{"id":2065,"date":"2023-07-23T21:06:43","date_gmt":"2023-07-23T21:06:43","guid":{"rendered":"https:\/\/statorials.org\/tr\/znin-sagindaki-alani-bulun\/"},"modified":"2023-07-23T21:06:43","modified_gmt":"2023-07-23T21:06:43","slug":"znin-sagindaki-alani-bulun","status":"publish","type":"post","link":"https:\/\/statorials.org\/tr\/znin-sagindