 Herramientas y técnicas de Keynote 15 Cada tema de Keynote consta de una familia de diapositivas maestras con elementos de diseño conjuntados. Las diapositivas maestras son plantillas que proporcionan elementos predefinidos, p .ej., diseños, tipos de letra, texturas, propiedades de gráficas, colores de fondo, etc. Cuando se desea crear una diapositiva que contenga ciertos elementos (como un título, un bloque de texto, una lista con viñetas o un gráfico) se selecciona la diapositiva maestra que se asemeje más a la que se necesite. Las diapositivas maestras contienen marcadores de posición que se pueden sustituir por el contenido que se desee.  El texto del marcador de posición (“Doble clic para editar”) muestra el aspecto que tiene el texto. Haga doble clic sobre este texto y comience a escribir lo que desee. Para obtener más información, consulte “Cómo añadir texto” en la página 41.  Los marcadores de posición de contenidos pueden contener imágenes, archivos de audio y películas. Arrastre su imagen hasta o película hasta el marcador de posición. Aunque puede arrastrar archivos multimedia a cualquier parte de una diapositiva (no únicamente a un marcador de posición), el uso de marcadores de posición de contenidos permite ajustar automáticamente el tamaño y la posición de la imagen o película. Para obtener más información, consulte “Uso de marcadores de posición de contenido” en la página 97. También se pueden añadir a cualquier diapositiva elementos propios, como tablas u otros objetos. Texto del marcador de posición Marcador de posición de contenidos para imágenes, películas u otros archivos multimedia 16 Capítulo 1 Herramientas y técnicas de Keynote La mayoría de los temas vienen con las siguientes diapositivas maestras: La ventana de Keynote Las ventanas de documentos Keynote tienen funciones de ayuda para desarrollar y organizar los pases de diapositivas. Estos elementos se pueden mostrar u ocultar independientemente:  La barra de herramientas situada en la parte superior de la ventana ofrece acceso rápido a las herramientas necesarias para crear las diapositivas. Para obtener más información, consulte “La barra de herramientas” en la página 22.  El navegador de diapositivas del lado izquierdo de la ventana ofrece una visión general visual del pase de diapositivas. Puede visualizar una miniatura de cada diapositiva o bien un esquema de texto. Consulte el apartado “Cómo cambiar de modo” en la página 18 para obtener más información. Diapositiva maestra Uso recomendado Título y subtítulo Página de título o títulos de sección de la presentación Título y viñetas Contenido Título y viñetas - 2 columnas Contenido visualizado en dos columnas Viñetas Páginas de contenido general con viñetas de texto; el área de texto ocupa toda la diapositiva En blanco Diseños con abundantes figuras Título - Superior o central Página de título o títulos de sección de la presentación Foto - Horizontal Foto horizontal con título inferior Foto - Vertical Foto vertical con título y subtítulo en el lado izquierdo Título, viñetas y foto Título de página o de sección con texto y foto Título y viñetas (izquierda o derecha) Diapositivas de contenido para colocar viñetas de texto a la izquierda o a la derecha y una figura en el lado opuesto de la diapositiva Capítulo 1 Herramientas y técnicas de Keynote 17  Puede escribir notas acerca de cada una de las diapositivas en el campo de notas del presentador. Estas anotaciones no son visibles durante el pase y pueden servir de referencia al realizar la presentación. Para más información, consulte “Cómo añadir notas del presentador” en la página 185. A continuación se describen los métodos para mostrar u ocultar independientemente estos elementos: m Para mostrar u ocultar la barra de herramientas, seleccione Visualización > “Mostrar barra de herramientas” o Visualización > Ocultar barra de herramientas. m Para mostrar el navegador de diapositivas, seleccione Visualización > Navegador o Visualización > Esquema. Para ocultarlo, seleccione Visualización > Solo diapositiva. m Para mostrar u ocultar las notas del presentador, seleccione Visualización > “Mostrar notas del presentador” o Visualización > Ocultar notas del presentador. El lienzo de la diapositiva: para crear cada diapositiva, escriba texto y añada objetos y contenidos. El campo de notas del presentador: permite añadir notas sobre cada diapositiva individual. Estas anotaciones no son visibles durante el pase y pueden servirle de referencia al realizar la presentación. El navegador de diapositivas: proporciona una visión general de la presentación. Puede visualizar una miniatura de cada diapositiva o bien un esquema de texto. La barra de herramientas: personalice la barra de herramientas añadiendo las herramientas que más utilice. Permite cambiar el tamaño de las miniaturas de las diapositivas. 18 Capítulo 1 Herramientas y técnicas de Keynote Cómo acercar o alejar Puede ampliar (acercar imagen) o reducir (alejar imagen) la visualización del lienzo de diapositiva. Estos son algunos modos de acercar o eliminar la imagen: m Seleccione Visualización > Ampliar/Reducir nivel de zoom. m Seleccione un nivel de ampliación en el menú local Zoom situado en la parte inferior izquierda del lienzo de diapositivas. Cómo cambiar de modo Keynote ofrece varios modos de visualizar, gestionar y organizar las diapositivas existentes en un documento de Keynote: modo navegador, modo esquema y modo mesa luminosa. También se puede ver únicamente el lienzo de la diapositiva. Para cambiar de un modo de visualización al otro: m Haga clic en Visualización en la barra de herramientas y seleccione una opción (o seleccione Visualización > Navegador, Esquema, Mesa luminosa o Solo diapositiva). Modo Navegador El modo Navegador muestra imágenes en miniatura de cada diapositiva y resulta muy útil para pases de diapositivas que contienen muchos gráficos, tablas y otros objetos. Este modo proporciona una buena visión general visual de las diapositivas, pero es posible que no se pueda leer todo el texto de las miniaturas. Puede manipular las diapositivas en el navegador de diapositivas para cambiar la posición y organizar las diapositivas. Arrastre este tirador hacia abajo para mostrar las diapositivas maestras. Para omitir una diapositiva durante una presentación, seleccione Diapositiva > Omitir diapositiva. Haga clic en el triángulo desplegable para mostrar u ocultar grupos de diapositivas sangradas. Visualice los elementos gráficos de las diapositivas rápidamente. Sangre las diapositivas para organizarlas en grupos. Para sangrar una diapositiva, arrástrela o selecciónela y pulse Tabulador. La diapositiva aquí seleccionada es la diapositiva con la que está trabajando. Visualice las miniaturas en distintos tamaños. Capítulo 1 Herramientas y técnicas de Keynote 19 Estos son algunos modos de trabajar en el modo navegador: m Para pasar al modo navegador, en la barra de herramientas haga clic en Visualización y seleccione Navegador, o seleccione Visualización > Navegador. m Para cambiar la posición o el nivel jerárquico de una diapositiva, arrástrela. m Para mostrar u ocultar grupos de diapositivas (diapositivas sangradas y su diapositiva “principal”), haga clic en los triángulos desplegables. m Para ampliar o reducir las imágenes en miniatura, haga clic en el botón de la esquina inferior izquierda y seleccione un tamaño. m Para duplicar una o más diapositivas contiguas, selecciónelas y seleccione Edición > Duplicar. Las diapositivas duplicadas se insertarán a continuación de las diapositivas seleccionadas. m Para copiar y pegar una o más diapositivas adyacentes, selecciónelas, seleccione Edición > Pegar, seleccione la diapositiva después de la cual desea pegar las diapositivas copiadas y seleccione Edición > Pegar. m Para mostrar las diapositivas maestras (lo que resulta de gran utilidad a la hora de crear diapositivas maestras o temas propios), arrastre el tirador situado en la parte superior derecha del navegador de diapositivas, o bien haga clic en Visualización en la barra de herramientas y seleccione “Mostrar diapositivas maestras” Para obtener más detalles, consulte el apartado “Cómo diseñar Temas y Diapositivas maestras” en la página 207. Modo Esquema El modo Esquema resulta de gran utilidad para ver la estructura de las presentaciones que contienen una gran cantidad de texto. Muestra el título y el texto con viñetas de cada una de las diapositivas del pase de diapositivas. Todos los títulos y los textos con viñetas se pueden leer perfectamente en el navegador de diapositivas. 20 Capítulo 1 Herramientas y técnicas de Keynote El modo esquema permite ordenar y reordenar con facilidad la posición de las viñetas de texto de la presentación al organizarla. Por ejemplo, puede añadir viñetas al texto directamente en el navegador de diapositivas. También puede arrastrar las viñetas de una diapositiva a otra, o arrastrarlas a un nivel superior o inferior de la estructura de la diapositiva. Estos son algunos modos de trabajar en el modo esquema: m Para pasar al modo esquema, en la barra de herramientas haga clic en Visualización y seleccione Esquema (o seleccione Visualización Esquema). m Para cambiar el tipo de letra utilizado en modo esquema, seleccione Keynote > Preferencias, haga clic en General y seleccione un tipo de letra y un tamaño en los menús locales “Tipo de letra del esquema”. m Para imprimir el modo esquema, seleccione Archivo > Imprimir. En el cuadro de diálogo Imprimir, seleccione Keynote en el menú local “Copias y páginas” y a continuación seleccione Esquema. Arrastre las viñetas a la izquierda o a la derecha para colocarlas en un nivel superior o inferior del esquema. Puede incluso arrastrar las viñetas de una diapositiva a otra. En el esquema, puede ver el texto de los títulos y de las viñetas. Es posible añadir y modificar texto directamente en el esquema. Haga doble clic en el icono de una diapositiva para ocultar el texto con viñetas en el navegador de diapositivas. Capítulo 1 Herramientas y técnicas de Keynote 21 Modo Mesa luminosa Si el pase de diapositivas contiene varias diapositivas y desea visualizar más miniaturas a la vez, utilice el modo mesa luminosa. Puede reordenar fácilmente las diapositivas arrastrándolas, como si se encontraran sobre la mesa luminosa de un fotógrafo. Estos son algunos modos de trabajar en el modo mesa luminosa: m Para pasar al modo mesa luminosa, haga clic en Visualización en la barra de herramientas y seleccione “Mesa luminosa” (o seleccione Visualización > Mesa luminosa). m Para ampliar o reducir las imágenes en miniatura, haga clic en el botón de la esquina inferior izquierda de la ventana y seleccione un tamaño. m Haga doble clic en una diapositiva para editarla o regresar a la vista anterior (navegador o esquema). En la vista de mesa luminosa puede añadir, eliminar, duplicar, omitir y reordenar diapositivas de la misma forma que en las vistas de navegador y esquema. Cómo ir a una diapositiva concreta Mientras trabaja en el documento, puede desplazarse fácilmente a cualquier diapositiva. Estos son los modos de acceder a una diapositiva en particular: m Para acceder a cualquier diapositiva, en el modo navegador o esquema del navegador de diapositivas haga clic en una miniatura. m Seleccione Diapositiva > Ir a y seleccione una de las opciones (Diapositiva siguiente, Diapositiva anterior, Primera diapositiva o Última diapositiva). 22 Capítulo 1 Herramientas y técnicas de Keynote La barra de herramientas La barra de herramientas de Keynote le brinda con un solo clic acceso a muchas de las acciones que se utilizan al trabajar en Keynote. Puede cambiar la posición, añadir y eliminar los botones de la barra de herramientas para adaptarlos a su estilo de trabajo. La selección por omisión de los botones de la barra de herramientas se muestra a continuación. Para personalizar la barra de herramientas: 1 Seleccione Visualización > “Personalizar barra de herramientas”, o bien, con la tecla Control pulsada, haga clic en la barra de herramientas y seleccione “Personalizar barra de herramientas”. 2 Realice los cambios que desee en la barra de herramientas. Para añadir un ítem a la barra de herramientas, arrastre su icono hasta la barra de herramientas de la parte superior. Para eliminar un ítem de la barra de herramientas, arrástrelo fuera de la misma. Para restaurar el conjunto por omisión de botones de la barra de herramientas, arrastre a la barra de herramientas el conjunto por omisión. Para hacer más grandes los iconos de la barra de herramientas, anule la selección de la opción “Utilizar tamaño pequeño”. Para mostrar solo iconos o solo texto, seleccione una opción en el menú local Mostrar. Para modificar la ubicación de los ítems en la barra de herramientas, arrástrelos. Recortar o eliminar partes no deseadas de una foto. Añadir un cuadro de texto libre, una figura, una tabla, una gráfica o un comentario. Reproducir un pase de diapositivas. Añadir diapositivas. Seleccionar una nueva vista, tema o diapositiva maestra. Animar colecciones de imágenes. Convertir un grupo de objetos en un objeto (o un objeto en sus componentes); distribuir objetos. Abrir las ventanas de herramientas. Capítulo 1 Herramientas y técnicas de Keynote 23 3 Cuando haya terminado, haga clic en Salir. Estas son algunas funciones rápidas de teclado para personalizar la barra de herramientas sin necesidad de seleccionar Visualización > Personalizar barra de herramientas:  Para eliminar un elemento, pulse la tecla Comando mientras arrastra ese elemento fuera de la barra de herramientas, o bien, con la tecla Control pulsada, haga clic en el elemento y seleccione Eliminar.  Para mover un elemento, pulse la tecla Comando mientras arrastra el elemento. Para ver una descripción de lo que hace un botón de la barra de herramientas, coloque el puntero sobre el mismo. La barra de formato Use la barra de formato para cambiar de forma rápida el aspecto del texto, las tablas, las gráficas y otros elementos de su pase de diapositivas.. Para mostrar y ocultar la barra de formato: m Seleccione Visualización > Mostrar barra de formato, o Visualización > Ocultar barra de formato. Los controles de la barra de formato dependen del objeto que esté seleccionado. Para ver una descripción de lo que hace un determinado control de la barra de formato, coloque el puntero sobre él. Cuando hay texto u objetos gráficos seleccionados, la barra de formato tiene el siguiente aspecto: Alinee el texto seleccionado. Cambie el tipo, el estilo, el tamaño y el color de letra. Seleccione el interlineado y el número de columnas. Añada un color de fondo a los cuadros de texto y las figuras. Ajuste la opacidad y la sombra de los cuadros de texto. Cambie el formato de los bordes de los cuadros de texto y las figuras 24 Capítulo 1 Herramientas y técnicas de Keynote Cuando hay una tabla seleccionada, la barra de formato adopta el siguiente aspecto: La ventana de inspectores Puede dar formato a mayoría de los elementos del pase de diapositivas mediante los diez inspectores de Keynote. Cada inspector se centra en un aspecto de formato diferente. Por ejemplo, el Inspector del documento contiene los ajustes de todo el pase de diapositivas. Se pueden abrir varios inspectores a la vez para trabajar en el documento más cómodamente. Por ejemplo, si abre tanto el inspector de figuras como el inspector de textos, podrá tener acceso a todas las opciones para aplicar formato a imágenes y textos. A continuación, se indica cómo abrir una ventana de Inspector: m Haga clic en Inspector en la barra de herramientas. m Para abrir más de una ventana Inspector, pulse la tecla Opción mientras hace clic en un botón Inspector, o seleccione Visualización > Nueva ventana de Inspector. Después de abrir la ventana de Inspector, haga clic en uno de los botones situados en la parte superior para mostrar un inspector diferente. Al hacer clic en el segundo botón desde la izquierda, por ejemplo, se muestra el inspector de diapositivas. Mantenga el puntero sobre los botones y otros controles del Inspector para ver la descripción de sus funciones. Cambie el formato del texto de las celdas de la tabla. Elija la disposición del texto en las celdas de la tabla.. Especifique el número de filas y columnas. Establezca la fila/ columna de cabecera y de pie. Cambie el formato de los bordes de las celdas.. Añada color de fondo a una celda. Haga clic en uno de estos botones para mostrar otro inspector. Capítulo 1 Herramientas y técnicas de Keynote 25 El visualizador multimedia El visualizador multimedia permite acceder a todos los archivos multimedia de la fototeca de iPhoto, la biblioteca de iTunes, biblioteca de Apertura y la carpeta Películas. Puede arrastrar un elemento del visualizador multimedia a una diapositiva o un contenedor de imágenes de un inspector. Para abrir el visualizador multimedia: m Haga clic en el botón Multimedia de la barra de herramientas, o seleccione Visualización > Mostrar visualizador multimedia. La ventana Colores Utilice la ventana Colores del Mac OS X para seleccionar colores para el texto, los objetos y las líneas. Para abrir la ventana Colores: m Haga clic en Colores en la barra de herramientas. Para más información, consulte “Uso de la ventana Colores” en la página 89. El panel Tipos de letra El panel de tipos de letra de Mac OS X (al que se puede acceder desde cualquier aplicación) le permite cambiar el tipo, el tamaño y otras opciones de la letra. Para abrir el panel “Tipo de letra”: m Haga clic en “Tipos de letra” en la barra de herramientas. Para obtener más información acerca del uso del panel “Tipo de letra” y cómo cambiar el aspecto del texto, consulte “Uso del panel “Tipo de letra” para dar formato al texto” en la página 46. La ventana Advertencias Cuando se importa un documento a Keynote, o se exporta un documento Keynote a otro formato, algunos elementos se podrían transferir de modo idéntico. En la ventana Advertencias se indican los problemas detectados. Es posible que reciba advertencias en otras situaciones, como al guardar un documento en una versión anterior de la aplicación. Si se detectan problemas, verá un mensaje que le permite revisar las advertencias. Si decide no revisarlas, puede ver la ventana Advertencias en cualquier momento seleccionando Visualización > Mostrar advertencias del documento. 26 Capítulo 1 Herramientas y técnicas de Keynote Si aparece una advertencia en la que se indica que falta un tipo de letra, puede seleccionar la advertencia y hacer clic en “Reemplazar tipo” para seleccionar un tipo de letra reemplazo. Puede copiar mensajes de advertencia y pegarlos en un documento para consultarlos posteriormente; estos mensajes pueden resultarle útiles a la hora de diagnosticar problemas. Funciones rápidas de teclado y menús de función rápida Puede usar el teclado para ejecutar muchas de las tareas y comandos de menús de Keynote. Si desea consultar una lista completa de funciones rápidas de teclado, abra Keynote y seleccione Ayuda > Funciones rápidas de teclado. Muchos objetos también tienen menús de función rápida con comandos que se pueden aplicar al objeto. Los menús de función rápida son especialmente útiles para trabajar con tablas y gráficas. Para abrir un menú de función rápida: m Pulse la tecla Control mientras hace clic sobre un objeto. 2 27 2 Cómo trabajar con un documento Keynote En este capítulo se explica cómo crear, abrir, importar y guardar documentos de Keynote. También se explica cómo añadir diapositivas, cómo organizarlas y cómo cambiar el tema, el diseño o la diapositiva maestra de una diapositiva. Es probable que desee realizar las lecciones de iniciación del libro Introducción a iWork ’08 antes de empezar a trabajar en Keynote. Estas lecciones le ayudarán a familiarizarse rápidamente con Keynote Cómo crear o abrir un pase de diapositivas Cada pase de diapositivas que cree constituirá su propio documento de Keynote. Puede crear un pase de diapositivas realizando cualquiera de las siguientes operaciones:  Crear un documento nuevo de Keynote  Importar un documento creado en PowerPoint o AppleWorks  Abrir un documento de Keynote existente Cómo crear un nuevo documento de Keynote Para crear un nuevo documento de Keynote: 1 Si Keynote no está abierto, ábralo haciendo clic en el icono correspondiente del Dock o haciendo doble clic en el icono del Finder. Si Keynote ya está abierto, seleccione Archivo > Nuevo. 2 En el selector de tema, seleccione un tema y haga clic en Seleccionar. Puede cambiar el tema del pase de diapositivas en cualquier momento (consulte “Cómo cambiar el tema, la diapositiva maestra o el diseño de una diapositiva” en la página 37) y puede usar más de un tema en un documento (consulte “Uso de varios temas” en la página 38). En el selector de tema, también puede seleccionar un tamaño de diapositiva (consulte “Cómo ajustar el tamaño de diapositiva” en la página 190). 28 Capítulo 2 Cómo trabajar con un documento Keynote Π Consejo: Puede configurar Keynote para que utilice el mismo tema al crear un documento nuevo. Seleccione Keynote > Preferencias, haga clic en General, seleccione “Usar tema” y, a continuación, seleccione un tema. Para cambiar el tema, haga clic en Seleccionar. Cómo importar un pase de diapositivas Si ya dispone de una presentación de diapositivas creada con Microsoft PowerPoint o con AppleWorks, puede importarla en Keynote y seguir trabajando en ella. A continuación, se indica como importar un documento de PowerPoint o AppleWorks: m En Keynote, seleccione Archivo > Abrir. En el cuadro de diálogo Abrir, busque el documento que desee importar y haga clic en Abrir. m En el Finder, arrastre el icono del documento de PowerPoint o AppleWorks hasta el icono de la aplicación Keynote. Cómo abrir un documento de Keynote existente Existen varias formas de abrir un documento creado con Keynote. A continuación, se muestran distintos procedimientos para abrir un documento de Keynote: m Para abrir un documento mientras trabaja en Keynote, seleccione Archivo > Abrir, seleccione el documento y haga clic en Abrir. m Para abrir un documento con el que ha trabajado hace poco, seleccione Archivo > “Abrir recientes” y seleccione el documento en el submenú. m Para abrir un documento de Keynote desde el Finder, haga doble clic en el icono del documento o arrástrelo hasta el icono de la aplicación Keynote. Puede abrir un documento de Keynote creado con una versión anterior de Keynote (en iWork ’05 o iWork ’06). Para que el documento pueda utilizarse de nuevo con iWork ’05 o iWork ’06, guárdelo en el mismo formato. Consulte “Cómo guardar una presentación en formato de iWork ’05 o iWork ’06” en la página 206. Aunque aparezca un mensaje que indique que falta un tipo de letra o un archivo, puede utilizar el documento. Keynotesustituye los tipos de letra para los tipos de letra no incluidos en el sistema. Para poder utilizar los tipos de letra que faltan, salga de Keynote y añada los tipos de letra a la carpeta Fonts (si desea más información, consulte la Ayuda Mac). Para que aparezcan los archivos de películas o de sonido que faltan, debe añadirlos al documento. Capítulo 2 Cómo trabajar con un documento Keynote 29 Cómo guardar documentos Los gráficos y los datos de las gráficas se guardan dentro de un documento de Keynote para poder mostrarse correctamente si el documento se abre en otro ordenador. Sin embargo, los tipos de letra no se incluyen en el documento. Por ello, si transfiere un documento de Keynote a otro ordenador, asegúrese de que los tipos de letra que utilice estén instalados en la carpeta Fonts de ese ordenador. Por omisión, los archivos de audio y de película se guardan con documentos de Keynote, pero puede cambiar este ajuste. Si no guarda archivos multimedia con el documento, tendrá que transferirlos por separado para poder ver el documento en otro ordenador. Cómo guardar un documento Es aconsejable guardar el documento con frecuencia mientras se trabaja. Después guardar el documento por primera vez, puede pulsar Comando + S para volver a guardarlo utilizando los mismos ajustes. Para guardar un documento por primera vez: 1 Seleccione Archivo > Guardar, o pulse Comando + S. 2 En el campo “Guardar como”, escriba un nombre para el documento. 3 Si la ubicación donde desea guardar el documento no está visible en el menú local Ubicación, haga clic en el triángulo desplegable situado a la derecha del campo “Guardar como”. 4 Seleccione la ubicación donde desea guardar el documento. 5 Si desea abrir el documento con Keynote en iWork ’05 o iWork ’06, seleccione “Guardar una copia como” y seleccione iWork ’05 o iWork ’06. (Si no aparece esta opción, haga clic en el triángulo desplegable situado a la derecha del campo “Guardar como”.) 6 Si usted u otra persona va a abrir el documento en otro ordenador, haga clic en “Opciones avanzadas” y configure las opciones que determinan qué elementos deben copiarse en el documento. Copiar películas y sonido en el documento: si selecciona esta opción los archivos de audio y vídeo se guardan con el documento, con lo que los archivos se reproducen si el documento se abre en otro ordenador. Si anula la selección de esta opción reducirá el tamaño del archivo, pero los archivos multimedia no se reproducirán en otro ordenador si no los transfiere a dicho ordenador. Copiar las imágenes del tema en el documento: si no selecciona esta opción y abre el documento en un ordenador que no tenga el mismo tema instalado (por ejemplo, si ha creado su propio tema), es posible que el documento presente una apariencia diferente. 30 Capítulo 2 Cómo trabajar con un documento Keynote 7 Haga clic en Guardar. Si el documento se creó con una versión anterior de Keynote, se le preguntará si desea guardar el documento en el mismo formato. Como norma general, solo puede guardar documentos de Keynote en ordenadores y servidores que utilicen Mac OS X. Keynote no es compatible con ordenadores con Mac OS 9 ni con servidores Windows que dispongan de Servicios para Macintosh. Para abrir un documento de Keynote en un ordenador con Windows, intente utilizar el software de servidor AFP disponible para Windows. Si tiene previsto compartir el documento con otros usuarios que no tengan instalado Keynote en sus ordenadores, puede exportar el documento para que pueda utilizarse en otra aplicación. Para obtener información acerca de cómo exportar el documento en otros formatos de archivo (como QuickTime, PowerPoint, PDF y Flash), consulte “Cómo compartir una presentación entre distintas plataformas” en la página 198. Cómo deshacer los cambios Si no desea guardar los cambios realizados en el documento desde que lo abrió o desde la última vez que lo guardó, puede deshacerlos. A continuación, presentamos distintas formas de deshacer cambios: m Para deshacer el cambio más reciente, seleccione Edición > Deshacer. m Para deshacer varios cambios, seleccione Edición > Deshacer varias veces. Puede deshacer todos los cambios realizados desde que abrió el documento o bien regresar a la última versión guardada. m Para deshacer una operación Edición > Deshacer o más de una, seleccione Edición > Rehacer una o varias veces. m Para deshacer todos los cambios realizados desde la última vez que guardó el documento, seleccione Archivo > “Volver a la versión guardada” y haga clic en Restaurar. Cómo guardar una copia del documento Si desea realizar una copia del documento, por ejemplo para crear una copia de seguridad o varias versiones, puede guardarlo con un nombre o en una ubicación diferente. (También puede automatizar el proceso de guardar una copia de seguridad, tal y como se explica en el apartado “Cómo guardar automáticamente una copia de seguridad del documento”.) Para guardar una copia de un documento: m Seleccione Archivo > “Guardar como” y especifique un nombre y una ubicación. El documento con el nuevo nombre permanecerá abierto. Para trabajar con la versión anterior, seleccione Archivo > “Abrir recientes” y elija la versión anterior en el submenú. Capítulo 2 Cómo trabajar con un documento Keynote 31 Cómo guardar automáticamente una copia de seguridad del documento Cada vez que guarde un documento, puede realizar una copia sin los cambios introducidos desde la última vez que lo guardó. De este modo, en caso de que cambie de opinión acerca de las modificaciones realizadas, podrá volver a la copia de seguridad del documento. A continuación, presentamos distintos procedimientos para crear y utilizar una copia de seguridad: m Para guardar automáticamente una versión de copia de seguridad de un documento, seleccione Keynote > Preferencias, haga clic en General y, a continuación, seleccione “Hacer copia de seguridad de la versión anterior”. La próxima vez que guarde el documento, se creará una copia de seguridad en la misma ubicación, con la indicación “Copia de seguridad de” antes del nombre del archivo. Sólo una versión (la última versión guardada) se guarda como copia de seguridad. Cada vez que guarda el documento, el nuevo archivo de copia de seguridad reemplaza al archivo de copia de seguridad anterior. m Para volver a la última versión guardada tras realizar cambios sin guardarlos, seleccione Archivo > Volver a la versión guardada. Los cambios en el documento abierto quedarán anulados. Cómo guardar un documento como un tema Puede modificar un tema, guardarlo para que se muestre en el selector de tema y volver a utilizarlo. Para guardar un documento como un tema: m Seleccione Archivo > Guardar tema. Consulte el apartado “Cómo diseñar Temas y Diapositivas maestras” en la página 207 para obtener más detalles. Cómo guardar términos de búsqueda para un documento Puede almacenar información (como el nombre del autor, palabras clave y comentarios) en los documentos de Keynote. En ordenadores con Mac OS X, puede utilizar Spotlight para localizar documentos que incluyan dicha información. Para almacenar información sobre un documento: 1 Haga clic en el botón Inspector de la barra de herramientas y, a continuación, haga clic en el botón “Inspector del documento”. 2 Haga clic en Spotlight. 3 Introduzca información en los campos. 32 Capítulo 2 Cómo trabajar con un documento Keynote Para buscar presentaciones que incluyan la información almacenada, haga clic en el icono de Spotlight situado en la parte superior derecha de la pantalla y, a continuación, escriba los términos que desee buscar. Cómo cerrar un documento sin salir de Keynote Cuando termine de trabajar con un documento, puede cerrarlo sin salir de Keynote. A continuación, presentamos distintos procedimientos para cerrar documentos y mantener la aplicación abierta: m Para cerrar el documento activo, seleccione Archivo > Cerrar o haga clic en el botón de cierre que encontrará en la esquina superior izquierda de la ventana del documento. m Para cerrar todos los documentos de Keynote abiertos, pulse la tecla Opción y seleccione Archivo > “Cerrar todo” o haga clic en el botón de cierre del documento activo. Si ha realizado cambios desde la última vez que guardó el documento, Keynote le pedirá que guarde el documento. Cómo añadir, eliminar y organizar diapositivas Cada diapositiva nueva que se crea utiliza una de las diapositivas maestras de Keynote (plantillas). Cada diapositiva maestra incluye una serie de elementos, como un título, texto con viñetas y marcadores de posición de contenidos (que contienen fotos). Cuando se crea un nuevo documento de Keynote, la primera diapositiva utiliza de forma automática la diapositiva maestra “Título y subtítulo”. Puede cambiar el diseño de la diapositiva maestra de una diapositiva en cualquier momento (consulte “Cómo aplicar una nueva diapositiva maestra a una diapositiva” en la página 38). Después de crear una nueva diapositiva, puede personalizarla añadiendo su propio texto, imágenes, figuras, tablas y gráficas, etc. Cómo añadir diapositivas A continuación, se indica cómo añadir una diapositiva: m Seleccione una diapositiva en el navegador de diapositivas y pulse Retorno. m Seleccione una diapositiva y haga clic en el botón Nueva (+) en la barra de herramientas. m Seleccione una diapositiva y, a continuación, seleccione Diapositiva > Diapositiva nueva. m Pulse la tecla Opción y arrastre una diapositiva hasta que vea un triángulo de color azul. Esta acción duplica la diapositiva arrastrada. m Seleccione una diapositiva y, a continuación, seleccione Edición > Duplicar. Capítulo 2 Cómo trabajar con un documento Keynote 33 Estos métodos añaden la nueva diapositiva tras la diapositiva seleccionada en el navegador de diapositivas. Para añadir una diapositiva en otra ubicación del pase de diapositivas, utilice los comandos Copiar y Pegar o arrastre la nueva dispositiva hasta el lugar que desee. En el navegador o en la vista de mesa luminosa, también se puede crear una nueva diapositiva arrastrando archivos de película, sonido o imagen desde el visualizador multimedia hasta la ubicación deseada del navegador de diapositivas. (Para abrir el visualizador multimedia, haga clic en Multimedia en la barra de herramientas.) Cuando se añade una nueva diapositiva, esta nueva diapositiva utiliza la diapositiva maestra de la diapositiva seleccionada en el navegador de diapositivas. (En el caso de los nuevos documentos de Keynote, la primera diapositiva utiliza la diapositiva maestra “Título y subtítulo” y la segunda diapositiva utiliza la diapositiva maestra “Título y viñetas”.) Es posible cambiar la diapositiva maestra de una diapositiva haciendo clic en Maestras en la barra de herramientas y seleccionando una nueva diapositiva maestra. Cómo reordenar diapositivas Las vistas del navegador, de esquema y de mesa luminosa facilitan la reorganización de las diapositivas. Para reordenar las diapositivas: 1 Haga clic en Visualización en la barra de herramientas y seleccione Navegador, Esquema o “Mesa luminosa”. 2 Seleccione una o varias diapositivas y arrástrelas hasta la nueva ubicación. Cómo agrupar las diapositivas En la vista del navegador, puede crear grupos de diapositivas; para ello, debe sangrar las diapositivas los niveles que sean necesarios. Las diapositivas sangradas (subordinadas) se denominan “secundarias”. El sangrado de las diapositivas no afecta a la reproducción del pase. Para ver la vista del navegador, haga clic en Visualización en la barra de herramientas y seleccione Navegador. A continuación, se indican una serie de formas de trabajar con grupos de diapositivas en la vista del navegador: m Para sangrar las diapositivas, selecciónelas y pulse Tabulador o arrástrelas hacia la derecha. Puede crear más niveles de sangrado volviendo a pulsar Tabulador o arrastrando las diapositivas más a la derecha. Pero solo puede sangrar una diapositiva hasta un nivel más profundo que la diapositiva anterior. m Para eliminar una sangría, arrastre las diapositivas hacia la izquierda o pulse Mayúsculas + Tabulador. 34 Capítulo 2 Cómo trabajar con un documento Keynote m Para mostrar o contraer (ocultar) un grupo de diapositivas, haga clic en el triángulo desplegable que se encuentra a la izquierda de la primera diapositiva situada encima del grupo. Si un grupo de diapositivas está contraído de modo que solo se ve la diapositiva superior en la vista del navegador, al eliminar la diapositiva superior también se eliminarán todas las diapositivas secundarias. Si el grupo no está contraído, cuando se elimine la diapositiva superior, todas las diapositivas secundarias subirán un nivel. m Para mover un grupo de diapositivas, seleccione la primera diapositiva del grupo (en la vista del navegador) y arrastre el grupo hasta una nueva ubicación en el navegador de diapositivas. Cómo eliminar diapositivas Puede eliminar una sola diapositiva o un grupo de diapositivas. A continuación, se indican algunas formas de eliminar diapositivas: m Para eliminar una diapositiva, selecciónela en el navegador de diapositivas y pulse la tecla Suprimir. Si desea eliminar varias diapositivas, con la tecla Mayúsculas pulsada, haga clic en las mismas para eliminarlas. Si elimina la primera diapositiva de un grupo cuando sus diapositivas subordinadas (secundarias) se encuentran visibles en el navegador de diapositivas, las diapositivas secundarias ascenderán un nivel en el esquema. m Para eliminar una diapositiva y todas sus diapositivas secundarias, ocúltelas (haga clic en la flecha situada a la izquierda de la diapositiva superior) y pulse la tecla Suprimir. Si borra una diapositiva de forma accidental, puede recuperarla seleccionando inmediatamente después Edición > Deshacer eliminar. Cómo omitir diapositivas Puede omitir una diapositiva al reproducir el pase de diapositivas sin tener que eliminarla del documento. Para omitir una o varias diapositivas: m Seleccione la diapositiva o las diapositivas que desee en el navegador de diapositivas o en la vista de mesa luminosa y, a continuación, seleccione Diapositiva > Omitir diapositiva. m Con la tecla Control pulsada, haga clic en la diapositiva y seleccione “Omitir diapositiva”. Para hacer visible una diapositiva omitida en un pase de diapositivas, selecciónela y, a continuación, seleccione Diapositiva > “No omitir diapositiva” (o bien, con la tecla Control pulsada, haga clic en la diapositiva y seleccione “No omitir diapositiva”). Capítulo 2 Cómo trabajar con un documento Keynote 35 Cómo añadir números de diapositiva Puede añadir números (similares a los números de página) a diapositivas individuales. O puede activar la numeración de una diapositiva maestra para que a cada diapositiva nueva basada en dicha diapositiva maestra se le asigne de forma automática un número de diapositiva ascendente. A continuación, se indica cómo añadir números de diapositiva: m Seleccione una diapositiva en el navegador de diapositivas, abra el inspector de las diapositivas, haga clic en Apariencia y, a continuación, seleccione “Número de diapositiva”. El número asignado refleja la ubicación de la diapositiva en el organizador (las diapositivas omitidas no se numeran). m Para añadir números de diapositiva a una diapositiva maestra, haga clic en Visualización en la barra de herramientas y seleccione “Mostrar diapositivas maestras”. En el navegador de diapositivas maestras, seleccione la diapositiva maestra que desee modificar. Abra el inspector de las diapositivas, haga clic en Apariencia y, a continuación, seleccione “Número de diapositiva”. Puede arrastrar el número a la posición que desee en la diapositiva, y puede utilizar el panel “Tipo de letra” para dar formato al número. Cómo utilizar los comentarios Mientras trabaja en el pase de diapositivas, puede añadir comentarios a las mismas. Por ejemplo, puede usar comentarios que le recuerden los cambios que desea realizar en la diapositiva. (Los comentarios no son lo mismo que las notas del presentador; consulte “Cómo añadir notas del presentador” en la página 185.) También es posible mover comentarios en el lienzo de la diapositiva. Si dispone de su propia pantalla de presentador al realizar una presentación, podrá ver los comentarios sin que los vea el público. Los comentarios siempre aparecen en la parte superior del lienzo de diapositivas, por lo que es posible que oculten parte del contenido de las diapositivas. Para ver todo el contenido, basta con que arrastre los comentarios fuera de la diapositiva, los oculte o modifique su tamaño. Añada comentarios a las diapositivas. Puede mostrar y ocultar los comentarios con facilidad. 36 Capítulo 2 Cómo trabajar con un documento Keynote A continuación, se muestran algunos modos de trabajar con los comentarios: m Para añadir un comentario, haga clic en Comentario en la barra de herramientas o seleccione Insertar > Comentario. Escriba una nota, idea o recordatorio y, a continuación, arrastre el comentario hasta la posición en la que desee colocarlo en el lienzo. m Para mostrar u ocultar los comentarios, haga clic en Visualización en la barra de herramientas y seleccione “Mostrar comentarios” u “Ocultar comentarios”. m Para cambiar el tamaño de un comentario, arrastre la esquina inferior derecha. m Para eliminar un comentario, haga clic en el icono x de la esquina superior derecha. m Para dar formato a un comentario, consulte las instrucciones de los apartados “Cómo definir el formato del tamaño y la apariencia del texto” en la página 44 y “Cómo rellenar un objeto con color” en la página 88. m Para que al imprimir se muestren los comentarios, asegúrese de que se encuentren visibles en el lienzo de diapositivas antes de proceder a la impresión. Cómo copiar o mover elementos entre distintas diapositivas Puede tomar el texto o un objeto de una diapositiva y colocarlo en otra diapositiva. A continuación, se indica cómo copiar y mover texto y objetos: m Para copiar (o cortar) y pegar texto o un objeto, seleccione el texto u objeto y, a continuación, seleccione Edición > Copiar o Edición > Cortar. Haga clic en el lugar donde desee pegar el texto u objeto y seleccione Edición > Pegar. Este método conserva el formato del texto. Para que el texto copiado adopte el formato del texto situado alrededor, seleccione Edición > Pegar con el mismo estilo. m Para eliminar texto o un objeto, selecciónelo y, a continuación, seleccione Edición > Eliminar o pulse la tecla Suprimir. Si elimina algún elemento accidentalmente, seleccione Edición > Deshacer para restaurarlo. m Para copiar una imagen de un documento de Keynote a otro, seleccione la imagen y arrastre su icono desde el campo “Información del archivo” del inspector de las dimensiones hasta una diapositiva del otro archivo de Keynote. Al utilizar el comando Copiar o el comando Cortar, el texto u objeto seleccionado se coloca en el Portapapeles, donde permanecerá hasta que seleccione de nuevo Copiar o Cortar (o hasta que apague el ordenador). El Portapapeles conserva los contenidos únicamente de una operación de copiar o cortar. Capítulo 2 Cómo trabajar con un documento Keynote 37 Cómo cambiar el tema, la diapositiva maestra o el diseño de una diapositiva Puede cambiar el tema, la diapositiva maestra o la disposición de una diapositiva en cualquier momento.  Tema: seleccione un tema distinto si desea modificar el aspecto general de una diapositiva (por ejemplo, el color de fondo, el tipo de letra y el “tono”, profesional o informal).  Diapositiva maestra: cambie la diapositiva maestra de una diapositiva si desea utilizar una disposición predefinida distinta. Por ejemplo, puede cambiar la diapositiva maestra de una diapositiva para orientar una foto de gran tamaño verticalmente en lugar de horizontalmente.  Disposición: cambie la disposición de una diapositiva si desea añadir, eliminar o modificar elementos de la misma, como cuadros de texto o marcadores de posición de objetos. Cómo modificar el tema Puede cambiar el tema de una diapositiva en cualquier momento seleccionándola y eligiendo otro tema mediante el botón Temas de la barra de herramientas. Para mantener los cambios de formato ya realizados o modificar el tema de todo el pase de diapositivas, siga estos pasos. Para cambiar el tema de una diapositiva o de un pase de diapositivas: 1 En el navegador de diapositivas, seleccione la diapositiva o las diapositivas cuyo tema desee cambiar. (Si desea cambiar todas las diapositivas, omita este paso.) 2 Haga clic en Temas en la barra de herramientas y seleccione “Selector de tema”. 3 Seleccione un tema nuevo. 4 Si ha realizado cambios de formato que no desea mantener en el nuevo tema (por ejemplo, si ha cambiado el texto del cuerpo a marrón pero ahora desea que presente el color de texto del nuevo tema) anule la selección de la opción “Conservar los cambios en el tema”. 5 Seleccione “Todas las diapositivas” o “Diapositivas seleccionadas” en el menú local “Aplicar tema a”. Puede utilizar varios temas en el mismo pase de diapositivas aplicando un nuevo tema solamente a algunas de las diapositivas. 6 Haga clic en Seleccionar para aplicar el nuevo tema. Para revertir una diapositiva a sus ajustes de tema por omisión, seleccione la diapositiva y, a continuación, seleccione Formato > Volver a aplicar diapositiva maestra a la diapositiva. 38 Capítulo 2 Cómo trabajar con un documento Keynote Uso de varios temas Puede utilizar varios temas en un pase de diapositivas para dividir visualmente en grupos las diapositivas. Para usar distintos temas para distintas diapositivas del pase: 1 En el navegador de diapositivas, seleccione la diapositiva o las diapositivas que desea que presenten un tema diferente. (Con la tecla Mayúsculas o la tecla Comando pulsada, haga clic para seleccionar varias diapositivas.) 2 Haga clic en Temas en la barra de herramientas y seleccione un nuevo tema. También puede hacer clic en Temas en la barra de herramientas, seleccionar “Selector de tema” y, a continuación, seleccionar “Diapositivas seleccionadas” en el menú local “Aplicar tema a”. Cómo aplicar una nueva diapositiva maestra a una diapositiva Puede cambiar el diseño de la diapositiva maestra de una diapositiva en cualquier momento. Por ejemplo, es posible que desee cambiar la diapositiva maestra de una foto de horizontal a vertical. Para seleccionar rápidamente otra diapositiva maestra, seleccione la diapositiva cuya diapositiva maestra desee modificar, haga clic en Maestras en la barra de herramientas y, a continuación, seleccione una diapositiva maestra distinta. También puede usar el inspector de las diapositivas para realizar el cambio. Para ello: 1 Seleccione la diapositiva cuyo diseño desea modificar. 2 Seleccione Visualización > “Mostrar inspector” y, a continuación, haga clic en el botón del inspector de diapositivas. 3 Haga clic en Apariencia. 4 Para aplicar una diapositiva maestra distinta, haga clic en el triángulo situado junto a la imagen en miniatura de la diapositiva y seleccione una diapositiva maestra en la lista local. Cómo cambiar el diseño de una diapositiva Puede añadir fácilmente un cuadro de título, cuadro de texto, marcador de posición de objeto o número de diapositiva con formato a diapositivas individuales. Para cambiar el diseño de una diapositiva: 1 Seleccione la diapositiva cuyo diseño desea modificar. 2 Seleccione Visualización > “Mostrar inspector” y, a continuación, haga clic en el botón del inspector de diapositivas. Capítulo 2 Cómo trabajar con un documento Keynote 39 3 Haga clic en Apariencia. 4 Para añadir un cuadro de título u otros elementos a la diapositiva, utilice las casillas situadas bajo la imagen en miniatura de la diapositiva maestra. 5 Para aplicar un fondo, seleccione un tipo de fondo en el menú local Fondo. Relleno de color: proporciona al fondo un único color sólido. Haga clic en el contenedor de color y seleccione un color en la ventana Colores. Relleno degradado: colorea el fondo con un degradado de color. Haga clic en el contenedor de cada uno de los colores y selecciónelos en la ventana Colores. Relleno de imagen: utiliza su propia imagen como fondo. Haga clic en Seleccionar y elija alguna imagen. Relleno de imagen teñida: utiliza su propia imagen con un tinte semiopaco. Haga clic en Seleccionar y elija alguna imagen. Si selecciona “Relleno de imagen” o “Relleno de imagen teñida”, seleccione una opción de escalado en el menú local. Consulte el apartado “Cómo rellenar un objeto con una imagen” en la página 90 para obtener más información. También puede modificar la diapositiva maestra de una diapositiva e incluso crear una nueva. Consulte el apartado “Cómo diseñar Temas y Diapositivas maestras” en la página 207 para obtener más información. Elija una imagen o un color para el fondo. Seleccione un diseño de diapositiva entre las diversas diapositivas maestras. Arrastre una imagen aquí desde el visualizador multimedia o desde el Finder. 40 Capítulo 2 Cómo trabajar con un documento Keynote Cómo realizar el mismo cambio en varias diapositivas Puede realizar el mismo cambio en varias diapositivas (por ejemplo, cambiar el tamaño del texto o la ubicación de un gráfico, o utilizar un color de fondo distinto); para ello, debe modificar la diapositiva maestra en la que se basan las diapositivas. Para realizar el mismo cambio en varias diapositivas: 1 Seleccione la diapositiva que desee modificar. 2 Haga clic en Visualización en la barra de herramientas y seleccione “Mostrar diapositivas maestras”. 3 En el navegador de diapositivas, haga clic en la diapositiva maestra de la diapositiva seleccionada (la diapositiva maestra presenta una marca de verificación junto a ella). 4 Realice los cambios que desee en la diapositiva maestra. Todas las diapositivas basadas en esta diapositiva maestra heredarán los cambios realizados en la misma. 3 41 3 Cómo trabajar con texto Este capítulo describe cómo añadir texto y cómo modificar el aspecto del texto, incluidas las listas. En Keynote, puede colocar texto en cuadros de texto, celdas de tablas y figuras. Cómo añadir texto Las diapositivas maestras incluyen texto de marcador de posición (que el usuario reemplaza por su propio texto) para los títulos y el texto del cuerpo de las diapositivas. El texto del título es más grande que el texto del cuerpo. La mayoría del texto del cuerpo posee viñetas (precedido por un “punto” u otro elemento decorativo); no obstante, se puede convertir a texto sin viñetas utilizando el panel Viñetas del Inspector de texto. Estos son algunos modos de añadir texto a una diapositiva: m Para añadir texto al título, haga doble clic en un marcador de posición de texto de título en el lienzo de la diapositiva y escriba su texto. m Para añadir texto al cuerpo, haga doble clic en un marcador de posición de texto del cuerpo en el lienzo de la diapositiva y empiece escribir. m Pulse Retorno para pasar a la siguiente línea. m Para sangrar una viñeta, pulse la tecla Tabulador. Para eliminar la sangría de una línea sangrada, pulse Mayúsculas + Tabulador. 42 Capítulo 3 Cómo trabajar con texto m Pulse las teclas Mayúsculas +Tabulador para desplazar la línea con viñeta a un nivel de sangría superior. Si la diapositiva que está editando no tiene texto de título ni de cuerpo, puede elegir otra diapositiva maestra o seleccionar Título o Cuerpo en el panel Apariencia del Inspector de diapositivas. También puede añadir un cuadro de texto libre al lienzo de la diapositiva. El texto de los cuatros de texto libre no se muestra en modo esquema. Cómo seleccionar texto Antes de aplicar formato o realizar cualquier otra operación sobre texto, deberá seleccionar el texto con el que desea trabajar. Estos son algunos modos de seleccionar texto: m Para seleccionar uno o más caracteres, haga clic delante del primer carácter y arrastre por los caracteres que desee seleccionar. m Para seleccionar una palabra, haga doble clic en la misma. m Para seleccionar un párrafo, haga clic tres veces en el párrafo. Haga doble clic en un cuadro de texto de título y escriba. El tipo y el tamaño de letra del título están predefinidos. Haga doble clic en un cuadro de cuerpo de texto y escriba para crear texto. El tipo de letra, el tamaño del texto y otros atributos están predefinidos. Capítulo 3 Cómo trabajar con texto 43 m Para seleccionar todo el texto de un documento, seleccione Edición > Seleccionar todo. m Para seleccionar bloques de texto, haga clic al comienzo del bloque de texto y, a continuación, haga clic en el final de otro bloque de texto mientras mantiene pulsada la tecla Mayúsculas. m Para seleccionar desde el punto de inserción hasta el inicio del párrafo, pulse la tecla flecha arriba mientras mantiene pulsadas las teclas Mayúsculas y Opción. m Para seleccionar desde el punto de inserción hasta el final del párrafo, pulse la tecla flecha abajo mientras mantiene pulsadas las teclas Mayúsculas y Opción. m Para ampliar la selección carácter a carácter, pulse la tecla flecha izquierda o flecha derecha mientras mantiene pulsada la tecla Mayúsculas. m Para ampliar la selección línea a línea, pulse la tecla flecha arriba o flecha abajo mientras mantiene pulsada la tecla Mayúsculas. m Para seleccionar varias palabras o bloques de texto que no son contiguos, seleccione el primer bloque de texto que desee seleccionar y, a continuación, seleccione el texto adicional mientras mantiene pulsada la tecla Comando. Cómo eliminar, copiar y pegar texto El menú Edición contiene comandos que le ayudarán a realizar operaciones de edición de textos. Estos son algunos modos de editar texto: m Para copiar (o cortar) y pegar texto, seleccione el texto y seleccione Edición > Copiar o Edición > Cortar. Haga clic en el lugar en el que desee pegar el texto. Para que el texto copiado conserve el formato de estilo, seleccione Edición > Pegar. Para que el texto copiado adopte el formato de estilo del texto que lo rodea, seleccione Edición > Pegar con el mismo estilo. m Para eliminar texto, seleccione el texto y seleccione Edición > Eliminar o pulse la tecla Suprimir. Si accidentalmente elimina texto, seleccione Edición > Deshacer para restaurarlo. Al utilizar el comando Copiar o el comando Cortar, el texto seleccionado se coloca en el Portapapeles, donde permanecerá hasta que seleccione de nuevo Copiar o Cortar, o hasta que apague su ordenador. El Portapapeles conserva los contenidos únicamente de una operación de copiar o cortar. 44 Capítulo 3 Cómo trabajar con texto Cómo definir el formato del tamaño y la apariencia del texto Puede dar todo el formato al texto utilizando los menús de Keynote, el inspector de texto o bien el panel “Tipo de letra”. Puede realizar las tareas básicas de formato de texto utilizando los comandos en los menús de. Si desea cambiar el tipo de letra, o si cambia con frecuencia el formato del texto, puede ser más fácil utilizar el panel “Tipo de letra” y el inspector de texto para definir el formato del texto. Uso del menú Formato para dar formato al texto Los elementos del submenú “Tipo de letra” del menú Formato le ofrecen un control básico al respecto del tamaño y la apariencia del texto. Cómo utilizar las opciones de negrita y cursiva con los menús Puede hacer que los caracteres se muestren en negrita o cursiva. Para que el texto aparezca en negrita o cursiva: 1 Seleccione el texto que desee convertir a negrita o cursiva, o haga clic si desea escribir nuevo texto. 2 Seleccione Formato > Tipo de letra > Negrita. O seleccione Formato > Tipo de letra > Cursiva. Algunos tipos de letra contienen varios tipos en negrita y cursiva. Para seleccionar entre diferentes tipos de negrita o cursiva, utilice el panel Tipo de letra. Consulte “Uso del panel “Tipo de letra” para dar formato al texto” en la página 46. Cómo crear texto con contorno con los menús Puede modificar el texto para que aparezca como un contorno. Para crear texto con contorno: 1 Seleccione el texto que desee que aparezca con contorno, o haga clic si desea escribir nuevo texto. 2 Seleccione Formato > Tipo de letra > Contorno. Cómo subrayar texto con los menús Puede subrayar texto y dar formato al subrayado para cambiar el estilo del subrayado o su color. Para subrayar texto: 1 Seleccione el texto que desee subrayar, o haga clic si desea escribir nuevo texto. 2 Seleccione Formato > Tipo de letra > Subrayar. Para modificar el estilo o el color del subrayado, haga clic en “Tipos de letra” en la barra de herramientas y utilice el botón “Subrayado de texto” del panel “Tipo de letra”. Consulte “Uso del panel “Tipo de letra” para dar formato al texto” en la página 46. Capítulo 3 Cómo trabajar con texto 45 Cómo cambiar el tamaño del texto con los menús Puede cambiar el tamaño de puntos del texto para hacerlo más grande o más pequeño. Para modificar el tamaño del texto seleccionado: 1 Seleccione el texto cuyo tamaño desee modificar. 2 Para cambiar el tamaño del texto en incrementos de 1 punto, seleccione Formato > Tipo de letra > Mayor. O seleccione Formato > Tipo de letra > Menor. También puede añadir los iconos de Mayor y Menor en la barra de herramientas. Seleccione Visualización > Personalizar y arrastre los iconos hasta la barra de herramientas. A continuación, haga clic en Salir. Para especificar un tamaño preciso para el texto seleccionado, haga clic en “Tipos de letra” en la barra de herramientas y utilice los controles de “Tamaño del panel” del panel “Tipo de letra”. Consulte “Uso del panel “Tipo de letra” para dar formato al texto” en la página 46. Cómo crear subíndices y superíndices con los menús Con esta opción podrá subir o bajar el texto respecto a su línea base. Para crear subíndices o superíndices: 1 Seleccione el texto que desee subir o bajar, o haga clic si desea escribir nuevo texto. 2 Para crear un subíndice o un superíndice con un tamaño de letra inferior al texto que acompaña, seleccione Formato > Tipo de letra > Línea base > Subíndice. O seleccione Formato > Tipo de letra > Línea base > Superíndice. 3 Para subir o bajar texto sin reducir el tamaño del tipo de letra, seleccione Subir o Bajar en el submenú Línea base. 4 Para restaurar el texto a la misma línea base que el texto del cuerpo, seleccione la opción “Valor por omisión” del submenú “Línea base”. Puede añadir los iconos de Subíndice y Superíndice a la barra de herramientas. Seleccione Visualización > Personalizar barra de herramientas, arrastre los iconos hasta la barra de herramientas y haga clic en Salir. Cómo cambiar el uso de mayúsculas del texto con los menús Puede crear de forma rápida bloques de texto en mayúsculas o minúsculas, o dar formato al texto con un título. Para modificar el uso de mayúsculas del texto: 1 Seleccione el texto que desee modificar, o haga clic si desea escribir nuevo texto. 2 Seleccione Formato > Tipo de letra > Mayúsculas y seleccione una opción del submenú. Seleccione “Todo mayúsculas” para cambiar el texto a mayúsculas. Seleccione Versalitas para cambiar el texto a versalitas, con mayúsculas más grandes para las letras en mayúsculas. 46 Capítulo 3 Cómo trabajar con texto Seleccione Título para cambiar el texto a un formato de título, que pone en mayúscula la primera letra de cada palabra. Seleccione Ninguno para cambiar el texto de todo mayúsculas a mayúsculas iniciales. Los caracteres en mayúsculas, como la primera palabra de cada frase, se quedan en mayúsculas, mientras el resto queda en minúsculas. Uso del panel “Tipo de letra” para dar formato al texto El panel “Tipo de letra” del Mac OS X le da acceso a todos los tipos de letra instalados en su ordenador. Proporciona la previsualización de los tipos disponibles (como negrita y cursiva) y de los tamaños de cada tipo de letra. Los botones del panel “Tipo de letra” permiten añadir subrayados, líneas de tachado, color y sombra al texto. También se puede cambiar el color de fondo de la diapositiva en el panel “Tipo de letra”. Para obtener información acerca de cómo instalar tipos de letra, crear y gestionar colecciones de tipos de letra, o para solucionar problemas relacionados con los tipos de letra, consulte Ayuda Mac. Para abrir el panel “Tipo de letra”: m Haga clic en Tipos de letra en la barra de herramientas. Es posible cambiar la apariencia de cualquier texto en su documento seleccionándolo y luego seleccionando opciones en el panel “Tipo de letra”. Cuando realiza cambios de formato en el panel “Tipo de letra”, el texto seleccionado cambia al instante, por lo que puede probar diferentes opciones de formato y ver rápidamente cuál queda mejor. Previsualice la tipografía seleccionada (es posible que tenga que elegir “Mostrar previsualización” en el menú Acción). Seleccione una tipografía para aplicarla al texto seleccionado del documento. Seleccione un tamaño de tipo de letra para aplicarlo al texto seleccionado del documento. El menú Acción. Cree efectos de texto interesantes utilizando estos botones. Aplique una sombra al texto seleccionado. Modifique la sombra con los controles de opacidad, difuminado, desplazamiento y ángulo. Busque tipos de letra escribiendo su nombre en el campo de búsqueda. Capítulo 3 Cómo trabajar con texto 47 A continuación resumimos las acciones de los botones de efectos de texto, de izquierda a derecha:  El menú local “Subrayar texto” permite elegir un estilo de subrayado (por ejemplo, simple o doble).  El menú local “Tachar texto” permite elegir un estilo de tachado (por ejemplo, simple o doble).  El menú local “Color del texto” permite aplicar un color al texto.  El menú local “Color del documento” permite aplicar un color al de fondo.  El botón “Sombreado del texto” aplica una sombra al texto seleccionado.  Los controles “Opacidad del sombreado”, “Difuminado del sombreado”, “Separación del sombreado” y “Ángulo del sombreado” sirven para determinar el aspecto que tendrá la sombra. En caso de que resulte imposible visualizar los botones de efectos de texto, seleccione Mostrar efectos del menú local Acción en la esquina inferior izquierda del panel “Tipo de letra”. Consejos para organizar los tipos de letra Si utiliza con frecuencia el panel “Tipo de letra”, existen algunas técnicas para ahorrar tiempo. Aquí tiene algunos consejos para utilizar el panel “Tipo de letra”: m Para localizar de forma rápida los tipos de letra que usa con frecuencia, organícelos en colecciones de tipos de letra. Haga clic en el botón Añadir (+) para crear una colección de tipos de letra y, a continuación, arrastre un tipo hasta la nueva colección. m Para facilitar el cambio de tipos de letra, deje abierto el panel “Tipo de letra”. En caso de que ocupe un espacio excesivo en la pantalla, redúzcalo arrastrando su control de tamaño (esquina inferior derecha del panel), para que solo las familias de tipos de letra y los tipos dentro de la colección seleccionada sean visibles. Para cerrarlo, haga clic de nuevo en el botón “Tipos de letra” o en el botón Cerrar situado en la esquina superior izquierda. Cómo cambiar de tipo de letra utilizando el panel “Tipo de letra” El panel “Tipo de letra” le ofrece un control avanzado sobre los tipos de letra. Utilice los controles de tamaño y los ajustes de tipografía para personalizar el aspecto de su texto. Para modificar el tipo de letra del texto seleccionado: 1 Haga clic en “Tipos de letra” en la barra de herramientas. 2 En el panel “Tipo de letra”, seleccione un estilo de tipo de letra en la columna Familia y, a continuación, seleccione el tipo en la columna Tipo. En caso de que resulte imposible visualizar todas las familias de tipos de letra que sabe que están instaladas en su ordenador, seleccione “Todos los tipos de letra” en la columna Colecciones o escriba el nombre del tipo que esté buscando en el campo de búsqueda, en la parte inferior del panel “Tipo de letra”. 48 Capítulo 3 Cómo trabajar con texto La previsualización del tipo de letra seleccionado aparece en el panel de previsualización en la parte superior del panel “Tipo de letra”. En caso de que resulte imposible visualizar el panel de previsualización, seleccione “Mostrar vista previa” del menú local Acción en la esquina inferior izquierda del panel “Tipo de letra”. 3 Ajuste el tamaño del tipo de letra utilizando el regulador de tamaño u otros controles de tamaño. 4 Defina los ajustes de tipografía del tipo de letra seleccionado usando el comando Tipografía en el menú local Acción. En la ventana Tipografía, haga clic en los triángulos desplegables para visualizar y seleccionar los diferentes efectos de tipografía disponibles para el tipo de letra seleccionado. Los distintos tipos de letra poseen diferentes efectos de tipografía disponibles. Consulte el apartado “Uso de características tipográficas avanzadas” en la página 53 para obtener más información. Cómo cambiar el subrayado utilizando el panel Tipo de letra Puede utilizar el panel Tipo de letra para cambiar la apariencia de los subrayados. Para modificar el subrayado del texto seleccionado: 1 Haga clic en “Tipos de letr”a en la barra de herramientas. 2 Haga clic en el botón “Subrayar texto” en el panel “Tipo de letra” (el primer botón a la izquierda) y seleccione Ninguno, Sencillo o Doble en el menú local. 3 Para cambiar el color del subrayado, seleccione Color en el menú local Subrayado y, a continuación, seleccione un color en la ventana Colores. Cómo añadir un tachado al texto utilizando el panel Tipo de letra Puede marcar el texto con una línea de tachado y hacer que el color de la línea sea diferente al color del texto. Para añadir un tachado al texto seleccionado: 1 Haga clic en “Tipos de letra” en la barra de herramientas. 2 Haga clic en el botón “Tachar texto” (el segundo botón desde la izquierda) y seleccione Ninguno, Sencillo o Doble en el menú local. Aparecerá una línea de tachado simple o doble sobre el texto seleccionado del mismo color que el texto. 3 Para cambiar el color de tachado, seleccione Color en el menú local “Tachar texto” y, a continuación, seleccione un color en la ventana Colores. La línea de tachado adoptará el color seleccionado en la ventana Colores, mientras que el texto conservará su color original. Capítulo 3 Cómo trabajar con texto 49 Cómo cambiar el color del texto utilizando el panel Tipo de letra Los cambios realizados sobre el color del texto en el panel Tipo de letra reemplazarán los cambios de color que se efectúen en el Inspector de texto y viceversa. (Para obtener más información acerca de cómo cambiar el color utilizando el Inspector de texto, consulte “Cómo cambiar el color del texto utilizando el Inspector de texto” en la página 58.) Para modificar el color del texto seleccionado: 1 Haga clic en “Tipos de letra” en la barra de herramientas. 2 Haga clic en el botón “Color del texto” del panel “Tipo de letra” (el tercer botón desde la izquierda) y luego seleccione un color en la ventana Colores. Consulte el apartado “Uso de la ventana Colores” en la página 89 para obtener instrucciones al respecto. Cómo cambiar el color de fondo del párrafo utilizando el panel Tipo de letra Puede utilizar el panel “Tipo de letra” para añadir un color detrás de un párrafo. Para modificar el color de fondo del párrafo seleccionado: 1 Haga clic en “Tipos de letra” en la barra de herramientas. 2 Haga clic en el botón “Color del documento” en el panel Tipo de letra (el cuarto botón desde la izquierda) y, a continuación, seleccione un color en la ventana Colores. Consulte el apartado “Uso de la ventana Colores” en la página 89 para obtener instrucciones al respecto. Cómo crear sombras en el texto utilizando el panel Tipo de letra Puede utilizar el panel Tipo de letra para crear y aplicar sombras en el texto. Para definir sombras en el texto seleccionado: 1 Haga clic en Tipos de letra en la barra de herramientas. 2 Haga clic en el botón “Sombreado del texto” en el panel “Tipo de letra” (el quinto botón desde la izquierda). 3 Arrastre el regulador “Opacidad de la sombra” (el primer regulador a la izquierda) hacia la derecha para oscurecer la sombra. 4 Arrastre el regulador “Difuminado de la sombra” (el regulador del medio) hacia la derecha para hacer la sombra más difusa. 5 Arrastre el regulador “Desplazamiento de la sombra” (el tercero) hacia la derecha para separar la sombra del texto. 6 Gire la rueda “Ángulo de la sombra” para ajustar la dirección de la misma. Además, es posible ajustar las sombras del texto en el inspector de la figura, según se describe en “Cómo añadir sombras” en la página 84. 50 Capítulo 3 Cómo trabajar con texto Cómo cambiar el tipo de letra utilizado en el esquema Puede cambiar el tipo de letra que se utiliza al visualizar el pase de diapositivas en el esquema. Para cambiar el tipo de letra utilizado en el modo Esquema: 1 Seleccione Keynote > Preferencias. 2 Si no se está mostrando el panel General, haga clic en General. 3 Seleccione un tipo de letra y un tamaño en los menús locales de tipo de letra de esquema. Cómo añadir acentos y caracteres especiales Para escribir caracteres con acentos (como ü), símbolos matemáticos, flechas u otros caracteres especiales, utilice el panel de preferencias Internacional o la Paleta de Caracteres. Además, es posible visualizar dónde se ubican los caracteres de otros idiomas en el teclado utilizando el Visor de Teclado (por ejemplo, para ver la disposición de las teclas del teclado italiano). Todas ellas son herramientas incorporadas del Mac OS X. Cómo añadir marcas de acento Puede utilizar el visor de teclado disponible en Preferencias del Sistema para añadir marcas de acentos a los caracteres. Para añadir marcas de acentos: 1 Seleccione el menú Apple > Preferencias del Sistema y haga clic en Internacional. 2 Haga clic en el menú Teclado y, a continuación, seleccione la opción siguiente al Visor de Teclado. 3 Seleccione “Mostrar Visor de Teclado” en el menú Teclado, a la derecha de la barra de menús (la que posee el aspecto de una bandera o símbolo alfabético). El Visor de Teclado muestra los caracteres del teclado. (Si ha seleccionado una disposición de teclado o método de entrada diferente en el menú Teclado, mostrará los caracteres de la disposición de teclado seleccionada.) Por ejemplo, si selecciona Estadounidense en el menú Teclado, se visualizarán los caracteres que aparecen en el teclado americano en el Visor de Teclado. 4 Para ver los diferentes acentos que es posible escribir de manera resaltada en el Visor de Teclado, pulse Opción, o las teclas Opción y Mayúsculas. Las teclas de acentos aparecen con contorno blanco. Según el teclado, puede que no resulte necesario pulsar las teclas de modificación para ver las teclas de acentos. 5 Sitúe el punto de inserción en el lugar del documento donde desee escribir. 6 Pulse la tecla de modificación que pulsó en el paso 4 (Mayúsculas, Opción, Opción + Mayúsculas o ninguna) y la tecla del teclado que esté en el mismo lugar que el acento que se visualiza en el Visor de Teclado. A continuación, suelte la tecla de modificación y pulse la tecla del carácter que desea acentuar. Capítulo 3 Cómo trabajar con texto 51 La tecla de acento modifica la tecla que escribe a continuación. Por ejemplo, en el teclado americano, para hacer que aparezca la “é”, pulse Opción y E (la tecla de acento) y, a continuación, la E (la tecla donde desea que aparezca el acento). Cómo ver distribuciones de teclado para otros idiomas Puede utilizar el Visor de teclado disponible en Preferencias del Sistema para ver dónde están ubicados los caracteres en teclados utilizados para otros idiomas. Debe poseer tipos de letra instalados para el idioma que desee visualizar en el Visor de Teclado. Para visualizar las distribuciones de teclado para diferentes idiomas: 1 Seleccione el menú Apple > Preferencias del Sistema y haga clic en Internacional. 2 Haga clic en el menú Teclado y, a continuación, seleccione la opción siguiente al Visor de Teclado. 3 Para visualizar la disposición de caracteres en los teclados utilizados en los diferentes países, seleccione la opción Activar situada junto a la disposición del teclado del país o al método de entrada. 4 Seleccione “Mostrar Visor de Teclado” en el menú Teclado, a la derecha de la barra de menús (la que posee aspecto similar a una bandera o a un carácter alfabético). El Visor de Teclado muestra los caracteres para la disposición de teclado o método de entrada seleccionado en el menú Teclado. Por ejemplo, si selecciona Estadounidense en el menú Teclado, se visualizarán los caracteres que aparecen en el teclado americano en el Visor de Teclado. 5 Para visualizar la disposición del teclado de diferentes países, seleccione su disposición de teclado en el menú Teclado. Cómo escribir caracteres especiales y símbolos Utilizando la Paleta de Caracteres de Mac OS X, usted puede insertar caracteres especiales, como símbolos matemáticos, letras con acentos, flechas y otros “dingbats”, y otras opciones. También puede utilizar esta paleta para introducir caracteres en japonés, chino tradicional, chino simplificado y coreano, así como caracteres de otros idiomas. Para insertar caracteres especiales o símbolos: 1 Sitúe el punto de inserción en el sitio donde desea que aparezca el carácter especial o el símbolo. 2 Seleccione Edición > Caracteres especiales, para abrir la Paleta de Caracteres (o seleccione Caracteres en el menú local Acción en la esquina inferior izquierda del panel “Tipo de letra”). 52 Capítulo 3 Cómo trabajar con texto 3 Seleccione el tipo de caracteres que desee visualizar en el menú local Visualización en la parte superior de la Paleta de Caracteres. En el caso de que resultara imposible ver el menú Visualización, haga clic en el botón de la esquina superior derecha de la ventana para mostrar su parte superior. Haga clic nuevamente en este botón para ocultar la parte superior de la ventana. En la versión 10.4 de Mac OS X, la Paleta de Caracteres presenta este aspecto: 4 Haga clic en un ítem en la lista de la izquierda para visualizar los caracteres que se encuentran disponibles en cada categoría. 5 Haga doble clic en el carácter o símbolo situado a la derecha que desea insertar en el documento o seleccione el carácter y haga clic en Insertar. Si el carácter o el símbolo tienen variaciones, aparecen en la parte inferior de la ventana al hacer clic en el triángulo “Información del caracter” o en el triángulo “Variación del tipo” la parte inferior de la paleta. Haga doble clic en un símbolo para insertarlo en el documento. Capítulo 3 Cómo trabajar con texto 53 Cómo utilizar las comillas tipográficas Las comillas tipográficas son comillas de apertura y cierre curvadas; las comillas de apertura son diferentes de las de cierre. Cuando no utilice comillas tipográficas, las marcas son rectas y no difieren entre las de apertura y las de cierre. Para utilizar comillas tipográficas: m Seleccione Keynote > Preferencias, haga clic en Autocorrección y seleccione “Usar comillas tipográficas”. Uso de características tipográficas avanzadas Ciertos tipos de letra, como Zapfino y Hoefler, tienen características avanzadas de tipografía, que le permiten crear diferentes efectos. Si utiliza cierto tipo de letra que posee diferentes efectos tipográficos, puede cambiar gran cantidad de ellos en el submenú “Tipo de letra” del menú Formato. Por ejemplo, es posible ajustar lo siguiente:  Interletraje: comprime o expande el espacio entre caracteres  Ligadura: utilice o cancele el uso de ligaduras estilísticas al principio o al final de las líneas que combinan dos o más caracteres de texto en un mismo glifo. En el submenú Ligadura, seleccione “Por omisión” para usar los ajustes de ligadura especificados en la ventana Tipografía para el tipo de letra que está utilizando, seleccione Ninguno para desactivar las ligaduras en el texto seleccionado, o seleccione Todas para activar las ligaduras adicionales en el texto seleccionado.  Línea de base: desplace el texto más arriba o más abajo del texto adyacente.  Mayúsculas: convierta caracteres a mayúsculas, minúsculas o mayúsculas iniciales (estilo título). En la ventana Tipografía se hallan disponibles características de tipografía avanzadas. Comillas rectas Comillas curvadas Con ligadura Sin ligadura 54 Capítulo 3 Cómo trabajar con texto Para abrir la ventana Tipografía: 1 Haga clic en “Tipos de letra” en la barra de herramientas. 2 En el panel “Tipo de letra”, seleccione Tipografía en el menú local Acción (en la esquina inferior izquierda). Cómo ajustar el suavizado de los tipos de letra Si los tipos de letra aparecen difusos, borrosos o cortados en su pantalla, puede ajustar el estilo de suavizado del tipo de letra o cambiar el tamaño del texto con el que Mac OS X comienza a suavizar los tipos de letra. Para suavizar los tipos de letra en la pantalla: 1 Abra Preferencias del Sistema y haga clic en Apariencia. 2 Seleccione un estilo de suavizado de tipo de letra en el menú local de la parte inferior. Dependiendo del tipo de pantalla que tenga, puede que note escasas diferencias o ninguna entre los estilos de suavizado. 3 Si planea utilizar tamaños de fuente pequeños en su documento, seleccione un tamaño de punto en el menú local “Desactivar suavizado de texto para tamaños de tipo de letra”. Cuando esté activado el suavizado de texto, los tipos de letra más pequeños puede resultar difíciles de leer. Cómo ajustar la alineación, el espaciado y el color del texto La principal herramienta para especificar los atributos del texto es el inspector de texto. Mediante el menú Formato puede realizar ajustes de alineación horizontal (como centrar el texto o alinearlo a la izquierda). Capítulo 3 Cómo trabajar con texto 55 Cómo utilizar el Inspector de texto para controlar la alineación, el espaciado y el color Mediante el panel Texto del inspector de texto se modifica el color del texto y su alineación. Además, es posible ajustar el espaciado entre caracteres y líneas de texto. Para abrir el panel Texto de la ventana de información del texto: m Haga clic en el botón Inspector de la barra de herramientas, haga clic en el botón Inspector de la tabla y, a continuación, haga clic en Texto. Cómo alinear texto horizontalmente Puede cambiar la alineación de los párrafos en una columna, celda de tabla, cuadro de texto o figura para que el texto quede alineado con el borde derecho o izquierdo, centrado, o alineado a la izquierda y a la derecha (justificado). Para alinear el texto a la izquierda, al centro, a la derecha o justificado: 1 Seleccione el texto que desee modificar. 2 Haga clic en el botón Inspector de la barra de herramientas, haga clic en el botón Inspector de texto y, a continuación, haga clic en Texto. Botones de alineación vertical: haga clic para alinear texto respecto a las partes superior, central o inferior del cuadro de texto, figura o celda de tabla. Arrastre para ajustar la cantidad de espacio entre el texto y los bordes interiores de los cuadros de texto, celdas de tabla y formas. Espacio entre caracteres y entre líneas: para ajustar el espacio entre caracteres, líneas y párrafos del texto seleccionado. Haga clic para cambiar el color del texto seleccionado. El botón “Inspector de texto”. Botones de alineación horizontal: Haga clic para alinear el texto seleccionado a la izquierda, a la derecha, en el centro, o a la izquierda y la derecha, o para utilizar la alineación especial de celda de tabla. 56 Capítulo 3 Cómo trabajar con texto 3 Haga clic en uno de los cinco botones de alineación horizontal, situados a la derecha del contenedor de color. De izquierda a derecha, estos botones tienen los siguientes efectos. El botón “Alineación izquierda” coloca todas las líneas del texto en el margen izquierdo del objeto. El botón Centrar ajusta el centro de cada línea del texto en el centro del objeto. El botón “Alineación derecha” coloca todas las líneas del texto en el margen derecho del objeto. El botón Justificar espacia los caracteres de la línea de manera que las líneas toquen tanto el margen izquierdo como el margen derecho del objeto. El botón “Alinear celda de tabla automáticamente” justifica el texto a la izquierda y los números a la derecha de una celda de tabla. Si desea sangrar la primera línea de texto del párrafo u obtener información acerca de cómo deshacer la sangría del párrafo, consulte “Cómo ajustar las sangrías” en la página 61. También puede alinear el texto horizontalmente seleccionando Formato > Texto > Alinear a la izquierda, Centrar, Alinear a la derecha o Justificar. Cómo alinear texto verticalmente Usted puede cambiar la alineación del texto de una celda de tabla, un cuadro de texto (excepto los cuadros de texto libre) o un figura para que el texto quede alineado con el borde superior o inferior o para que quede centrado entre ellos. Para alinear el texto por arriba, por abajo o en el centro de un cuadro de texto, celda de tabla o figura: 1 Seleccione el cuadro de texto, celda de tabla o figura cuya alineación desee modificar. 2 Haga clic en el botón Inspector de la barra de herramientas, haga clic en el botón Inspector de texto y, a continuación, haga clic en Texto. 3 Haga clic en uno de los tres botones de alineación vertical, situados debajo de Color y Alineación. Cómo ajustar el espaciado entre líneas de texto Puede aumentar o disminuir la distancia entre líneas de texto. Para ajustar el espaciado: 1 Seleccione el texto que desee modificar. 2 Haga clic en el botón Inspector de la barra de herramientas, haga clic en el botón Inspector de texto y, a continuación, haga clic en Texto. Capítulo 3 Cómo trabajar con texto 57 3 Mueva el regulador de Línea a la izquierda para reducir el espaciado o a la derecha para aumentarlo. Para especificar un valor de espaciado de línea preciso, escriba un valor de punto en el campo Línea, o haga clic en la flecha arriba o la flecha abajo situadas junto al campo. 4 Seleccione una opción de espaciado de líneas en el menú local Espaciado de líneas que aparece cuando hace clic en el texto situado debajo del campo Línea. Espaciado de líneas estándar (Sencillo, Doble, Múltiple): el espacio entre líneas es proporcional al tamaño del tipo de letra. Utilícelo para dejar fija la distancia relativa entre los trazos ascendentes (partes de las letras que se extienden hasta la parte superior de la línea) y los trazos descendentes (partes de las letras que se extienden hasta la parte inferior). Sencillo ajusta el espaciado de líneas a espacio sencillo, mientras que Doble lo ajusta a doble espacio. Múltiple le permite ajustar los valores de interlineado entre sencillo y doble, o más del doble. Como mínimo: la distancia desde una línea a la siguiente no será menor al valor que ajuste; pero puede ser mayor para tipos de letra de mayor tamaño para evitar la superposición de las líneas de texto. Utilícelo para dejar fija la distancia entre líneas y evitar la superposición ante el aumento del tamaño del texto. Exacto: la distancia entre las líneas de base. Entre: este valor aumenta el espacio entre líneas en lugar de aumentar la altura de las líneas. En cambio, el espacio doble duplica la altura de cada línea. Cómo ajustar el espaciado antes o después de un párrafo Puede aumentar o reducir el espaciado antes o después de los párrafos. Para ajustar la cantidad de espacio antes y después del párrafo: 1 Seleccione los párrafos que desee modificar. 2 Haga clic en el botón Inspector de la barra de herramientas, haga clic en el botón “Inspector de texto” y, a continuación, haga clic en Texto. Menú local Espaciado de líneas: Haga clic en el texto situado debajo del campo Línea y elija una opción de espaciado de línea. Campo Línea: Escriba un valor (o haga clic en las flechas) para especificar el espacio entre las líneas de texto de un párrafo. 58 Capítulo 3 Cómo trabajar con texto 3 Arrastre el regulador Antes del párrafo o Después del párrafo. Además, es posible especificar un valor preciso (5 puntos, por ejemplo) en los cuadros de texto. Si los valores de Antes del párrafo y de Después del párrafo para párrafos contiguos no es el mismo, el valor de espaciado superior será el que se utilice. Por ejemplo, si el valor de Antes del párrafo del párrafo actual es de 12 puntos y el párrafo anterior tiene un valor Después del párrafo de 14 puntos, el espaciado entre los párrafos será de 14 puntos. El espaciado antes de párrafo no se muestra si el párrafo es el primero en un cuadro de texto, una figura o una celda de tabla. Para ajustar el espaciado alrededor del texto en cuadros, formas y celdas de tabla, utilice el control “Margen interno”, que se describe en “Cómo cambiar el margen interno del texto en objetos” en la página 62. Cómo ajustar el espaciado entre caracteres Puede aumentar o disminuir la cantidad de espacio entre caracteres. Para ajustar la cantidad de espacio entre caracteres: 1 Seleccione el texto que desee modificar, o haga clic si desea escribir nuevo texto. 2 Haga clic en el botón Inspector de la barra de herramientas, haga clic en el botón Inspector de texto y, a continuación, haga clic en Texto. 3 Arrastre el regulador Carácter o especifique un nuevo porcentaje en el campo Carácter. También puede ajustar el espacio entre los caracteres seleccionados seleccionando Formato > Tipo de letra > Interletraje y seleccionando una opción en el submenú. Cómo cambiar el color del texto utilizando el Inspector de texto Los cambios realizados sobre el color del texto en el inspector de texto reemplazarán los cambios de color que se efectúen en el panel “Tipo de letra” y viceversa. (Para obtener más información acerca de cómo cambiar el color utilizando el panel Tipo de letra, consulte “Cómo cambiar el color del texto utilizando el panel Tipo de letra” en la página 49.) Para modificar el color del texto: 1 Seleccione el texto cuyo color desea modificar o haga clic en el texto para ubicar el punto de inserción. 2 Haga clic en el botón Inspector de la barra de herramientas, haga clic en el botón Inspector de la tabla y, a continuación, haga clic en Texto. 3 Haga clic en el contenedor de color. 4 Elija un color en la ventana Colores. Consulte el apartado “Uso de la ventana Colores” en la página 89 para obtener más información. Capítulo 3 Cómo trabajar con texto 59 Cómo ajustar las tabulaciones para alinear el texto Puede alinear el texto en puntos específicos estableciendo tabulaciones en un cuadro de texto, celda de tabla o figura. Para mover el punto de inserción hasta una tabulación, pulse Opción + Tabulador. Puede trabajar con ajustes de tabulaciones controlando los símbolos de tabulaciones en las reglas horizontales. Para ver los símbolos de las tabulaciones existentes en la regla horizontal haga clic en Visualización en la barra de herramientas, seleccione “Mostrar reglas” y, a continuación, seleccione parte del texto de una diapositiva. Para establecer tabulaciones en listas, consulte “Cómo utilizar listas con viñetas, numeradas y ordenadas (Esquemas)” en la página 62. Éstos son algunos modos de trabajar con reglas: m Para mostrar u ocultar las reglas, haga clic en Visualización en la barra de herramientas y seleccione “Mostrar reglas” u “Ocultar reglas”. m Para cambiar las unidades de medida en las reglas, seleccione Keynote > Preferencias, haga clic en Reglas y seleccione un elemento en el menú local “Unidades de la regla”. m Para mostrar las medidas como un porcentaje de la distancia en sentido horizontal, seleccione Keynote > Preferencias, haga clic en Reglas y seleccione “Mostrar las unidades de la regla como porcentaje”. m Para colocar el punto de origen horizontal de la regla en el centro de la diapositiva, seleccione Keynote > Preferencias, haga clic en Reglas y seleccione “Situar el origen en el centro de la regla”. m Para reutilizar los ajustes de la regla en cualquier punto del documento, seleccione Formato > Texto > Copiar regla y formato > Texto > Pegar regla. Al modificar los ajustes de la regla en las preferencias de Keynote, los nuevos ajustes se aplican a todas las diapositivas que se visualizan en Keynote, hasta que vuelven a modificarse dichos ajustes. Tabulación decimal Tabulación derecha Tabulación centrada Tabulación izquierda Los símbolos azules del tabulador aparecen en la regla horizontal cuando se selecciona texto tabulado. 60 Capítulo 3 Cómo trabajar con texto Cómo establecer nuevas tabulaciones Puede utilizar la regla horizontal para añadir una nueva tabulación. Para crear una nueva tabulación: 1 Haga clic en Visualización en la barra de herramientas y seleccione “Mostrar reglas”. 2 Haga clic en la regla horizontal para colocar un símbolo de tabulación en la posición donde desee ajustar la tabulación. Si no sucede nada, haga clic en el texto para establecer el punto de inserción. 3 Con la tecla Control pulsada, haga clic en el símbolo de tabulador y seleccione una opción en el menú de función rápida. Tabulación izquierda: alinea el lado izquierdo del texto con la tabulación. Tabulación centrada: sitúa el centro del texto en la tabulación. Tabulación derecha: alinea el lado derecho del texto con la tabulación. Tabulación decimal: para números, alinea el carácter decimal (un punto o una coma) con la tabulación. También puede hacer doble clic en el símbolo de tabulador repetidamente hasta que aparezca el tipo de tabulador deseado. Cómo cambiar una tabulación Puede cambiar la ubicación y el tipo de las tabulaciones utilizando la regla horizontal. Para cambiar las tabulaciones: 1 Haga clic en Visualización en la barra de herramientas y seleccione Mostrar Reglas. 2 Para mover una tabulación, arrastre su símbolo de tabulador azul a lo largo de la regla horizontal. 3 Para cambiar de tipo la tabulación, con la tecla Control pulsada, haga clic en el símbolo de tabulador y seleccione una opción en el menú de función rápida. O bien, haga doble clic en el símbolo de tabulador en la regla repetidamente hasta que aparezca el tipo de tabulador deseado. Seleccione de entre estos tipos de tabuladores. Capítulo 3 Cómo trabajar con texto 61 Cómo eliminar una tabulación Puede eliminar de forma rápida una tabulación utilizando la regla horizontal. Para eliminar tabulaciones: 1 Haga clic en Visualización en la barra de herramientas y seleccione Mostrar Reglas. 2 Arrastre el símbolo de tabulación fuera de la regla horizontal. Cómo ajustar las sangrías Es posible modificar la cantidad de espacio entre el texto y el borde interior de un cuadro de texto, una figura o una celda de tabla. Cómo ajustar sangrías de párrafos Puede cambiar el sangrado arrastrando los controles de sangrado en la regla de texto. Para ajustar las sangrías utilizando las reglas: 1 Haga clic en Visualización en la barra de herramientas y, a continuación, seleccionar “Mostrar reglas”. 2 Para cambiar la sangría derecha, arrastre el icono de sangría derecha (triángulo azul hacia abajo en el lado derecho de la regla horizontal) hacia el lugar donde desea que termine el borde derecho del párrafo. 3 Para cambiar la sangría izquierda, arrastre el icono de sangría izquierda (triángulo azul hacia abajo en el lado izquierdo de la regla) hacia el lugar donde desea que termine el borde izquierdo del párrafo. Para modificar el margen izquierdo independientemente de la sangría izquierda, mantenga pulsada la tecla Opción mientras arrastra. 4 Para cambiar la tabulación de la primera línea, arrastre la sangría de la primera línea (rectángulo azul) hacia donde desee que comience la primera línea. Si desea que la primera línea quede a la misma altura que el margen izquierdo, asegúrese de que el rectángulo esté alineado con el icono de sangría izquierda. Para crear una sangría francesa, arrastre el rectángulo hacia la izquierda del icono de sangría izquierda. Para utilizar los ajustes de la regla en cualquier punto del documento, seleccione Formato > Texto > Copiar regla y formato > Texto > Pegar regla. Sangría de la primera línea Sangría derecha Sangría izquierda 62 Capítulo 3 Cómo trabajar con texto Cómo cambiar el margen interno del texto en objetos Además, es posible cambiar la cantidad de espacio entre el texto y el borde interior del cuadro de texto, la figura o la celda de tabla. Esta medida se denomina el margen interior. La cantidad de espacio que indique se aplica por igual alrededor del texto en todos sus lados. Para ajustar el espacio entre el texto y el interior de los cuadros de texto, formas o celdas de tablas: 1 Seleccione el cuadro de texto, la figura o la celda de tabla. (Si el punto de inserción se encuentra dentro del objeto, pulse Comando + Retorno para salir del modo de edición de texto y seleccione el objeto.) 2 Haga clic en el botón Inspector de la barra de herramientas, haga clic en el botón Inspector de texto y, a continuación, haga clic en Texto. 3 Arrastre el regulador “Insertar margen” hacia la derecha para aumentar el espacio entre el texto y el borde interior del objeto, o escriba el número que desee en el cuadro “Insertar margen” y pulse Retorno. También puede hacer clic en las flechas para incrementar o disminuir el espacio. Cómo ajustar sangrías para listas Para sangrar listas con viñetas, listas numeradas y listas ordenadas, se utiliza el inspector del texto. Consulte el apartado “Cómo utilizar listas con viñetas, numeradas y ordenadas (Esquemas)” para más detalles. Cómo utilizar listas con viñetas, numeradas y ordenadas (Esquemas) Keynote proporciona viñetas y numeración con estilos de formato previo para crear listas sencillas u ordenadas (esquemas). Las listas con viñetas y numeradas son listas sencillas que carecen de la inserción de niveles jerárquicos de información que resultan visibles en los esquemas. Cómo generar listas de forma automática Al utilizar la generación automática de listas, Keynote aplica formato automáticamente a una lista basándose en lo que usted escribe. Para utilizar esta opción, seleccione Keynote > Preferencias, haga clic en Autocorrección y asegúrese de que esté seleccionada la opción “Detectar listas automáticamente”. Indique la cantidad de espacio que desee alrededor del texto dentro de un cuadro de texto, una forma o una celda de tabla. Capítulo 3 Cómo trabajar con texto 63 Éstos son algunos modos de generar listas de forma automática: m Para crear una lista con viñetas, escriba una viñeta (•), un espacio, texto y, a continuación, pulse Retorno. Para escribir una viñeta, pulse Opción + 8. m Para crear una lista con etiquetas que sean asteriscos (*) o guiones (-), escriba un asterisco o un guión, un espacio, algo de texto, y pulse Retorno. m Para crear una lista con etiquetas que sean números o letras, escriba un número o letra, un punto, un espacio, algo de texto, y pulse Retorno. m Para volver al texto normal al final de la lista, pulse Retorno dos veces. Puede utilizar cualquiera de los formatos de caracteres del menú local estilo de numeración del Inspector de texto. Para acceder a este menú, haga clic en Viñetas en el “Inspector del texto” y seleccione Números en el menú local “Viñetas y numeración”. Cómo utilizar listas con viñetas Aunque puede utilizar la generación automática de listas para crear una lista con viñetas sencilla, si utiliza el inspector de texto contará con más opciones para dar formato a las listas con viñetas. Para añadir y dar formato a una lista con viñetas: 1 Sitúe el punto de inserción donde desee que comience la lista. 2 Haga clic en Inspector en la barra de herramientas, haga clic en el botón Inspector de texto y haga clic en Viñetas. 3 Seleccione un estilo de viñeta del menú local “Viñetas y numeración”. Para utilizar un carácter escrito como viñeta, seleccione “Viñetas de text” o y seleccione un carácter de la lista o escriba un carácter nuevo en el campo. Para utilizar una de las viñetas de imagen que se incluyen en Keynote, seleccione “Viñetas de imagen” y seleccione una de las imágenes de la lista. Para utilizar su propia imagen como viñeta, seleccione Imagen personalizada en el cuadro de diálogo Abrir que aparece. 4 Para cambiar el tamaño de una viñeta de imagen, especifique un porcentaje del tamaño de la imagen original en el campo Tamaño. O seleccione la opción “Proporcional al texto” y especifique un porcentaje del tamaño del texto; esta opción mantiene la relación imagen- texto de las viñetas, incluso si cambia posteriormente el tamaño del tipo de letra. 5 Para ajustar el espacio entre las viñetas y el margen izquierdo, utilice el campo “Sangría de viñeta”. Para ajustar el espacio entre las viñetas y el texto, utilice el campo “Sangría de texto”. 64 Capítulo 3 Cómo trabajar con texto 6 Para colocar las viñetas más arriba o más abajo en relación con el texto, utilice el campo Alinear. Utilice estas técnicas para añadir y sangrar los elementos con viñetas en su lista:  Para añadir un nuevo tema en el nivel actual de sangría, pulse Retorno.  Para crear un párrafo sin viñetas dentro de un tema, pulse Retorno mientras mantiene pulsada la tecla Mayúsculas.  Para introducir un nuevo tema en el siguiente nivel inferior o superior de sangría, pulse Retorno y haga clic en una de las flechas contiguas al campo “Nivel de sangría”. También puede hacer clic y mantener pulsado una viñeta y arrastrar hacia la derecha, hacia la izquierda, hacia abajo y a la derecha o hacia abajo y a la izquierda.  Para volver al texto normal al final de la lista, pulse Retorno dos veces o pulse Retorno y seleccione “Sin viñetas” en el menú local “Viñetas y numeración”. Puede que también necesite ajustar el nivel de sangría. Cómo utilizar listas numeradas Aunque puede utilizar la generación automática de listas para crear una lista numerada sencilla, utilizando el Inspector de texto tendrá más opciones para dar formato a las listas numeradas. Consulte “Cómo generar listas de forma automática” en la página 62 para obtener más información acerca de la generación automática de listas. Para añadir y dar formato a una lista numerada: 1 Sitúe el punto de inserción donde desee que comience la lista. 2 Haga clic en Inspector en la barra de herramientas, haga clic en el botón Inspector de texto y haga clic en Viñetas. 3 Seleccione Números en el menú local Viñetas y numeración, a continuación seleccione un estilo de numeración en el menú local, directamente debajo del mismo. 4 Para ajustar el espacio entre los números y el margen izquierdo, utilice el campo Sangría de números. Para ajustar el espacio entre los números y el texto, utilice el campo Sangría de texto. Utilice estas técnicas para añadir y sangrar los elementos en su lista:  Para añadir un nuevo tema en el nivel actual de sangría, pulse Retorno.  Para crear un párrafo sin números dentro de un tema, pulse Retorno mientras mantiene pulsada la tecla Mayúsculas.  Para introducir un nuevo tema en el siguiente nivel inferior o superior de sangría, pulse Retorno y haga clic en una de las flechas contiguas al campo “Nivel de sangría”. También puede hacer clic y mantener pulsado un número y arrastrar hacia la derecha, hacia la izquierda, hacia abajo y a la derecha o hacia abajo y a la izquierda.  Para volver al texto normal al final de la lista, pulse Retorno dos veces o pulse Retorno y seleccione “Sin viñetas” en el menú local “Viñetas y numeración”. Puede que también necesite ajustar el nivel de sangría. Capítulo 3 Cómo trabajar con texto 65  Para añadir un párrafo existente a una lista numerada, haga clic en el párrafo, seleccione un estilo de numeración y haga clic en “Continuar desde la anterior”.  Para iniciar una nueva secuencia de numeración en una lista, haga clic en “Empezar en” y especifique el número con el que desea iniciar la secuencia. Si quiere que los elementos de la lista cuenten con subtemas etiquetados (como en un esquema), utilice una lista ordenada en lugar de una lista numerada. Cómo utilizar listas ordenadas (Esquemas) Las listas ordenadas (o esquemas) ofrecen diferentes estilos de numeración para cada nivel de sangría en una lista, permitiéndole crear una jerarquía en la información. Por ejemplo:  Puede crear un esquema utilizando una secuencia numerada como la siguiente según avanza desde el nivel superior hacia niveles inferiores: I, A, 1, a), (1), (a), i), (1) y (a).  Puede crear un esquema de estilo legal, que anexa un número o letra adicional en cada nivel inferior: 1, 1.1, 1.1.1 y así sucesivamente. Puede añadir y dar formato a listas ordenadas utilizando el Inspector de texto. Para añadir y dar formato a una lista ordenada: 1 Sitúe el punto de inserción donde desee que comience la lista. 2 Haga clic en el botón Inspector de la barra de herramientas, haga clic en el botón Inspector de la tabla y, a continuación, haga clic en Lista. 3 Para crear una lista de estilo legal, seleccione Numeración progresiva en el menú local “Viñetas y numeración”. De lo contrario, seleccione Números. 4 Seleccione un estilo de numeración del menú local que aparece justo debajo del mismo. 5 Para ajustar el espacio entre los números y el margen izquierdo, utilice el campo Sangría de números. Para ajustar el espacio entre los números y el texto, utilice el campo “Sangría de texto”. Utilice estas técnicas para añadir y sangrar los elementos en su lista:  Para añadir un nuevo tema en el nivel actual de sangría, pulse Retorno.  Para crear un párrafo sin números dentro de un tema, pulse Retorno mientras mantiene pulsada la tecla Mayúsculas.  Para introducir un nuevo tema en el siguiente nivel de sangría inferior, pulse Tabulador. Para introducir un nuevo tema en el siguiente nivel superior, pulse Mayúsculas + Tabulador. Para moverse entre los diferentes niveles, también puede hacer clic y mantener pulsado un número y arrastrar hacia la derecha, hacia la izquierda, hacia abajo y a la derecha o hacia abajo y a la izquierda.  Para volver al texto normal al final de la lista, pulse Retorno dos veces o pulse Retorno y seleccione Sin Viñetas en el menú local Viñetas y numeración. Puede que también necesite ajustar el nivel de sangría. 66 Capítulo 3 Cómo trabajar con texto  Para añadir un párrafo existente a una lista numerada, haga clic en el párrafo, seleccione un estilo de numeración y haga clic en “Continuar desde la anterior”.  Para iniciar una nueva secuencia de numeración en una lista, haga clic en “Empezar en” y especifique el número con el que desea iniciar la secuencia. Cómo utilizar cuadros de texto y figuras para resaltar el texto Los cuadros de texto y las figuras se utilizan para destacar un texto respecto al cuerpo principal del texto de una diapositiva. Cómo añadir cuadros textos libres Varias diapositivas maestras proporcionan cuadros de texto, pero usted puede añadir uno o más “cuadros de texto libres” a una diapositiva. Los cuadros de texto libres son similares a los cuadros de texto que se proporcionan en diversas diapositivas maestras. La principal diferencia reside en que el texto de los cuadros de texto libres no aparece en el modo esquema. Se pueden arrastrar cuadros de texto libres a cualquier parte de una diapositiva. Para crear una caja de texto libre: 1 Haga clic en “Cuadro de texto” en la barra de herramientas (o seleccione Insertar > Cuadro de texto). 2 En el cuadro de texto que aparecerá, haga doble clic sobre el texto y escriba. Los cuadros de texto libre se ensanchan en sentido horizontal (hasta el ancho de la diapositiva) para ajustarse a la longitud del texto. Para utilizar todo el ancho de la diapositiva para el texto, omita el siguiente paso. 3 Para ajustar un ancho fijo para el cuadro de texto, arrastre sus tiradores. Después de ajustar el ancho (o cuando el cuadro ocupa todo el ancho de la diapositiva), el cuadro de texto se ensancha en sentido vertical para ajustarse a la longitud del texto. Al eliminar texto, el cuadro se reduce automáticamente. 4 Cuando haya terminado de escribir, haga clic fuera del cuadro de texto. O, para dejar de modificar el texto y seleccionar el cuadro, pulse Comando + Retorno. 5 Arrastre el cuadro de texto y colóquelo en la diapositiva. También puede dibujar un cuadro de texto libre. Con la tecla Opción pulsada, haga clic en “Caja de texto” en la barra de herramientas y arrastre el puntero con forma de cruz por la ventana del documento para crear un cuadro de texto del tamaño que desee. Si desea saber más sobre la modificación de los cuadros de texto, consulte el apartado “Cómo definir el formato de los cuadros de texto o las figuras” en la página 68. Capítulo 3 Cómo trabajar con texto 67 Cómo presentar texto en columnas Puede crear columnas en un cuadro de texto o una figura rectangular. Cuando el texto haya rellenado una columna, pasará a la siguiente columna. Para crear y dar formato a columnas: 1 Seleccione el cuadro de texto que desee dividir en columnas. 2 En la barra de herramientas haga clic en Inspector, haga clic en el botón “Inspector de texto” y haga clic en Columnas. 3 Para indicar cuántas columnas desea, utilice el campo Columnas. 4 Si quiere que todas las columnas tengan la misma anchura, seleccione “Igualar ancho de columnas”. Para definir columnas con distintos anchos, anule la selección de la opción “Igualar ancho de columnas”, haga doble clic en un valor de Columna en la tabla y escriba un nuevo ancho. 5 Para cambiar la distancia entre columnas, haga doble clic en un valor de Corondel y modifíquelo. Cómo introducir texto en formas En todas las formas, excepto las líneas, es posible insertar texto. Para añadir texto a formas: 1 Inserte una figura donde desee en la diapositiva. Para obtener información acerca de cómo añadir figuras, consulte “Cómo añadir una figura predibujada” en la página 92 y “Cómo añadir una figura personalizada” en la página 92. 2 Haga doble clic en la figura y escriba el texto que desee. Si el texto supera los límites del borde de la figura, aparecerá un indicador de solapamiento. 3 Para cambiar el tamaño de la figura, selecciónela y arrastre los tiradores de selección. (Si el punto de inserción se encuentra dentro de la figura, pulse Comando + Retorno para salir del modo edición de texto y seleccione la figura.) Es posible dar formato al texto dentro de las figuras. También puede girar una figura pero mantener su texto horizontal. Después de girar la figura, seleccione Formato > Figura > Restaurar tiradores de texto y objeto. El indicador de solapamiento muestra que el texto supera los bordes de la figura. 68 Capítulo 3 Cómo trabajar con texto 4 Para añadir texto a una figura que forma parte de un grupo, haga doble clic en la zona de texto de cualquiera de las figuras del grupo. Si cambia el tamaño del grupo, todo cambiará de tamaño salvo el texto. Aún podrá editar y dar formato al texto. Consulte el apartado “Cómo agrupar y bloquear objetos” en la página 87 para obtener más información acerca de la agrupación de objetos. Cómo definir el formato de los cuadros de texto o las figuras Además, es posible cambiar la cantidad de espacio entre el texto y el borde interior del cuadro de texto, la figura o la celda de tabla. Consulte el apartado “Cómo cambiar el margen interno del texto en objetos” en la página 62 para obtener instrucciones al respecto. Utilice el inspector de la figura para ajustar el formato de los bordes, las sombras, la opacidad, el color de relleno y otros parámetros de los cuadros de texto o las figuras. Para obtener más información acerca de cómo ajustar las propiedades de objeto, consulte el “Modificación de objetos” en la página 81 Cómo utilizar hipervínculos Es posible convertir textos, imágenes y figuras en hipervínculos que abren otra diapositiva, un documento de Keynote, una página web o un mensaje de correo electrónico, o que detienen un pase de diapositivas. Use este tipo de hipervínculo Para realizar esta acción Notas Página web Abrir una página en un navegador web Keynote abrirá su navegador por omisión. Mensaje de correo electrónico Abrir un nuevo mensaje de correo electrónico con el asunto y la dirección especificados Keynote abrirá su aplicación de correo por omisión. Diapositiva Abrir otra diapositiva de la presentación Seleccione la diapositiva siguiente, anterior, la primera o la última; la última diapositiva visualizada; o una diapositiva específica. Archivo Keynote Abrir otro documento de Keynote Si transfiere la presentación a otro ordenador, recuerde transferir el otro documento también. Salir del pase de diapositivas Parar el pase de diapositivas Keynote se abre en modo de edición hacia la última diapositiva. Este texto subrayado es un hipervínculo. La flecha azul indica que este cuadro de texto es un hipervínculo. Capítulo 3 Cómo trabajar con texto 69 Cómo enlazar a una página web Puede añadir un hipervínculo que abra una página web en su navegador web por omisión. Para añadir un hipervínculo que abre una página web: 1 Seleccione el texto o el objeto que desee convertir en un hipervínculo. Si escribe el texto que empieza por “www” o “http” (o lo copia de otro documento), ese texto se convertirá automáticamente en un hipervínculo. Para desactivar esta opción, seleccione Keynote > Preferencias, haga clic en Autocorrección y anule la selección de “Detectar automáticamente direcciones web y de correo electrónico”. Este ajuste es específico del ordenador, por lo que si el documento se abre en un ordenador con un ajuste diferente, se utilizará el ajuste de ese ordenador. 2 Haga clic en Inspector en la barra de herramientas, haga clic en el botón Inspector de vínculos y seleccione “Activar como hipervínculo”. 3 Seleccione Página web en el menú local “Enlazar con”. 4 Escriba la dirección de la página web en el campo URL. 5 Si desea cambiar el texto que se muestra como hipervínculo en el documento, escriba un texto nuevo en el campo Mostrar. Cómo enlazar a un mensaje de correo electrónico predirigido Puede añadir un hipervínculo en el que puede hacer clic para crear un mensaje de correo electrónico predirigido en su aplicación de correo por omisión. Para añadir un hipervínculo que se vincule con un mensaje de correo electrónico: 1 Seleccione el texto o el objeto que desee convertir en un hipervínculo. Si escribe una dirección de correo electrónico (o la copia de otro documento), ese texto se convertirá automáticamente en un hipervínculo. Para desactivar esta función, seleccione Keynote > Preferencias, haga clic en Autocorrección y, a continuación, anule la selección de “Detectar automáticamente direcciones web y de correo electrónico”. Este ajuste es específico del ordenador, por lo que si el documento se abre en un ordenador con un ajuste diferente, se utilizará el ajuste de ese ordenador. Botón “Inspector de hipervínculos” Escriba el URL con el que desea crear un enlace. Escriba el texto del vínculo que desea que se muestre en la diapositiva. 70 Capítulo 3 Cómo trabajar con texto 2 Haga clic en Inspector en la barra de herramientas, haga clic en el botón Inspector de vínculos y seleccione “Activar como hipervínculo”. 3 Seleccione Mensaje de correo electrónico en el menú local “Enlazar con”. 4 Escriba la dirección de correo electrónico del destinatario en el campo Para. 5 De forma opcional, puede escribir una línea de asunto en el campo Asunto. 6 Para que el hipervínculo muestre texto personalizado, escriba el nuevo texto en el campo Mostrar. (Esta opción no estará disponible si selecciona como un hipervínculo un objeto en lugar de texto.) Cómo enlazar con una diapositiva Añada un hipervínculo que muestre una diapositiva concreta. Para añadir un hipervínculo que se enlace con una diapositiva: 1 Seleccione el texto o el objeto que desee convertir en un hipervínculo. 2 Haga clic en Inspector en la barra de herramientas, haga clic en el botón “Inspector de hipervínculos” y seleccione “Activar como hipervínculo”. 3 En el menú local “Enlazar con”, seleccione Diapositiva. 4 Seleccione la opción que describe la diapositiva que desea mostrar (siguiente, anterior, primera o última; última visualizada; o un número de diapositiva concreto). Puede utilizar hipervínculos para controlar la navegación durante un pase de diapositivas. Consulte “Cómo crear presentaciones del tipo “solo hipervínculos”” en la página 183. Escriba el asunto del mensaje. Escriba la dirección de correo electrónico del destinatario. Escriba el texto del vínculo que se mostrará en la diapositiva. Capítulo 3 Cómo trabajar con texto 71 Cómo enlazar con un archivo de Keynote Cómo agregar un hipervínculo que abre otro archivo de Keynote. Para añadir un hipervínculo que abre otro documento de Keynote: 1 Seleccione el texto o el objeto que desee convertir en un hipervínculo. 2 Haga clic en Inspector en la barra de herramientas, haga clic en el botón “Inspector de hipervínculos” y seleccione “Activar como hipervínculo”. 3 Seleccione Archivo de Keynote en el menú local “Enlazar con”. 4 Desplácese hasta el archivo y haga clic en Abrir. 5 Si desea cambiar el texto que se muestra como hipervínculo en el documento, escriba un texto nuevo en el campo Mostrar. Al hacer clic en un enlace a otro documento de Keynote, el nuevo pase de diapositivas comenzará a reproducirse desde la primera diapositiva. Cómo utilizar un hipervínculo para detener un pase de diapositivas Añada un hipervínculo para detener un pase de diapositivas. Para añadir un hipervínculo que detenga un pase de diapositivas: 1 Seleccione el texto o el objeto que desee convertir en un hipervínculo. 2 Haga clic en Inspector en la barra de herramientas, haga clic en el botón Inspector de hipervínculos y seleccione “Activar como hipervínculo”. 3 En el menú local “Enlazar con”, seleccione “Salir del pase de diapositivas”. Cómo subrayar texto de hipervínculos El texto de los hipervínculos aparece subrayado por omisión, pero se puede suprimir el subrayado si se desea. Éstos son algunos modos de activar y desactivar el subrayado: m Para impedir que los nuevos textos de hipervínculos aparezcan subrayados automáticamente, seleccione Keynote > Preferencias, haga clic en General y anule la selección de “Subrayar los hipervínculos de texto al crearlos”. m Para eliminar el subrayado de un texto de hipervínculo existente, selecciónelo, haga clic en “Tipos de letra” en la barra de herramientas; en el panel Tipo de letra seleccione Ninguno en el menú local Subrayado. m Para subrayar un texto de hipervínculo que no está subrayado, haga clic en “Tipos de letra” en la barra de herramientas; en el panel Tipo de letra seleccione Sencillo en el menú local Subrayado. 72 Capítulo 3 Cómo trabajar con texto Cómo sustituir texto de forma automática Keynote se puede configurar para que reconozca y reemplace texto que no desea y lo sustituya por el texto que sí desea. Por ejemplo, si escribe “lso”, Keynote puede cambiarlo automáticamente por “los”. Para configurar la sustitución automática de texto: 1 Seleccione Keynote > Preferencias. 2 Haga clic en Autocorrección y seleccione una opción: Para convertir automáticamente las comillas simples y dobles en comillas tipográficas (de modo que las comillas de inicio y de cierre no sean idénticas), seleccione la opción “Usar comillas tipográficas”. Para asegurarse de que la primera palabra de una frase comienza en mayúscula, seleccione “Corregir uso de mayúsculas”. Para convertir de forma automática las letras de “1º”, “2º”, “3º”, etc., en superíndices, seleccione “Convertir sufijos numéricos en superíndices”. Para hacer que Keynote detecte automáticamente que un texto que se acaba de escribir es una dirección de correo electrónico o una dirección URL, seleccione “Detectar automáticamente direcciones web y de correo electrónico”. Las direcciones web y de correo electrónico que escribe se convierten automáticamente en hipervínculos para Mail o Safari. Para cambiar uno o varios caracteres por otros, seleccione “Sustitución de símbolos y texto”. A continuación, utilice las filas de la tabla para definir y activar sustituciones específicas. Por ejemplo, para hacer que al escribir los caracteres (c), Keynote los convierta automáticamente en el símbolo ©, ponga una marca de selección en la columna Activo. Para definir su propia sustitución, haga clic en el botón Añadir (+). Para eliminar un elemento seleccionado, haga clic en el botón Eliminar (–). Después de especificar los ajustes de sustitución, éstos se aplicarán a cualquier texto que se modifique o añada a los documentos de Keynote. Cómo insertar un espacio duro Puede insertar un espacio duro entre palabras para asegurarse de que esas palabras aparezcan siempre en la misma línea de texto. Para insertar un espacio duro: m Pulse la barra espaciadora mientras mantiene pulsada la tecla Opción. Capítulo 3 Cómo trabajar con texto 73 Cómo comprobar la ortografía Keynote puede detectar errores ortográficos en el documento y ayudar a encontrar la ortografía correcta de palabras mal escritas. Cómo buscar las palabras mal escritas Es posible configurar el revisor ortográfico para que indique los errores de ortografía mientras escribe, o bien podrá comprobar el documento completo o el texto seleccionado en todo momento. Aparecerá una línea roja debajo de las palabras con errores ortográficos. Éstos son algunos modos de buscar las palabras con errores ortográficos: m Para comprobar la ortografía mientras escribe, seleccione Edición > Ortografía > Comprobar ortografía mientras escribe. Para desactivar la revisión ortográfica mientras escribe, haga clic en Edición > Ortografía > “Comprobar ortografía mientras escribe” para anular la selección de esta opción (asegúrese de que no se vea la marca junto al comando de menú). m Para comprobar la ortografía desde el punto de inserción hasta el final del documento, haga clic para colocar el punto de inserción y seleccione Edición > Ortografía > Comprobar ortografía. Para limitar la revisión ortográfica a una parte específica del documento, seleccione el texto que desea revisar antes de seleccionar el comando. Se resaltará la primera palabra con errores ortográficos que se encuentre. En ese momento, es posible corregirla o volver a seleccionar el mismo comando de menú para continuar revisando el documento. Para aumentar la velocidad de la revisión, pulse Comando + punto y coma (;) para continuar revisando el documento. m Para comprobar la ortografía y visualizar sugerencias para las palabras con errores ortográficos, seleccione Edición > Ortografía > Ortografía. Se abrirá la ventana Ortografía y podrá usarla tal y como se describe en “Cómo trabajar con las sugerencias de ortografía”, el siguiente apartado. 74 Capítulo 3 Cómo trabajar con texto Cómo trabajar con las sugerencias de ortografía Utilice la ventana Ortografía para trabajar con palabras alternativas. Para trabajar con las palabras sugeridas: 1 Seleccione Edición > Ortografía > Ortografía. Se abrirá la ventana Ortografía y la primera palabra con errores ortográficos aparecerá resaltada: 2 Compruebe que está seleccionado el idioma adecuado en el menú local Diccionario. Cada idioma utiliza un diccionario de ortografía diferente. 3 Para reemplazar la palabra incorrecta en el texto, haga doble clic en la palabra u ortografía correcta en la lista Sugerencias. 4 Si la palabra correcta no aparece en la lista Sugerencias, pero conoce la ortografía correcta, seleccione la palabra mal escrita en la ventana Ortografía, escriba la palabra correcta y haga clic en Corregir. 5 Si la ortografía actual es la correcta y desea dejarla tal cual, haga clic en Ignorar o Aprender. Utilice Aprender si se trata de un término que utiliza a menudo y desea añadirlo al diccionario de ortografía. Si ha utilizado la opción Aprender y, más adelante, decide que no desea incluir la palabra en el diccionario, escriba la palabra en el campo de texto situado bajo de la lista Sugerir y, a continuación, haga clic en Olvidar. 6 Si no aparecen opciones alternativas en la lista Sugerencias, seleccione la palabra con errores en la ventana Ortografía e inténtelo con otra ortografía. Haga clic en Sugerencias para ver si aparecen nuevas posibilidades en la lista Sugerencias. 7 Haga clic en Buscar siguiente y repita los pasos del 3 al 6 hasta que no encuentre más errores ortográficos. También puede mantener pulsada la tecla Control y hacer clic en una palabra con errores ortográficos. Desde el menú local podrá seleccionar una ortografía alternativa opcional, hacer clic en Aprender o en Ignorar. Capítulo 3 Cómo trabajar con texto 75 Cómo buscar y reemplazar texto Puede buscar todos los ejemplos de una palabra o frase en su documento y, opcionalmente, cambiarlas por otras diferentes. Éstos son algunos modos de buscar y reemplazar texto: m Seleccione Edición > Buscar > Buscar, haga clic en Sencillo o en Avanzado para configurar los criterios de buscar/reemplazar y, a continuación, haga clic en un botón para buscar/ reemplazar. Sencillo: en el campo Buscar, escriba el texto que desee buscar y escriba el texto por el que desee sustituirlo en el campo Reemplazar. Avanzado: además de escribir el texto para Buscar y Reemplazar, puede configurar criterios adicionales para buscar/reemplazar. Reemplazar todorealiza de forma automática la operación de buscar/reemplazar sin su control. Reemplazar: reemplaza la selección actual por el texto de reemplazo. Reemplazar y buscar: reemplaza la selección actual por el texto de reemplazo y busca inmediatamente la siguiente instancia. Siguiente o Anterior: busca la instancia anterior o siguiente del texto indicado en Buscar. m Utilice los demás comandos del submenú Edición > Buscar. Buscar siguiente o Buscar anterior: busca la instancia siguiente o la instancia anterior del texto especificado actualmente en Buscar. Usar selección para buscar: busca la siguiente instancia del texto seleccionado. Ir a la selección: muestra el texto seleccionado cuando no se esté mostrando en ese momento. 4 76 4 Cómo trabajar con sonido, películas, gráficos y otros objetos En este capítulo se describen las técnicas para añadir y modificar imágenes, figuras, sonido y otros objetos. Un objeto es un elemento que se puede añadir a un documento y, a continuación, manipular. Las imágenes, figuras, películas, archivos de audio, vistas web, tablas, gráficas y cuadros de texto son objetos. Entre las imágenes se incluyen las fotografías o los archivos PDF. Pueden utilizarse películas y sonido a lo largo de un pase de diapositivas o solo con determinadas diapositivas. Entre las figuras se incluyen figuras simples predibujadas (como triángulos y flechas) y figuras personalizadas que dibuje el usuario. Las vistas web son instantáneas de páginas web que pueden mostrarse en una diapositiva. Cómo seleccionar objetos Para poder mover, modificar o realizar otras operaciones en objetos, primero debe seleccionarlos. Un objeto seleccionado tiene tiradores que le permiten mover o manipular los objetos. A continuación, se indica cómo seleccionar y anular la selección de objetos: m Para seleccionar un único objeto, haga clic en cualquier parte del mismo (si no tiene relleno, haga clic en el borde). m Para seleccionar varios objetos de una diapositiva, mantenga pulsada la tecla Mayúsculas mientras hace clic en los objetos. m Para seleccionar todos los objetos de una diapositiva, haga clic en ella y pulse Comando + A. m Para seleccionar un objeto que forme parte de un grupo, primero debe desagrupar los objetos. Seleccione el grupo y, a continuación, seleccione Disposición > Desagrupar. m Para anular la selección de objetos de un grupo de objetos seleccionados, mantenga pulsada la tecla Comando y, a continuación, haga clic en los objetos cuya selección desee anular. Capítulo 4 Cómo trabajar con sonido, películas, gráficos y otros objetos 77 Copia o duplicado de objetos La técnica utilizada para copiar un objeto depende de dónde desee colocar la copia. Si la copia va a estar lejos del original o en otro documento, lo más fácil suele ser copiar y pegar. Si está trabajando con un objeto que se encuentra cerca del original, la duplicación suele ser más fácil. A continuación, se indica cómo copiar objetos: m Para copiar y pegar un objeto, selecciónelo y, a continuación, seleccione Edición > Copiar. Haga clic donde desee que aparezca la copia. Seleccione Edición > Pegar. m Para duplicar un objeto de una diapositiva, mantenga pulsada la tecla Opción mientras arrastra el objeto. También puede duplicar el objeto. Seleccione el objeto y, a continuación, seleccione Edición > Duplicar. La copia aparece en la parte superior del original, ligeramente desplazada. Arrastre la copia a la ubicación deseada. m Para copiar una imagen de un documento de Keynote a otro, seleccione la imagen y arrastre su icono desde el campo “Información del archivo” del inspector de las dimensiones hasta una diapositiva del otro archivo de Keynote. Cómo eliminar objetos La eliminación de objetos es rápida y sencilla. Para eliminar objetos: m Seleccione los objetos y pulse la tecla Suprimir. Si, accidentalmente, elimina un objeto, seleccione Edición > Deshacer Eliminar. Cómo desplazar objetos Para mover objetos, puede arrastrarlos o bien cortarlos y pegarlos. A continuación, se indica cómo mover objetos: m Haga clic en el objeto para seleccionarlo (aparecen los controles de selección), y arrástrelo a una nueva ubicación. m Para limitar el movimiento del objeto en horizontal, vertical o un ángulo de 45 grados, empiece a arrastrar el objeto mientras mantiene pulsada la tecla Mayúsculas. m Para mover el objeto en pequeños incrementos, pulse una de las teclas de flecha, de manera que el objeto se mueva un punto a la vez. Para mover el objeto diez puntos a la vez, mantenga pulsada la tecla Mayúsculas mientras pulsa una tecla de flecha. m Para ver la posición del objeto mientras la mueve, seleccione Keynote > Preferencias y, a continuación, seleccione “Mostrar el tamaño y la posición al desplazar objetos” en el panel General. 78 Capítulo 4 Cómo trabajar con sonido, películas, gráficos y otros objetos m Para alinear objetos con precisión por sus bordes o centros, puede utilizar guías de alineación. Consulte el apartado “Uso de guías de alineación” en la página 79 para más detalles. m Seleccione el objeto y elija Edición > Cortar. Sitúe el punto de inserción donde desee que aparezca el objeto, y luego seleccione Edición > Pegar. Evite arrastrar un objeto mediante los tiradores de selección, ya que puede modificar e tamaño del objeto de forma inadvertida. Cómo mover un objeto hacia delante o hacia atrás (creación de capas con objetos) Si los objetos se superponen o si el texto y los objetos se superponen, puede cambiar el orden de los objetos en la capa. Para mover un objeto delante o detrás del texto u otro objeto: 1 Seleccione el objeto que desea mover. 2 Para mover un objeto capa por capa, seleccionar Disposición > “Traer adelante” o “Enviar atrás”. 3 Para mover un objeto a la parte superior o inferior de la pila, seleccione Disposición > “Traer al frente” o “Enviar al fondo”. Si apila con frecuencia objeto, puede añadir los botones Frente, Fondo, Adelante y Atrás a la barra de herramientas para trabajar de forma más eficaz. Para obtener información acerca de cómo personalizar la barra de herramientas, consulte “La barra de herramientas” en la página 22. Cómo alinear objetos Existen varias formas de alinear los objetos en las diapositivas. Alineación de objetos entre sí en una diapositiva Puede alinear rápidamente objetos entre sí si aparecen en la misma diapositiva. Para alinear objetos: 1 Con la tecla Mayúsculas pulsada, haga clic en los objetos que desea alinear para seleccionarlos. 2 Seleccione Disposición > “Alinear objetos” y, a continuación, seleccione una de las opciones de alineación del submenú. Izquierda: coloca los objetos de manera que sus bordes izquierdos se alineen verticalmente con el primer objeto que seleccione. Centrar: coloca los objetos de manera que sus centros se alineen verticalmente con el primer objeto que seleccione. Derecha: coloca los objetos de manera que sus bordes derechos se alineen verticalmente con el primer objeto que seleccione. Capítulo 4 Cómo trabajar con sonido, películas, gráficos y otros objetos 79 Arriba: coloca los objetos de manera que sus bordes superiores se alineen horizontalmente con el primer objeto que seleccione. Medio: mueve los objetos verticalmente para que sus centros se alineen horizontalmente con el primer objeto que seleccione. Abajo: coloca los objetos de manera que sus bordes inferiores se alineen horizontalmente con el primer objeto que seleccione. También puede alinear objetos entre sí arrastrándolos y utilizando guías de alineación para determinar cuándo están colocados correctamente. Consulte el apartado “Uso de guías de alineación” para obtener más información. Espaciado uniforme de objetos en una diapositiva Puede colocar rápidamente una cantidad igual de espacio entre los objetos, independientemente de su tamaño. Para espaciar objetos de manera uniforme: 1 Seleccione los objetos. 2 Seleccione Disposición > “Distribuir objetos” y, a continuación, seleccione una opción del submenú. Horizontalmente: ajusta el espaciado horizontal entre objetos. Verticalmente: ajusta el espaciado vertical entre objetos. Uso de guías de alineación Puede activar las guías de alineación para que le sirvan de ayuda a la hora de alinear los objetos en una diapositiva. Los ajustes de las guías de alineación se aplican a todos los documentos de Keynote. Para activar las guías de alineación: 1 Seleccione Keynote > Preferencias y haga clic en Reglas. 2 Para mostrar las guías cuando el centro de un objeto se alinee con otro objeto o el centro de la diapositiva, seleccione “Mostrar las guías en el centro del objeto”. 3 Para mostrar las guía cuando los bordes de un objeto se alinean con otro objeto, seleccione “Mostrar guías en los bordes del objeto”. 4 Para cambiar el color de las guías de alineación, haga clic en el contenedor de color y seleccione un color en la ventana Colores. Las guías de alineación no aparecen en las diapositivas impresas. Para mostrar u ocultar las guías, seleccione Visualización > “Mostrar guías” o Visualización > “Ocultar guías”. Para ocultar temporalmente las guías de alineación, mantenga pulsada la tecla Comando mientras arrastra un objeto. También puede crear sus propias guías de alineación para ayudarle a colocar objetos en la misma posición en diferentes diapositivas. 80 Capítulo 4 Cómo trabajar con sonido, películas, gráficos y otros objetos Cómo crear sus propias guías de alineación Puede crear sus propias guías de alineación para que le sirvan de ayuda a la hora de colocar los objetos. Para crear una guía de alineación: 1 Haga clic en Visualización en la barra de herramientas y, a continuación, seleccionar “Mostrar reglas”. 2 Coloque el puntero sobre una regla y arrástrela al lienzo de diapositivas. Aparece una guía de alineación. 3 Arrastre la guía al lugar que desee de la diapositiva. Para eliminar una guía de alineación que haya creado, arrástrela fuera del borde de la diapositiva. Uso de cuadrículas maestras Además de activar las guías de alineación en una diapositiva, puede activar cuadrículas verticales y horizontales que dividan la diapositiva en secciones iguales. Las cuadrículas aparecen en las diapositivas maestras y aparecen en las diapositivas si un objeto (su centro o su borde, según las preferencias de alineación de objetos) se alinea con una cuadrícula. Las cuadrículas no aparecen en las diapositivas impresas. Para activar las cuadrículas maestras: 1 Seleccione Keynote > Preferencias y haga clic en Reglas. 2 Seleccione una o ambas opciones de “Cuadrículas maestras”. 3 Introduzca un valor porcentual en el campo para especificar la cercanía de las líneas de la cuadrícula. 4 Para cambiar el color de la cuadrícula, haga clic en “Cuadrícula maestra” y seleccione un color en la ventana Colores. Para ocultar temporalmente la cuadrícula, mantenga pulsada la tecla Comando mientras arrastra un objeto. Cómo ajustar la posición de los objetos con precisión Utilice el inspector de las dimensiones para colocar los objetos de forma precisa. Para ajustar la posición exacta de un objeto: 1 Seleccione el objeto que desea ubicar. 2 Haga clic en Inspector en la barra de herramientas y, a continuación, haga clic en el botón “Inspector de las dimensiones”. 3 Introduzca los valores X e Y en los campos Posición. Capítulo 4 Cómo trabajar con sonido, películas, gráficos y otros objetos 81 Las coordenadas específicas determinan la posición de la esquina superior izquierda del campo contenedor del objeto.  El valor del eje X se mide desde el borde izquierdo del lienzo de la diapositiva.  El valor del eje Y se mide desde el borde superior del lienzo de la diapositiva. Si se rota un objeto, las coordenadas X e Y especifican la esquina superior izquierda del campo contenedor girado. Cuando se introducen los valores de las coordenadas X e Y para las posiciones de línea en el inspector de las dimensiones, las coordenadas de inicio corresponden al primer extremo que creó. Si más adelante voltea o hace girar la línea, las coordenadas de inicio seguirán correspondiendo al primer extremo. Modificación de objetos Puede cambiar el tamaño de los objetos, cambiar su orientación, modificar los estilos de borde, añadirles sombras y reflejos y ajustar su opacidad. Cambiar el tamaño de los objetos También puede cambiar el tamaño de un objeto arrastrando sus tiradores o escribiendo las dimensiones exactas. A continuación, se indica cómo cambiar el tamaño de objetos: m Para cambiar el tamaño de un objeto arrastrándolo, seleccione el objeto y, a continuación, arrastre uno de sus tiradores de selección. Para cambiar el tamaño de un objeto en una dirección, arrastre un tirador lateral en lugar de un tirador de esquina. Para modificar el tamaño del objeto desde su centro, pulse la tecla Opción mientras arrastra. Para mantener las proporciones de un objeto, mantenga pulsada la tecla Mayúsculas mientras arrastra. También puede hacer clic en el Inspector en la barra de herramientas, hacer clic en el botón “Inspector de las dimensiones” y, a continuación, seleccionar “Mantener proporciones” antes de arrastrar. Coloque una línea fija en la diapositiva especificando las coordenadas X e Y para su segundo extremo. Coloque una línea fija en la diapositiva especificando las coordenadas X e Y para su primer extremo. 82 Capítulo 4 Cómo trabajar con sonido, películas, gráficos y otros objetos Para ver el tamaño de un objeto cuando arrastra un tirador de selección, seleccione Keynote > Preferencias y, a continuación, seleccione “Mostrar el tamaño y la posición al desplazar objetos” en el panel General. m Para cambiar el tamaño de un objeto con las proporciones exactas, seleccione el objeto, haga clic en Inspector en la barra de herramientas, haga clic en el botón “Inspector de las dimensiones” y, a continuación, utilice los controles Anchura y Altura. m Para cambiar el tamaño de varios objetos a la vez, seleccione los objetos, haga clic en Inspector en la barra de herramientas, haga clic en el botón “Inspector de las dimensiones” y, a continuación, escriba valores nuevos en los campos Anchura y Altura. m Seleccione el objeto y, a continuación, haga clic en “Tamaño original” en el inspector de las dimensiones. Volteo y giro de objetos Puede voltear o girar cualquier objeto. Por ejemplo, si desea usar una imagen de una flecha en su documento, pero necesita que apunte en una dirección distinta, puede ubicarla vertical u horizontalmente, o hacer que apunte hacia cualquier ángulo. A continuación, se indica cómo cambiar la orientación de un objeto: m Para voltear un objeto horizontal o verticalmente, seleccione el objeto y, a continuación, seleccione Disposición > “Volteo horizonta”l o Disposición > “Volteo vertical”. También puede hacer clic en Inspector en la barra de herramientas, hacer clic en el botón “Inspector de las dimensiones” y, a continuación, usar los botones de volteo. m Para girar un objeto, seleccione el objeto, mantenga pulsada la tecla Comando y mueva el puntero hacia un tirador de selección activo hasta que se convierta en una flecha curvada con dos puntas y, a continuación, arrastre un tirador de selección. Para girar un objeto en incrementos de 45 grados, pulse las teclas Mayúsculas y Comando mientras arrastra un tirador de selección. También puede hacer clic en Inspector en la barra de herramientas, hacer clic en el botón “Inspector de las dimensiones” y, a continuación, arrastrar la rueda de girar o utilizar los controles de ángulo para ajustar el ángulo del objeto. m Para girar una figura y mantener su texto horizontal, después de girar la figura, seleccione Formato > Figura > Restaurar tiradores de texto y objeto. Capítulo 4 Cómo trabajar con sonido, películas, gráficos y otros objetos 83 Cambio del estilo de bordes En el caso de figuras, elementos de una gráfica, cuadros de texto y celdas de tabla, puede seleccionar un estilo de línea y un color para el borde del objeto, o especificar que no desea bordes. También puede añadir bordes alrededor de imágenes importadas. Ajuste el estilo de línea y color del borde usando el inspector de la figura y la ventana Colores. Para ajustar el estilo y color de la línea del borde de un objeto: 1 Seleccione el objeto que desea modificar. 2 Haga clic en Inspector en la barra de herramientas y, a continuación, haga clic en el botón “Inspector de la figura”. 3 Seleccione Línea en el menú local Trazo. 4 Seleccione un estilo de línea en el menú local. Para las tablas, solo están disponibles la línea sólida y la opción Ninguno. 5 Para cambiar el grosor de línea, escriba un valor en el campo Trazo (o haga clic en las flechas). 6 Para cambiar el color de la línea, haga clic en el contenedor de color y seleccione un color. 7 Para que la línea tenga un punto final, como una punta de flecha o un círculo, seleccione puntos finales sobre derecha e izquierda en los menús locales. Cómo enmarcar objetos Encierre los cuadros de texto, las imágenes, las películas, las figuras y los marcadores de posición de contenidos dentro de bordes gráficos (los llamados marcos de imagen). A continuación, presentamos distintos procedimientos para trabajar con marcos de imagen: m Si desea añadir un marco de imagen, seleccione el contenido o el marcador de posición multimedia, haga clic en Inspector en la barra de herramientas y, a continuación, haga clic en el botón “Inspector de la figura”. Seleccione “Marco de imagen” en el menú local Trazo y, a continuación, haga clic en la miniatura para seleccionar uno. Seleccione un tipo de extremo de línea en estos menús locales. Haga clic en el contenedor de color y seleccione un color de línea. Escriba un grosor de línea. (“px” es la abreviatura de píxeles.) Seleccione un estilo de línea. Seleccione Línea. 84 Capítulo 4 Cómo trabajar con sonido, películas, gráficos y otros objetos Algunos marcos de imagen se pueden ajustar. Para ajustar el marco, utilice el regulador de escala o escriba un porcentaje específico en el campo adyacente. m Si desea cambiar un marco de imagen, seleccione el contenido o el marcador de posición multimedia enmarcado, haga clic en Inspector en la barra de herramientas y, a continuación, haga clic en el botón “Inspector de la figura”. Seleccione “Marco de imagen“ en el menú local Trazo y, a continuación, haga clic en la flecha situada junto a la miniatura para seleccionar un marco de imagen nuevo. m Para eliminar un marco de imagen del contenido o el marcador de posición multimedia, seleccione el contenido o el marcador de posición multimedia y, a continuación elija un estilo de línea (o Ninguno) en el menú local Trazo. Cómo añadir sombras Las sombras proporcionan a los objetos una sensación de profundidad. La sombra de un objeto aparece sobre cualquier objeto que esté detrás. Puede crear diferentes efectos de sombra o eliminar la sombra de un objeto. Haga clic en esta flecha o en la miniatura para seleccionar un estilo de marco. Modifique el color de la sombra en el contenedor de color. Seleccione la opción para añadir una sombra a un objeto seleccionado. Cambie el ángulo de la sombra con la rueda Ángulo. Los valores de Desplazamiento, Difuminación y Opacidad cambian la apariencia de la sombra. Capítulo 4 Cómo trabajar con sonido, películas, gráficos y otros objetos 85 Para añadir una sombra a un objeto: 1 Seleccione el objeto. 2 Haga clic en Inspector en la barra de herramientas y, a continuación, haga clic en el botón “Inspector de la figura”. 3 Seleccione Sombra para añadir una sombra al objeto. Anule la selección de Sombra para eliminar una sombra. 4 Ajuste el ángulo de la sombra con los controles de ángulo. 5 Para ajustar la distancia de la sombra con respecto al objeto, utilice los controles de desplazamiento. Un valor de desplazamiento de sombra elevado hace que la sombra de un objeto se vea más larga y un poco más separada del mismo. 6 Para ajustar la suavidad del borde de la sombra, utilice los controles de difuminado. Un valor alto de difuminación hace que la sombra del objeto se vea más difusa; un valor bajo le da a la sombra bordes más definidos. 7 Para cambiar la transparencia de la sombra, utilice los controles de opacidad. No utilice el regulador de opacidad situado en la parte inferior del inspector de la figura, que sirve para controlar la opacidad del objeto. 8 Para cambiar el color de la sombra, haga clic en el contenedor “Color de la sombra” y seleccione un color. También puede utilizar los controles de sombra del inspector de la figura para añadir sombras al texto. Seleccione el texto al que desea añadir sombras y utilice los controles tal como se ha descrito. Este objeto posee las propiedades de sombra por omisión. La sombra de este objeto está ajustada sobre un ángulo diferente. La sombra de este objeto posee un valor de desplazamiento alto. La sombra de este objeto posee el factor de difuminación más bajo. Este objeto posee un color de sombra diferente. La sombra de este objeto posee un valor de difuminación alto. 86 Capítulo 4 Cómo trabajar con sonido, películas, gráficos y otros objetos Cómo añadir un reflejo Puede añadir a un objeto un reflejo vertical hacia abajo. Para añadir un reflejo a un objeto: 1 Seleccione el objeto. 2 Haga clic en Inspector en la barra de herramientas y, a continuación, haga clic en el botón “Inspector de la figura”. 3 Seleccione Reflejo y arrastre el regulador para aumentar o reducir la cantidad de reflejo. Ajuste de Opacidad Puede crear efectos interesantes haciendo que los objetos sean más o menos opacos. Si se ubica un objeto con opacidad baja encima de otro objeto, por ejemplo, el objeto situado debajo se muestra a través del de arriba. Dependiendo de cuán alto o bajo sea el ajuste de opacidad, los objetos de atrás pueden volverse muy visibles, en parte oscurecidos o totalmente imposibles de ver (con una opacidad del 100%). Para cambiar la opacidad de un objeto: 1 Seleccione el objeto. 2 Haga clic en Inspector en la barra de herramientas y, a continuación, haga clic en el botón “Inspector de la figura”. 3 Arrastre el regulador de opacidad o introduzca un porcentaje en el campo adyacente. Capítulo 4 Cómo trabajar con sonido, películas, gráficos y otros objetos 87 En el caso de las figuras, puede ajustar la opacidad de los colores del relleno y el trazo independientemente de la opacidad del objeto. Si mueve el regulador Opacidad en la ventana Colores para modificar el relleno o trazo de un color, ese valor de opacidad se convierte en el valor máximo de opacidad del objeto. Luego, cuando modifique la opacidad del objeto en el inspector de la figura, estará cambiando de forma relativa el nivel de opacidad ajustado en la ventana Colores. Si cambia la opacidad de un objeto y después no puede Restaurar el color de relleno del objeto al 100%, puede deberse a que la opacidad se ajustó en menos del 100% en la ventana Colores. Para solucionarlo, seleccione el objeto, seleccione Visualización > Mostrar colores y, a continuación, ajuste la opacidad en la ventana Colores al 100%. Cómo agrupar y bloquear objetos Agrupe los objetos que desea mantener juntos y bloquee los objetos que no desea que se muevan accidentalmente. Cómo agrupar y desagrupar objetos Es posible agrupar objetos para moverlos, copiarlos, redimensionarlos y orientarlos como si fuesen un solo objeto. Es posible editar el texto asociado a una figura u objeto de texto de un grupo, pero no modificar los demás atributos de cada objeto específico del grupo. Los objetos agrupados se crean como una unidad durante las composiciones de objetos. Para agrupar objetos: 1 Mantenga pulsada la tecla Comando (o Mayúsculas) mientras selecciona los objetos que desea agrupar. Si no puede seleccionar un objeto, es posible que esté bloqueado. 2 Seleccione Disposición > Agrupar o haga clic en Agrupar en la barra de herramientas. Para desagrupar un objeto agrupado, seleccione el grupo y, a continuación, seleccione Disposición > Desagrupar o haga clic en Desagrupar en la barra de herramientas. Si el grupo está bloqueado, desbloquéelo primero. Este círculo está ajustado en el 100% de opacidad en el “Inspector de la figura”. El relleno de color está ajustado al 50% de opacidad en la ventana de colores. El contorno del círculo está ajustado al 100% de opacidad en la ventana de colores. Este círculo está ajustado en el 100% de opacidad en el “Inspector de la figura”. Este círculo está ajustado en el 50% de opacidad en el “Inspector de la figura”. 88 Capítulo 4 Cómo trabajar con sonido, películas, gráficos y otros objetos Si agrupa un objeto al que se le asignó un efecto de composición, el efecto es eliminado. Al desagrupar un objeto agrupado que incluya un efecto de composición asignado, también se eliminará el efecto de composición. Bloqueo y desbloqueo de objetos Puede bloquear objetos para evitar moverlos de manera accidental mientras trabaja. Los objetos individuales o agrupados que estén bloqueados no se pueden mover, eliminar ni modificar hasta que se desbloqueen. Los objetos bloqueados se pueden seleccionar, copiar o duplicar; cuando se copia o duplica un objeto bloqueado, el nuevo objeto también estará bloqueado. Para bloquear objetos: 1 Mantenga pulsada la tecla Comando (o Mayúsculas) mientras selecciona los objetos que desea bloquear. 2 Seleccione Disposición> Bloquear. Para desbloquear un objeto, selecciónelo y, a continuación, seleccione Disposición > Desbloquear. Cómo rellenar objetos Rellene un objeto con un color sólido, un degradado de color o una imagen. Cómo rellenar un objeto con color Utilice el “Inspector de la figura” para rellenar un objeto con un color sólido o un degradado de color, donde dos colores se mezclen gradualmente entre sí. Para cambiar el color de relleno de un objeto: 1 Seleccione el objeto. 2 Haga clic en Inspector en la barra de herramientas y, a continuación, haga clic en el botón “Inspector de la figura”. 3 Para aplicar un color de relleno sólido, seleccione “Relleno de color” en el menú local Relleno. Haga clic en el contenedor de color situado debajo del menú local Relleno para abrir la ventana Colores y, a continuación, seleccione un color en la ventana Colores. 4 Para rellenar un objeto con un degradado de color, seleccione “Relleno degradado” en el menú local Relleno. Haga clic en cada paleta de colores y seleccione cada color en la ventana Colores. Para ajustar la dirección del gradiente, use la rueda o campo Ángulo. Para voltearlo horizontal o verticalmente, haga clic en los botones de ángulo con forma de flecha. Capítulo 4 Cómo trabajar con sonido, películas, gráficos y otros objetos 89 Para invertir el gradiente, haga clic en la flecha de dos puntas que está junto a las paletas de colores. A continuación, se proporcionan instrucciones para utilizar la ventana Colores. Uso de la ventana Colores Utilice la ventana Colores para seleccionar un color para los objetos. Puede usar la rueda de color en la ventana Colores para seleccionar diferentes colores. El color que seleccione aparece en el cuadro en la parte superior de la ventana Colores. Puede guardar ese color para su uso futuro situándolo en la paleta de colores. Para aplicar los colores seleccionados en la ventana Colores a un objeto de la diapositiva, debe colocar el color en el contenedor de color apropiado de un panel de inspector. Puede seleccionar un contenedor de color en uno de los inspectores y, a continuación, hacer clic en un color de la rueda de color. También puede arrastrar un color desde la paleta de colores o desde el cuadro de color hasta un contenedor de color de uno de los inspectores. Haga clic sobre cada paleta de colores para seleccionar colores. Cambie la orientación del degradado o ajuste su dirección usando los botones de flecha o la rueda Ángulo, o escribiendo un valor. Haga clic sobre la flecha de dos puntas para invertir el gradiente. El color seleccionado en la rueda de color aparece en este cuadro. (Los dos colores de este cuadro indican que la opacidad está ajustada en menos del 100%.) Use el regulador para ajustar los matices más claros y oscuros en la rueda de color. Arrastre los colores desde el cuadro de color para guardarlos en la paleta de colores. Haga clic para seleccionar un color en la rueda de color. Arrastre el regulador de opacidad hacia la izquierda para hacer el color más transparente. Haga clic en el icono de búsqueda y luego haga clic en cualquier elemento de la pantalla para buscar el color equivalente. Haga clic en un botón para visualizar distintos modelos de colores. 90 Capítulo 4 Cómo trabajar con sonido, películas, gráficos y otros objetos Para seleccionar un color: 1 Abra la ventana Color haciendo clic en Colores en la barra de herramientas o haciendo clic en un contenedor de color de uno de los inspectores. 2 Haga clic en cualquier parte de la rueda de color. El color seleccionado aparece en el cuadro de colores en la parte superior de la ventana Colores. 3 Para que el color se vuelva más claro o más oscuro, arrastre el regulador sobre el lado derecho de la ventana Colores. 4 Para que el color se vuelva más transparente, arrastre el regulador de Opacidad hacia la izquierda o introduzca un valor porcentual en el campo Opacidad. 5 Para utilizar la paleta de colores, ábrala arrastrando el tirador de la parte inferior de la ventana Colores. Para guardar un color en la paleta, arrástrelo desde el cuadro de color hasta la paleta de colores. Para eliminar un color de la paleta, arrastre un cuadrado en blanco hasta el color que desea eliminar. 6 Para igualar el color de otro elemento de la pantalla, haga clic en la lupa situada a la izquierda del cuadro de color en la ventana Colores. Haga clic sobre el ítem en la pantalla cuyo color desee igualar. El color aparece en el cuadro de colores. Seleccione el elemento que desee colorear en la ventana del documento y, a continuación, arrastre el color desde el cuadro de colores hasta el elemento. Cómo rellenar un objeto con una imagen Puede rellenar una figura, un cuadro de texto, una tabla, una celda de una tabla, el fondo de una gráfica o una serie de gráficas con una imagen. Para rellenar un objeto con una imagen: 1 Seleccione el objeto que desee rellenar con una imagen. 2 Si el inspector de la figura no está abierto, haga clic en el botón Inspector de la barra de herramientas y, a continuación, haga clic en el botón “Inspector de la figura”. 3 En el inspector de la figura, seleccione “Relleno de imagen” o “Relleno de imagen teñida” y, a continuación, seleccione una imagen. También puede arrastrar un archivo de imagen desde el Finder o el visualizador multimedia hasta el contenedor de imágenes del inspector de la figura. También puede arrastrar una imagen a una celda de una tabla o una serie de gráficas. Utilice el menú local para ajustar el tamaño de la imagen dentro del objeto. Para modificar la imagen, arrastre una imagen sobre el contenedor de imagen. Capítulo 4 Cómo trabajar con sonido, películas, gráficos y otros objetos 91 4 Seleccione una escala de imagen del menú local. Escalar hasta ajustar: redimensiona la imagen para lograr el mejor ajuste posible a las dimensiones del objeto. Si la forma del objeto es diferente de la imagen original, es posible que algunas partes de la imagen no aparezcan; también puede aparecer un espacio en blanco alrededor de la imagen. Escalar hasta llenar: amplía o reduce la imagen de manera que quede un espacio vacío mínimo a su alrededor, aunque la forma del objeto y de la imagen sea distinta. Ajustar: modifica el tamaño de la imagen para ajustarla a las dimensiones del objeto y la distorsiona si la forma del objeto es diferente de la de la imagen original. Tamaño original: ubica la imagen dentro del objeto sin alterar sus dimensiones originales. Si la imagen es más grande que el objeto, solo se ve parte de la imagen en el mismo. Si la imagen es más pequeña que el objeto, queda un espacio en blanco alrededor del mismo. En mosaico: repite la imagen dentro del objeto si la imagen es más pequeña que el mismo. Si la imagen es más grande que el objeto, solo se ve parte de la imagen dentro del mismo. 5 Si ha seleccionado “Relleno de imagen teñida”, haga clic en el contenedor de color (situado a la derecha del botón Seleccionar) para seleccionar un color de tinte. Arrastre el regulador Opacidad en la ventana Colores para que el teñido sea más oscuro o más claro. (Si arrastra el regulador de Opacidad en el inspector de la figura, cambiará la opacidad tanto del teñido como de la imagen.) Escalar hasta llenar En Mosaico (imagen grande) Tamaño original Escalar hasta ajustar Estirar En Mosaico (imagen pequeña) En Mosaico (imagen grande) Haga clic para seleccionar un color de tinte para la imagen. 92 Capítulo 4 Cómo trabajar con sonido, películas, gráficos y otros objetos Uso de figuras Keynote ofrece distintas figuras predibujadas que puede añadir a las diapositivas. También puede crear sus propias figuras personalizadas. Cómo añadir una figura predibujada Puede insertar figuras predibujadas, como triángulos, flechas, círculos y rectángulos, para utilizarlos como gráficos simples. A continuación, se indica cómo añadir una figura predibujada: m Haga clic en Figuras en la barra de herramientas y, a continuación, seleccione una figura en el submenú Figuras. También puede seleccionar Insertar > Figura > figura. m También puede crear una de las figuras incluidas desde el centro de la figura. Con la tecla Opción pulsada, haga clic en Figuras en la barra de herramientas, seleccione una figura y arrastre el puntero con forma de cruz. Pulse la tecla Mayúsculas mientras arrastra para conservar las proporciones de la figura (por ejemplo, para que los triángulos mantengan todos sus lados iguales). Cómo añadir una figura personalizada Puede utilizar la herramienta de dibujo para crear sus propias figuras. Para crear una figura personalizada: 1 Haga clic en Figuras en la barra de herramientas y seleccione la herramienta de dibujo (o seleccione Insertar > Figura > Dibujar una figura). El cursor pasará de ser una flecha a mostrar la punta de una pluma. 2 Haga clic en cualquier punto del documento para crear el primer punto de la figura personalizada. 3 Haga clic para crear más puntos. Cada punto que añada se conectará al anterior. La figura se rellenará con el color por omisión del tema que esté utilizando. Para borrar un segmento que acabe de crear, pulse la tecla Suprimir. Puede pulsar Suprimir varias veces. 4 Para dejar de dibujar y cerrar la figura (es decir, añadir una línea sólida entre el último punto y el primero), haga clic en el primer punto. Capítulo 4 Cómo trabajar con sonido, películas, gráficos y otros objetos 93 Para dejar de dibujar y dejar la abierta la figura (sin ninguna línea entre el primer punto y el último), de forma que pueda completarla más adelante, pulse Esc o haga doble clic en el último punto creado. Para finalizar y cerrar una figura abierta, haga clic una vez en la figura para seleccionarla y, a continuación, haga clic en la figura por segunda vez para mostrar sus puntos. Haga doble clic en uno de los dos puntos de cualquiera de los extremos del segmento abierto. El puntero se convertirá en una pluma. Para añadir puntos adicionales, haga clic en otras ubicaciones, en función de sus necesidades. Cuando esté listo para dejar de dibujar y cerrar la figura, haga clic en el punto final del segmento abierto. Cómo convertir figuras en editables Además de cambiar el tamaño de las figuras, puede manipular los puntos de las mismas. Para editar una figura de esta forma, debe convertirla en editable. A continuación, se indica cómo convertir figuras en editables: m Para convertir una figura predibujada en editable, seleccione la figura y, a continuación, seleccione Formato > Figura > Convertir en editable. Aparecerán puntos rojos en la figura. Arrástrelos para editar la figura. Más adelante, para editar una figura predibujada que se haya convertido en editable, haga doble clic en ella lentamente. m Para convertir una figura personalizada en editable, haga clic una vez en la figura para seleccionarla y, a continuación, haga clic una segunda vez para mostrar sus puntos. Manipulación de los puntos de una figura Puede cambiar el contorno de una figura añadiendo, moviendo o eliminando sus puntos. En primer lugar, debe convertir la figura en editable, tal y como se describe en “Cómo convertir figuras en editables” en la página 93. Aquí está el segmento abierto. Haga clic en un punto y arrástrelo para modificar la figura. 94 Capítulo 4 Cómo trabajar con sonido, películas, gráficos y otros objetos A continuación, se indica cómo manipular los puntos de una figura: m Para añadir un punto, convierta la figura en editable, pulse la tecla Opción y, a continuación, mantenga el puntero sobre el borde de la figura. El puntero se convierte en una punta de pluma con un signo más (+). Haga clic en la ubicación del borde donde desee añadir un punto y, si es necesario, mueva el punto. m Para mover un punto, convierta la figura en editable, haga clic en el punto y, a continuación, arrástrelo a otra ubicación. Para mover varios puntos a la vez, haga clic en varios puntos con la tecla Mayúsculas pulsada y arrastre. m Para eliminar un punto, convierta la figura en editable, haga clic en el punto y, a continuación, pulse la tecla Suprimir. Para borrar varios puntos a la vez, pulse Mayúsculas, haga clic en varios puntos con la tecla Mayúsculas pulsada y pulse Suprimir. Cómo modificar la forma de una curva Puede expandir o contraer una curva, o cambiar su ángulo. Para modificar la forma de una curva: 1 Convierta la figura en editable. 2 Haga clic en un control circular rojo de la curva que va a modificar. Aparecerá un tirador de control a ambos lados del control circular. 3 Para ampliar o contraer la curva, arrastre el control circular o uno de los tiradores de control. 4 Para cambiar el ángulo de la curva, mueva los tiradores de control hacia la derecha o hacia la izquierda. Se obtienen efectos diferentes cuando se mueven los tiradores juntos o por separado. Vaya probando hasta que obtenga el efecto deseado. Para mover los tiradores de control a la vez, pulse la tecla Opción y, a continuación, arrastre uno de ellos. Para mover solo un tirador de control, pulse la tecla Comando antes de arrastrar un tirador. Para modificar la curva, arrastre un tirador de control o gire uno o ambos tiradores de control. También puede arrastrar un punto para modificar la curva. Capítulo 4 Cómo trabajar con sonido, películas, gráficos y otros objetos 95 Cómo modificar la forma de un segmento recto Puede cambiar el ángulo entre dos segmentos, o cambiar la longitud de un segmento. Para modificar la forma de un segmento recto: 1 Convierta la figura en editable. 2 Haga clic en un punto angular. 3 Arrastre el punto hacia la derecha o hacia la izquierda para cambiar el ángulo entre los dos segmentos unidos. 4 Arrastre el punto hacia fuera o hacia dentro para cambiar la longitud de uno de los segmentos. Transformación de puntos angulares en puntos curvados y viceversa Puede convertir uno o más puntos en curvas o curvas en puntos. A continuación, se indica cómo transformar puntos angulares en puntos curvados y viceversa: m Para transformar un punto angular en uno curvado, convierta la figura en editable y haga doble clic en el punto angular. m Para transformar un punto curvado en uno angular, convierta la figura en editable y haga doble clic en el punto curvado. m Para convertir todos los puntos angulares de una o varias figuras en puntos curvados, convierta las figuras en editables, selecciónelas y, a continuación, elija Formato > Figura > Redondear contorno. m Para convertir todos los puntos angulares de una o varias figuras en puntos curvados, convierta las figuras en editables, selecciónelas y, a continuación, elija Formato > Figura > Afilar contorno. Una vez que una figura sea editable, puede utilizar los comandos Redondear Contorno y Afilar Contorno sin tener que volver a hacerla editable. Cómo editar figuras predibujadas concretas Algunas figuras predibujadas tienen controles de edición especiales integrados. 96 Capítulo 4 Cómo trabajar con sonido, películas, gráficos y otros objetos Edición de un rectángulo redondeado El rectángulo redondeado tiene un control circular que le permite modificar los vértices. Para editar un rectángulo redondeado: m Seleccione la figura y arrastre el control circular hacia la izquierda para afilar los vértices y hacia la derecha para redondearlos. Edición de flechas simples y dobles Las flechas tienen tres controles especiales. A continuación, se indica cómo editar flechas simples o dobles tras seleccionarlas: m Arrastre el control de la cola o la punta de la flecha para aumentar o reducir la longitud de la cola sin cambiar la forma de la punta de flecha. m Arrastre el control circular hacia arriba o hacia abajo para cambiar el ancho de la cola. m Arrastre el control circular hacia la izquierda o hacia la derecha para cambiar el tamaño de la punta de flecha. Arrastre este control para afilar o redondear el vértice. Arrastre este control para cambiar la longitud de la cola. Arrastre este control hacia arriba o hacia abajo para cambiar el ancho de la cola. Arrastre este control hacia la izquierda o la derecha para cambiar el tamaño de la punta de flecha. Capítulo 4 Cómo trabajar con sonido, películas, gráficos y otros objetos 97 Edición de una estrella La figura de estrella tiene un regulador para aumentar o reducir el número de puntos de la estrella y un control circular para cambiar los ángulos entre los puntos. A continuación, se indica cómo editar una estrella: m Cuando selecciona la figura de una estrella, aparece el regulador. Arrastre el regulador para aumentar o reducir el número de puntas de la estrella. m Arrastre el control circular para cambiar los ángulos entre los puntos de la estrella. Edición de un polígono El polígono tiene un regulador para aumentar o reducir el número de lados del polígono. Para editar polígonos: m Cuando selecciona el polígono, aparece el regulador. Arrastre este regulador para aumentar o reducir el número de lados del polígono. Uso de marcadores de posición de contenido Muchas diapositivas maestras de Keynote incluyen de marcadores de posición de fotos. En realidad, estos marcadores de posición de fotos son “marcadores de posición de contenidos”. Puede arrastrar sus imágenes, películas y archivos de audio a estos marcadores de posición, y el tamaño y la posición del archivo multimedia se ajustarán automáticamente. Es fácil reemplazar un elemento de un marcador de posición de contenido arrastrando un archivo nuevo sobre este; no es necesario eliminar el archivo antiguo antes. Arrastre este control para cambiar los ángulos entre los puntos de la estrella. Compruebe el número de puntas que tiene la estrella. Arrastre este regulador para aumentar o reducir el número de puntas de la estrella. Arrastre este regulador para aumentar o reducir el número de lados del polígono. Compruebe en el número de lados que tiene el polígono. 98 Capítulo 4 Cómo trabajar con sonido, películas, gráficos y otros objetos Si no está seguro de si una foto u otro elemento de contenido de una diapositiva es un marcador, mantenga el puntero sobre dicho elemento y compruebe si aparece una etiqueta que le indica que arrastre hasta él su propio archivo multimedia. A continuación, se indica cómo trabajar con marcadores de posición de contenido: m Arrastre un archivo del visualizador multimedia, Finder u otra aplicación al marcador de posición de contenido. Para abrir el visualizador multimedia, haga clic en Multimedia en la barra de herramientas. Haga clic en un botón situado en la parte superior de la ventana para buscar archivos de audio, imágenes o películas. m Para cambiar el contenido de un marcador de posición de contenido, arrastre un archivo multimedia nuevo sobre el contenido existente. m Para convertir un marcador de posición de imagen en una imagen, seleccione la imagen y seleccione a continuación Formato > Avanzado > “Definir como marcador de posición de contenidos” (elimine la marca de verificación). m Para eliminar un marcador de posición de contenido, selecciónelo y pulse la tecla Suprimir. m Para crear un marcador de posición de contenido, añada una foto, película o archivo de audio a una diapositiva. Cambie el tamaño del archivo y ajuste los atributos que desee (añada un reflejo, un marco de imagen, etc.) Seleccione Formato > Avanzado > “Definir como marcador de posición de contenidos” (asegúrese de que aparezca una marca de verificación junto al nombre del comando). Cómo trabajar con imágenes Keynote acepta todos los formatos compatibles con QuickTime, entre los que se encuentran los siguientes tipos de archivos gráficos:  TIFF  GIF  JPEG  PDF  PSD  EPS  PICT Después de importar una imagen en un documento, puede enmascararla (recortarla) y cambiar el brillo y otros ajustes. Puede colocar una imagen dentro de una figura, un cuadro de texto, una gráfica o una celda de tabla. Keynote también le permite trabajos con gráficos con transparencia (gráficos de canal alfa). Capítulo 4 Cómo trabajar con sonido, películas, gráficos y otros objetos 99 Cómo importar una imagen Importe una imagen directamente desde el Finder o desde el visualizador multimedia. A continuación, se indica cómo importar un archivo de imagen: m Arrastre un archivo de imagen desde el Finder hasta el documento y colóquelo donde desee. m Arrastre una imagen al navegador de diapositivas para crear una nueva diapositiva que contenga dicha imagen. m Haga clic en Multimedia en la barra de herramientas, haga clic en Fotos en el visualizador multimedia, seleccione el álbum donde se encuentre la imagen y, a continuación, arrastre una miniatura para colocarla donde desee. m Seleccione Insertar > Seleccionar, seleccione el archivo y, a continuación, haga clic en Insertar. Arrastre la imagen para colocarla donde la desee. Por omisión, si el tamaño de una imagen colocada en una diapositiva es mayor que la propia diapositiva, Keynote submuestrea la imagen para que se ajuste a la diapositiva. (Una imagen cuya resolución se ha reducido presenta menos píxeles que la imagen original; se elimina parte de la información de la imagen.) Las imágenes en formato JPEG siguen siendo imágenes JPEG; otros formatos se convierten a TIFF. Una vez que se haya reducido la imagen para ajustarla a la diapositiva, no podrá restaurarla a su tamaño original haciendo clic en “Tamaño original” en el inspector de las dimensiones. Para evitar el uso de imágenes submuestreadas y utilizarlas con su tamaño original, seleccione Keynote > Preferencias, haga clic en General y, a continuación, anule la selección de la opción “Reducir las imágenes hasta ajustarlas a las diapositivas”. Cómo enmascarar (recortar) imágenes Puede recortar imágenes sin modificar los archivos de imagen enmascarando partes de los mismos. Cómo recortar una imagen mediante la máscara por omisión (rectangular) Puede utilizar una máscara rectangular para definir los márgenes de una imagen. Para recortar una imagen mediante la máscara por omisión (rectangular): 1 Importe la imagen que desee enmascarar (consulte el apartado “Cómo importar una imagen” en la página 99 para obtener instrucciones). 2 Seleccione la imagen y haga clic en el botón Máscara en la barra de herramientas. 100 Capítulo 4 Cómo trabajar con sonido, películas, gráficos y otros objetos Aparecerá una máscara sobre la imagen, así como una serie de controles. 3 Para cambiar el tamaño de la imagen, arrastre el regulador situado sobre el botón “Editar máscara”. 4 Para perfeccionar la máscara, siga alguno de estos pasos:  Arrastre los tiradores de selección para cambiar el tamaño de la máscara. Para limitar las proporciones de la máscara, mantenga pulsada la tecla Mayúsculas mientras arrastra.  Para girar la máscara, mantenga pulsada la tecla Comando mientras arrastra un tirador de selección de la esquina.  Arrastre la imagen para colocar la parte que desea mostrar. Para mover la máscara, haga clic en el borde de puntos de la misma y arrástrelo. 5 Para que solo sea visible el área situada bajo la máscara, haga doble clic en la máscara o en la imagen, pulse Retorno y haga clic fuera de la imagen o en “Editar máscara”. 6 Para redimensionar o girar la imagen enmascarada, arrastre, o arrastre con la tecla Comando pulsada, los tiradores de selección. 7 Para anular la selección de la imagen y ocultar los controles de la máscara, haga clic fuera de la imagen. Cómo enmascarar una imagen con una figura Puede utilizar una figura para definir los límites de una imagen. Para enmascarar una imagen con una figura: 1 Realice una de las siguientes acciones:  Seleccione la imagen y, a continuación, seleccione Formato > Enmascarar con figura > figura.  Con la tecla Mayúsculas pulsada, haga clic para seleccionar una figura y una imagen y, a continuación, haga clic en Máscara en la barra de herramientas (o seleccione Formato > Enmascarar con la figura seleccionada). 2 Arrastre la imagen para colocar la parte que desea mostrar. Para mover la máscara, haga clic en el borde de puntos de la misma y arrástrelo. 3 Para cambiar el tamaño de la imagen, arrastre el regulador situado sobre el botón “Editar máscara”. Arrastre los tiradores de selección para redimensionar la máscara. Arrastre la imagen para colocar la parte que desea mostrar. Arrastre el regulador para redimensionar la imagen. Haga clic para mostrar u ocultar el área exterior de la máscara. Capítulo 4 Cómo trabajar con sonido, películas, gráficos y otros objetos 101 4 Arrastre los tiradores de selección para cambiar el tamaño de la máscara. 5 Para que sólo esté visible el área situada bajo la máscara, haga doble clic en la máscara o en la imagen, pulse Retorno y haga clic fuera de la imagen o en “Editar máscara”. 6 Para redimensionar la imagen enmascarada, haga clic en Editar máscara y arrastre los tiradores de selección. 7 Para anular la selección de la imagen y ocultar los controles de la máscara, haga clic fuera de la imagen. Para modificar una imagen enmascarada, haga doble clic sobre ella. Nota: Si utiliza como máscara una figura que incluya texto, el texto se eliminará. Para restaurar el texto, seleccione Edición > Deshacer máscara con figura. También puede arrastrar una imagen para enmascarar una figura con ella. Cómo desenmascarar una imagen Puede eliminar una máscara y restaurar la imagen original. Para desenmascarar una imagen: m Seleccione la imagen enmascarada y haga clic en Desenmascarar en la barra de herramientas (o seleccione Formato > Desenmascarar). Eliminación del fondo o de elementos no deseados de una imagen La herramienta “Alfa instantáneo” le permite convertir determinados colores de una imagen en transparentes. Esta característica es útil para eliminar un fondo no deseado u otros colores. Obtendrá los mejores resultados eliminando colores sólidos con márgenes claros. Para eliminar áreas que no se diferencian tan claramente, seleccione un área más pequeña y repita del proceso. Para eliminar elementos no deseados: 1 Seleccione la imagen. 2 En la barra de herramientas, haga clic en Alfa (o seleccione Formato > Alfa instantáneo). 102 Capítulo 4 Cómo trabajar con sonido, películas, gráficos y otros objetos 3 Haga clic en el color que desee convertir en transparente y arrastre el ratón lentamente sobre el mismo. A medida que se arrastra, la selección crece para incluir el área contigua que utiliza el color similar. Puede controlar la parte de la imagen seleccionada arrastrando menos o más. 4 Repita el paso 3 tantas veces como desee. Puede restaurar las partes eliminadas de la imagen en cualquier momento. Para restaurar la imagen original, seleccione Formato > Eliminar alfa instantáneo. Para restaurar partes de la imagen eliminadas con alfa instantáneo, seleccione Edición > “Deshacer alfa instantáneo” hasta que se restauren las partes. Cambio del brillo, el contraste y otros ajustes de una imagen Puede cambiar el brillo, el contraste y otros ajustes de las imágenes para mejorar su calidad o crear efectos interesantes. Los ajustes que realice no afectarán la imagen original sino únicamente su apariencia en Keynote. Al arrastrar se selecciona al área contigua que utiliza un color similar al seleccionado. Si arrastra más aquí.... ...se selecciona una parte mayor de la imagen. Capítulo 4 Cómo trabajar con sonido, películas, gráficos y otros objetos 103 Para ajustar una imagen: 1 Seleccione la imagen. 2 Seleccione Visualización > Mostrar Ajustar imagen. 3 Use los controles para realizar ajustes. Botón Mejorar: ajusta la imagen de forma automática. Brillo: ajusta la luminosidad de la imagen. Contraste: ajusta el contraste entre los tonos claros y los oscuros. Puede hacer las sombras más oscuras, agudizar los bordes de los objetos y resaltar los colores. Si aumenta mucho el contraste de una foto, se parecerá más a una ilustración. Saturación: cambia la intensidad del color. Temperatura: introduce más calidez (tonos más naranjas) o frialdad (tonos más azules). Tinte: modifica la cantidad de tonos rojos y verdes de la imagen. Nitidez: agudiza y atenúa el foco de la imagen. Exposición: ajusta las sombras y los resaltados. Histograma: le ayuda a comprender la relación que existe entre las sombras (representadas en el lado izquierdo de la pantalla) y los resaltados (representados en el lado derecho) de la imagen. Niveles: cambia los niveles de los tonos claros y oscuros. Niveles automáticos: hace que Keynote mejore los colores automáticamente. Ajuste el contraste entre los tonos claros y los oscuros. Cambie la intensidad del color. Introduzca tonos más cálidos o más fríos. Cambie la proporción del tono rojo y el tono verde. Agudice o atenúe el foco. Ajuste las sombras y los resaltados. Comprenda la relación entre sombras y resaltados. Cambie los niveles de los tonos oscuros y claros. Restaure los ajustes originales. Ajuste la luminosidad. Mejore los colores automáticamente. 104 Capítulo 4 Cómo trabajar con sonido, películas, gráficos y otros objetos 4 Para restaurar los ajustes originales, haga clic en “Restaurar imagen”. Para guardar los cambios realizados, guarde el documento. Los ajustes en el momento de guardar el documento pueden verse siempre que se abra la ventana “Ajustar imagen”. Uso del sonido y películas Puede añadir audio (un archivo de música o una lista de reproducción de su biblioteca de iTunes, o cualquier otro archivo de sonido) a un documento de Keynote. Puede hacerlo de las siguientes formas:  En una diapositiva individual. El sonido se reproduce cuando la diapositiva aparece y se detiene cuando el pase de diapositivas avanza. Consulte “Cómo añadir sonido a una diapositiva” en la página 105.  Como banda sonora de todo el pase de diapositivas. El sonido comienza a reproducirse cuando se inicia el pase de diapositivas. Consulte “Cómo añadir una banda sonora a un pase de diapositivas” en la página 105.  Como narración grabada. Puede grabarse mientras explica cada diapositiva. Consulte “Cómo añadir una narración” en la página 107. También puede añadir películas de vídeo o Flash que se reproducirán en una diapositiva. Para que Flash funcione con QuickTime 7.1.3 y versiones posteriores, seleccione menú Apple > Preferencias del Sistema, haga clic en QuickTime, en Avanzado y seleccione “Activar Flash”. Keynote acepta todos los tipos de archivo QuickTime o iTunes, incluidos los siguientes:  MOV  FLASH  MP3  MPEG-4  AIFF  AAC Nota: Algunos archivos multimedia están protegidos por la legislación sobre propiedad intelectual y derechos de autor. Asimismo, algunos archivos de música descargados de Internet sólo pueden reproducirse en el ordenador en el que se han descargado. Asegúrese de que posee autorización para utilizar las imágenes que desea añadir a las diapositivas. Importante: Para asegurarse de que las películas y otros contenidos multimedia puedan reproducirse y visualizarse al transferir el documento a otro ordenador, asegúrese de tener seleccionada la opción “Copiar películas y sonido en el documento”; después de seleccionar Guardar o “Guardar como”, haga clic en el triángulo desplegable situado junto al campo y, a continuación, en “Opciones avanzadas”. Capítulo 4 Cómo trabajar con sonido, películas, gráficos y otros objetos 105 Cómo añadir sonido a una diapositiva Añada sonido que se reproduzca cuando aparezca una diapositiva y que se detenga cuando se mueva a la siguiente diapositiva. A continuación, se indica cómo añadir sonido a una diapositiva: m Arrastre un archivo de sonido desde el Finder hasta una diapositiva. m Haga clic en Multimedia en la barra de herramientas, seleccione iTunes en el menú local, seleccione una lista de reproducción y, a continuación, arrastre un archivo al lienzo de diapositivas o a un marcador de posición de contenido. (También puede arrastrar una lista de reproducción.) Si lo desea, puede controlar con más precisión el momento de inicio y detención de la música mediante los efectos “Iniciar audio” y “Detener audio” del inspector de la composición. Para obtener más información, consulte “Cómo animar las diapositivas con composiciones de objetos” en la página 113. Cómo añadir una banda sonora a un pase de diapositivas Si añade una banda sonora, la música comienza a reproducirse cuando el pase de diapositivas se inicia. Puede elegir entre reproducir la música una sola vez o repetidamente, o puede desactivarla. Para añadir una banda sonora: 1 Haga clic en el botón Inspector de la barra de herramientas y, a continuación, haga clic en el botón “Inspector del documento”. 2 Haga clic en el botón Audio. 3 Arrastre un archivo de audio o una lista de reproducción desde el visualizador multimedia hasta el contenedor Audio del inspector de documentos. Si modifica una lista de reproducción, el cambio no se reflejará en la banda sonora hasta que vuelva a añadir la lista de reproducción. También puede arrastrar un archivo de sonido desde el Finder. 4 Para repetir el archivo de sonido mientras dure la presentación, seleccione Bucle en el menú local del inspector de documentos. Botón “Inspector del documento” Arrastre aquí un archivo de sonido para reproducirlo durante el pase de diapositivas. Para repetir el archivo de sonido, seleccione Bucle. Ajuste el volumen de la banda sonora. El botón Audio Previsualice su archivo de sonido. 106 Capítulo 4 Cómo trabajar con sonido, películas, gráficos y otros objetos Cómo añadir una película Puede añadir una película a una diapositiva para que se reproduzca cuando aparezca la diapositiva o cuando el presentador haga clic con el ratón. A continuación, se indica cómo añadir una película: m Arrastre un archivo de película desde el Finder hasta el lienzo de diapositivas o hasta un marcador de posición de contenido. m Haga clic en Multimedia en la barra de herramientas; a continuación, haga clic en Películas, seleccione un archivo y arrástrelo hasta el lienzo de diapositivas o hasta un marcador de posición de contenido. m Seleccione Insertar > Seleccionar, seleccione el archivo de película y, a continuación, haga clic en Insertar. Al reproducir una película durante una presentación, los controles de películas se muestran en pantalla al mover el puntero sobre la película si está seleccionada la opción “Mostrar controles de reproducción cuando el puntero esté sobre una película” en el panel “Pase de diapositivas” de las preferencias de Keynote. Los controles disponibles dependen del tamaño (dimensiones) de la película: cuanto más pequeña es la película, menos controles se ven. Véase también “Creación de composiciones de películas” en la página 125. Cómo ajustar los parámetros de reproducción de contenidos multimedia En el inspector de QuickTime puede cambiar determinados ajustes, como cuándo iniciar y detener la película y qué fotograma mostrar hasta que comience la reproducción de la misma. Para definir las preferencias de reproducción multimedia: 1 Haga clic en Inspector en la barra de herramientas y, a continuación, haga clic en el botón “Inspector de QuickTime”. 2 Haga clic en la película o en el objeto de sonido para seleccionarlo. 3 Para iniciar y detener la película en fotogramas o momentos concretos, arrastre los reguladores de inicio y detención. 4 Para especificar el fotograma de una película que debe mostrarse hasta que empiece la reproducción de la misma (que recibe el nombre de “fotograma póster”), arrastre el regulador “Fotograma póster” hasta que la película muestre la imagen deseada. 5 Para iniciar la película cuando el presentador haga clic con el ratón (en lugar de cuando aparezca la diapositiva), seleccione “Iniciar película al hacer clic”. 6 Seleccione una opción de repetición del menú local Repetición: Ninguno: ejecutar una sola vez. Bucle: repetir continuamente. Bucle adelante y atrás: reproduce adelante y atrás continuamente. Capítulo 4 Cómo trabajar con sonido, películas, gráficos y otros objetos 107 7 Para aumentar o disminuir el volumen de reproducción, arrastre el regulador Volumen hacia la izquierda o hacia la derecha. Cómo añadir una narración Puede grabarse mientras explica cada diapositiva. Al avanzar a la siguiente diapositiva o composición, también se graban los tiempos. Para grabar un pase de diapositivas: 1 Si utiliza un micrófono externo en lugar del micrófono incorporado en el ordenador, conecte el micrófono y utilice el panel Sonido de Preferencias del Sistema para configurar los ajustes de entrada. 2 Seleccione la diapositiva donde desee que empiece la grabación. No tiene por qué seleccionar la primera diapositiva, aunque un pase de diapositivas grabado solo se reproduce desde la primera diapositiva grabada. Si selecciona una diapositiva omitida, la grabación comenzará en la diapositiva no omitida anterior más cercana. 3 Realice una de las siguientes acciones:  Abra el inspector de documentos, haga clic en Audio y, a continuación, haga clic en Grabar.  Seleccione Archivo > Grabar pase de diapositivas. 4 A medida que se reproduzca la presentación, diríjase al micrófono para hablar y grabar su narración. Una luz de roja intermitente en la esquina superior izquierda de la pantalla indica que la grabación está en curso. 5 Para avanzar a la siguiente diapositiva, haga clic con el ratón o pulse la tecla de flecha derecha. Ajuste el volumen de reproducción. Seleccione si la película debe comenzar al hacer clic (en lugar de cuando aparezca la diapositiva). El botón “Inspector de QuickTime” Seleccione los fotogramas donde debe comenzar y terminar la reproducción de la película. Seleccione el fotograma que debe mostrarse hasta que la película comience a reproducirse. Ajuste las opciones de repetición de reproducción. Utilice estos controles para visualizar la película o reproducir el sonido mientras edita el pase de diapositivas. 108 Capítulo 4 Cómo trabajar con sonido, películas, gráficos y otros objetos En la siguiente tabla se muestran otras formas que puede utilizar para controlar la presentación mientras está grabando. Nota: Al grabar un pase de diapositivas, se selecciona automáticamente la opción Grabada en el menú local Presentación del inspector de documentos. Cómo grabar encima de un pase de diapositivas grabado Si graba un pase de diapositivas y, a continuación, modifica las diapositivas, es posible que la grabación no esté sincronizada con las diapositivas. Puede grabar encima parte o de todo un pase de diapositivas grabado. Para grabar encima de parte o de todo el pase de diapositivas grabado: 1 Seleccione la diapositiva donde desee iniciar la grabación. 2 Abra el inspector de documentos y haga clic en Audio. 3 Haga clic en Grabar. 4 Si la diapositiva seleccionada se había grabado previamente, realice una de las siguientes operaciones:  Para reemplazar la grabación anterior comenzando desde la diapositiva seleccionada, haga clic en “Record & Replace”. En caso de que se haya grabado antes de la primera diapositiva grabada, el contenido permanecerá intacto.  Para reemplazar toda la grabación, haga clic en “Grabar desde el principio”. 5 Si la diapositiva seleccionada se había grabado previamente, realice una de las siguientes operaciones:  Para adjuntar una nueva grabación al final de la anterior, haga clic en “Record & Append”.  Para reemplazar toda la grabación, haga clic en “Grabar desde el principio”. Cómo reproducir un pase de diapositivas grabado Al reproducir un pase de diapositivas grabado, puede utilizar todas las funciones rápidas de teclado de las presentaciones normales (que se describen en “Cómo controlar una presentación con el teclado” en la página 192). También hay una serie de opciones especiales para reproducir pases de diapositivas grabados. Pulse o haga clic en Para W (pantalla en blanco), F (bloquear) o B (pantalla en negro) Poner en pausa la grabación. Pulse cualquier tecla para reanudar la grabación del pase de diapositivas. Indicador de grabación rojo1 Poner en pausa la grabación. Esc Detener la reproducción y guardar la grabación. 1 Para hacer clic en el indicador, debe estar seleccionada la opción “Mostrar el puntero cuando se mueva el ratón” en el panel “Pase de diapositivas” de las preferencias de Keynote. Capítulo 4 Cómo trabajar con sonido, películas, gráficos y otros objetos 109 Para reproducir un pase de diapositivas grabado:  Para escuchar la narración, haga clic en el botón Reproducir del panel Audio del inspector de documentos. Para ajustar el volumen, arrastre el regulador Volumen.  Para reproducir una presentación grabada, haga clic en Reproducir en la barra de tareas y seleccione Visualización > Reproducir pase de diapositivas, o bien Visualización > Reproducir pase de diapositivas grabado. Tenga en cuenta que un pase de diapositivas grabado solo se reproduce desde la primera diapositiva grabada, que quizá no sea la primera diapositiva del documento. Si hace clic en Reproducir en la barra de herramientas y la presentación no se reproduce de la forma esperada, asegúrese de haber seleccionado la opción Grabada en el menú local Presentación del inspector de documentos. Cómo eliminar una grabación Para eliminar una grabación: m Abra el inspector de documentos, haga clic en Audio y, a continuación, haga clic en Borrar. m Seleccione Archivo > Borrar grabación. Cómo añadir vistas web Es posible mostrar una instantánea de una página web (denominada “vista web”) en diapositivas. Cuando el documento se abre, Keynote puede actualizar automáticamente la instantánea con la página web actual. (El ordenador en el que se reproduce el pase de diapositivas debe estar conectado a Internet.) Por omisión, la instantánea es un hipervínculo sobre el que se puede hacer clic durante la presentación para abrir la página web en un navegador; puede desactivar el vínculo en el inspector de hipervínculos. La flecha azul indica que durante una presentación puede hacer clic en la vista web para abrir la página web en el navegador. Inserte una instantánea de una página web que se actualice automáticamente al abrir el pase de diapositivas. 110 Capítulo 4 Cómo trabajar con sonido, películas, gráficos y otros objetos Para añadir una vista web a una diapositiva: 1 Seleccione Insertar > Vista web. 2 En el inspector de hipervínculos, escriba la dirección URL de la página (www.apple.com/es, por ejemplo). También puede arrastrar el icono de una dirección URL desde la barra de direcciones de un navegador hasta el lienzo de diapositivas; arrastre el icono hasta el navegador de diapositivas para añadir una nueva diapositiva y crear una vista web en la misma en un solo paso. 3 Para actualizar la página web de forma automática y periódica, seleccione “Actualizar automáticamente”. Si no selecciona “Actualizar automáticamente,” puede actualizar la página web en cualquier momento haciendo clic en Actualizar ahora. 4 También puede cambiar de tamaño o de posición la vista web (la imagen de la página web se importa a tamaño completo). La vista web conserva la misma resolución cuando se cambia de tamaño. 5 Por omisión, la vista web es un hipervínculo de forma automática, sobre el que puede hacer clic durante una presentación para abrir la página en un navegador. Para desactivar esta característica, anule la selección de “Activar como hipervínculo” en el inspector de hipervínculos. Cuando esta opción está seleccionada, puede hacer clic sobre la vista web durante una presentación para abrir la página en un navegador. Capítulo 4 Cómo trabajar con sonido, películas, gráficos y otros objetos 111 Cómo convertir un objeto en un hipervínculo Además de los hipervínculos de texto, puede convertir imágenes y figuras en hipervínculos que realicen las siguientes acciones al hacer clic en ellos durante una presentación:  Ir a una diapositiva concreta  Abrir una página web en Internet  Abrir otro documento de Keynote  Abrir un mensaje de correo electrónico  Salir del pase de diapositivas Consulte el apartado “Cómo utilizar hipervínculos” en la página 68 para obtener instrucciones al respecto. Convierta las imágenes en hipervínculos que abren otra diapositiva, un documento de Keynote, una página web o un mensaje de correo electrónico. La flecha pequeña de color azul (únicamente visible durante la edición de diapositivas) indica que el elemento es un hipervínculo sobre el que se puede hacer clic. 5 112 5 Uso del movimiento en pases de diapositivas En este capítulo se explica cómo añadir interés visual utilizando transiciones de dispositivas y composiciones de objetos. Una vez que haya creado y organizado sus diapositivas, podrá animar el texto y los objetos para añadir énfasis e interés visual.  Las transiciones proporcionan efectos visuales al desplazarse de una dispositiva a la siguiente.  Las composiciones de objetos animan los elementos de las diapositivas. Cómo añadir transiciones entre diapositivas Keynote proporciona una amplia variedad de estilos de transición. Puede controlar la duración de una transición, y puede especificar el momento de iniciarla (automáticamente o al hacer clic). Puede configurar las transiciones de diapositivas en el inspector de las diapositivas. Defina el tiempo para completar la transición. Defina el tiempo de espera para que las transiciones que comienzan automáticamente empiecen a producirse. Ajuste la dirección de la transición. Seleccione el modo de iniciación de la transición. Seleccione una transición. Algunas transiciones presentan opciones adicionales. Haga clic para previsualizar la transición. El botón “Inspector de las diapositivas”. Capítulo 5 Uso del movimiento en pases de diapositivas 113 Para añadir un efecto de transición entre las diapositivas: 1 Seleccione una diapositiva. 2 Haga clic en el botón Inspector de la barra de herramientas y, a continuación, haga clic en el botón “Inspector de las diapositivas”. 3 Haga clic en Transición. 4 Seleccione una opción en el menú local Efecto. Si ve “Efectos no reproducibles en este equipo”, significa que las transiciones mostradas requieren que su ordenador disponga de una tarjeta gráfica avanzada. 5 Seleccione una opción en el menú local Dirección (no aplicable a todos los efectos). 6 Para cambiar el tiempo necesario para completar la transición, escriba un valor en el campo Duración (o haga clic en las flechas). 7 Seleccione una opción en el menú local “Comenzar transición”. Al hacer clic: inicia la transición cuando se hace clic para avanzar a la siguiente diapositiva. Automáticamente: inicia la transición cuando transcurra el tiempo especificado en el campo Demora. 8 Si selecciona un efecto con opciones adicionales (como Mosaico, Invertir o “Fundido en color”), seleccione los ajustes adicionales que desee. Para ver la transición, haga clic en la imagen en el panel Transición del inspector de las diapositivas o haga clic en el botón Reproducir de la barra de herramientas. Si utiliza las transiciones de cubo o de simetría: puede que algunas partes de esas transiciones no estén visibles si se ha seleccionado la opción “Aumentar el tamaño de las diapositivas hasta ajustarlas a la pantalla” en el panel “Pase de diapositivas” de las preferencias de Keynote (seleccione Keynote > Preferencias y, a continuación, haga clic en “Pase de diapositivas”). Para asegurarse de que estas transiciones no se solapen durante el pase de diapositivas, anule la selección de la opción “Aumentar el tamaño de las diapositivas hasta ajustarlas en la pantalla” o seleccione una o ambas de las opciones “Reducir las transiciones para evitar solapamientos” del panel “Pase de diapositivas”. Cómo animar las diapositivas con composiciones de objetos Puede utilizar las composiciones de objetos para animar elementos individuales o agrupados de una dispositiva:  Los efectos de entrada mueven los elementos dentro de una diapositiva.  Los efectos de salida mueven los elementos fuera de una diapositiva.  Las composiciones de acciones animan los elementos de una diapositiva.  Las composiciones inteligentes son composiciones de acciones predefinidas que sirven para animar las imágenes. 114 Capítulo 5 Uso del movimiento en pases de diapositivas Puede crear varias composiciones de objetos en una diapositiva, y puede aplicar varias composiciones al mismo objeto. Por ejemplo, puede hacer que el texto con viñetas se muestre línea por línea. O bien, puede mostrar partes individuales de una gráfica una por una para captar la atención de los espectadores o para generar suspense. Puede hacer que una imagen se mueva al interior de la diapositiva desde el lado izquierdo y, después, hacer que se mueva fuera de la diapositiva hacia el lado derecho. Cómo mover objetos dentro o fuera de las diapositivas utilizando efectos de composición Para mover elementos dentro o fuera de una diapositiva, comience con la dispositiva completa (todos los elementos visibles) y, a continuación, defina una composición para cada elemento que desee que aparezca o desaparezca. Para mover automáticamente un objeto dentro o fuera de una diapositiva: 1 En una diapositiva, seleccione el objeto que desee mover dentro o fuera de la diapositiva. Con la tecla Mayúsculas pulsada, haga clic para seleccionar varios objetos. 2 Haga clic en el botón Inspector de la barra de herramientas y, a continuación, haga clic en el botón “Inspector de la composición”. 3 Para hacer que el objeto se mueva al interior de la diapositiva, haga clic en Entrada. Para hacer que el objeto salga de la diapositiva, haga clic en Salida. Defina el tiempo para completar la composición. Seleccione los elementos que desee incluir. Abra el cajón “Orden de composición” para reordenar las composiciones. Defina el tipo de animación, la dirección y el orden de composición de cada uno de los objetos. Componga objetos completos o en partes. El botón “Inspector de la composición” Utilice las animaciones de la sección Entrada para introducir elementos en una diapositiva y las de la sección Salida para retirar objetos de la diapositiva. Establezca tiempos individuales para los elementos o intercale elementos. Haga clic para una vista previa de la composición. Capítulo 5 Uso del movimiento en pases de diapositivas 115 4 Seleccione una opción en el menú local Efecto. Si está aplicando el efecto a una composición inteligente: algunas composiciones inteligentes utilizan efectos que también pueden emplearse para mover las imágenes dentro y fuera de la diapositiva. Si utiliza alguna de estas composiciones inteligentes, verá la opción “Usar composición inteligente” en el menú Efecto. Para obtener más información, consulte “Cómo animar las imágenes utilizando composiciones inteligentes” en la página 119. 5 Para cambiar la dirección en la que el objeto debe entrar o salir de la diapositiva, seleccione una de las opciones del menú local Dirección (no todos los efectos disponen de esta opción). 6 Para cambiar la forma en que debe componerse el objeto (ya sea de forma íntegra o en partes), seleccione una de las opciones del menú local Reparto. Las opciones del menú local Reparto cambian en función del objeto seleccionado. Por ejemplo, las opciones de una tabla incluyen la composición por fila o por columna; las opciones de texto incluyen la composición por párrafo. Para obtener más información, consulte “Cómo animar tipos específicos de objetos” en la página 123. 7 Para ajustar el tiempo que tarda un objeto (o un elemento del objeto) en aparecer y desaparecer, escriba un valor en el campo Duración (o haga clic en las flechas). Para ajustar distintas duraciones para elementos individuales del objeto, seleccione “Establecer tiempos distintos para cada elemento”. En el cajón “Orden de composición”, seleccione cada uno de los elementos, seleccione “Automáticamente” en el menú local “Iniciar composición” y escriba un valor en el campo Demora. 8 Para evitar que algunas partes del objeto formen parte de la composición, seleccione cualquier opción distinta de Primero y Último en el menú local “Componer desde el”. Para ver la composición, haga clic en la imagen en el inspector de la composición o haga clic en el botón Reproducir de la barra de herramientas. También puede visualizar una composición de un solo elemento haciendo clic en el cajón “Orden de composición”. Objetos agrupados: si agrupa o desagrupa objetos que tienen una composición definida, se elimina el efecto de composición. Después de definir una composición de objetos, también puede realizar las siguientes operaciones:  Cambiar el orden en que se producen las composiciones. Consulte “Cómo reordenar las composiciones de objetos” en la página 121.  Especificar si empezar la composición automáticamente (tras un intervalo de tiempo especificado) o al hacer clic. Consulte “Cómo activar las composiciones de objetos” en la página 121. 116 Capítulo 5 Uso del movimiento en pases de diapositivas  Intercalar las fases de la composición de distintos objetos. Consulte “Cómo crear composiciones que intercalen las partes de un objeto” en la página 122.  Aplicar composiciones de acciones para mover o modificar el objeto en la diapositiva. Consulte los dos siguientes temas para obtener instrucciones al respecto. Puede crear una composición de objetos en una diapositiva maestra de forma de los efectos de la composición aparezcan en todas las diapositivas creadas a partir de ella. Consulte el apartado “Cómo definir transiciones por omisión” en la página 218 para obtener instrucciones al respecto. Cómo animar los objetos de las diapositivas (composiciones de acciones) Las composiciones de acciones le permiten mover los objetos de una diapositiva. Para mover un objeto de una ubicación a otra en una diapositiva: 1 Abra el inspector de la composición (haga clic en el botón Inspector de la barra de herramientas y, a continuación, haga clic en el botón “Inspector de la composición”). 2 Haga clic en Acción. 3 En una diapositiva, seleccione un objeto (una imagen, figura, cuadro de texto, gráfica, película o cualquier otro archivo multimedia, o tabla). Defina el tiempo para completar la composición. Haga clic para previsualizar la composición. Utilice los efectos de acción para animar los elementos de una diapositiva. Haga que los elementos se muevan, se contraigan, se amplíen, se fundan, giren, etc. Haga clic para reordenar las fases de la composición. Para mover las composiciones, cambie la ruta del objeto de recta a curva, o a la inversa. Haga clic para añadir otra ruta al movimiento del objeto. Ajuste los efectos de animación. El botón “Inspector de la composición”. Capítulo 5 Uso del movimiento en pases de diapositivas 117 4 Seleccione Mover en el menú local Efecto. Aparecerá una línea roja conectada a una versión “fantasma” (transparente) del objeto, que mostrará el destino del objeto. 5 Para modificar el movimiento, realice una de las siguientes acciones: Cambie la dirección o la distancia a la que se mueve el objeto arrastrando el objeto fantasma. Cambie la ruta de forma recta a forma curva haciendo clic en el botón Ruta curva en el inspector de la composición. Cambie la forma de una ruta curva arrastrando uno de sus nodos o tiradores de nodo. Para obtener un mayor control, haga clic en un nodo (un punto de una ruta) y arrastre sus tiradores. Controle la velocidad y la naturaleza del movimiento del objeto seleccionando una opción en el menú local Aceleración en el inspector de la composición. Para mover una ruta y sus objetos de inicio y finalización, arrastre la ruta. Con la tecla Mayúsculas pulsada, puede hacer clic para seleccionar varias rutas. Añada un nodo (punto) a una ruta manteniendo pulsada la tecla Opción mientras hace clic en la ruta. 6 Para mover el objeto por una nueva ruta, haga clic en el botón “Añadir ruta”, situado junto al último objeto fantasma, o haga clic en el botón “Añadir acción” en el inspector de la composición. Utilice estos tiradores de nodos para cambiar la forma de la ruta. Para añadir otra ruta para el objeto, haga clic en el botón “Añadir ruta” (situado junto al último objeto fantasma). 118 Capítulo 5 Uso del movimiento en pases de diapositivas 7 Para reordenar las fases de la composición de acciones, haga clic en “Más opciones” y arrastre las composiciones del cajón “Orden de composición”. (Para obtener más información, consulte “Cómo reordenar las composiciones de objetos” en la página 121.) Una vez que se anula la selección de un objeto y de todas sus rutas, puede volver a verlas haciendo clic en el botón “Mostrar ruta” de color rojo en el objeto. Cómo hacer que los objetos se fundan, giren, se amplíen o se contraigan Utilice composiciones de acciones para hacer que los objetos de una diapositiva giren, o para cambiar su opacidad o su tamaño. Para modificar un objeto utilizando un efecto de composición de acciones: 1 Abra el inspector de la composición (haga clic en el botón Inspector de la barra de herramientas y, a continuación, haga clic en el botón “Inspector de la composición”). 2 Haga clic en Acción. 3 En una diapositiva, seleccione un objeto (una imagen, figura, cuadro de texto, gráfica, película o cualquier otro archivo multimedia, o tabla). 4 Seleccione una de las opciones del menú local Efecto y utilice los controles para especificar el aspecto que deben presentar los objetos cuando se complete la transformación. Para hacer que el objeto se funda, seleccione Opacidad en el menú local Efecto y, a continuación, arrastre el regulador Opacidad para ajustar la opacidad final del objeto. El objeto comenzará a moverse a partir de esa ubicación. Arrastre un objeto fantasma a la ubicación donde desee que el objeto deje de moverse. Puede incluso mover objetos fuera de la diapositiva. Haga clic en el botón “Mostrar ruta” para ver todas las fases de una composición de acciones. Capítulo 5 Uso del movimiento en pases de diapositivas 119 Para girar el objeto, seleccione Rotación en el menú local Efecto y, a continuación, arrastre los controles Dirección y Aceleración para ajustar la dirección y la velocidad de rotación del objeto. Para contraer o expandir el objeto, seleccione Escala en el menú local Efecto y, a continuación, arrastre los controles de Escala para ajustar el tamaño final del objeto (hasta un 200%). Cómo animar las imágenes utilizando composiciones inteligentes Keynote ofrece composiciones predefinidas que puede utilizar para animar una colección con sus propias fotos y otras imágenes. Estas animaciones reciben el nombre de composiciones inteligentes. Para configurar una composición inteligente: 1 Haga clic en el botón “Composiciones inteligentes” de la barra de herramientas y seleccione una opción. 2 Arrastre las imágenes desde el panel Fotos del visualizador multimedia (si no está abierto, haga clic en Multimedia en la barra de herramientas) hasta los rectángulos de la ventana de fotos de la composición inteligente. Haga clic para una vista previa de la composición. Especifique las fotos que desee incluir en la composición. Muestre algunas de las fotos a mayor tamaño que otras. Ajuste los efectos de animación. Especifique cómo alinear imágenes. 120 Capítulo 5 Uso del movimiento en pases de diapositivas También puede arrastrar fotos y otros archivos de imagen desde el Finder. 3 Utilice la ventana de fotos de la composición inteligente para modificar la composición inteligente de cualquiera de estas formas: Para reordenar las imágenes, arrástrelas hasta la ventana de fotos de la composición inteligente. Para eliminar una imagen de la composición, arrástrela fuera de la ventana de fotos, o selecciónela y pulse la tecla Suprimir. Para que todas las fotos tengan el mismo tamaño, seleccione “Ajustar imágenes al mismo tamaño”. Para utilizar los tamaños relativos de las fotos, anule la selección de la opción “Ajustar imágenes al mismo tamaño”. Algunas composiciones inteligentes muestran imágenes en dos estados. Utilice los botones de tamaño y el regulador Escala para especificar el tamaño de cada estado. 4 Utilice el panel Acción del inspector de la composición para modificar la composición inteligente de cualquiera de estas formas: Para cambiar determinados ajustes, como la dirección, la alineación y la perspectiva, utilice los controles del inspector de la composición. (Los ajustes disponibles dependerán del efecto que seleccione.) Para cambiar la duración de la composición, escriba un valor en el campo Duración (o haga clic en las flechas). Para especificar si una fase de la composición debe comenzar automáticamente al hacer clic, seleccione una de las opciones del menú local “Iniciar composición” en el cajón “Orden de composición”. (Para obtener más información, consulte “Cómo activar las composiciones de objetos” en la página 121.) Para ajustar distintos tiempos para fotos individuales, seleccione “Establecer tiempos distintos para cada elemento” y, a continuación, en el cajón “Orden de composición”, seleccione cada una de las fotos y cambie sus ajustes. Algunas composiciones inteligentes muestra imágenes en dos estados; utilice estos botones y el regulador para cambiar el tamaño de la imagen en cada estado. Seleccione esta opción para que todas las imágenes tengan el mismo tamaño. Anule la selección de esta opción para usar tamaños relativos en las fotos. Arrastre las fotos hasta aquí. La señal roja indica que la foto fo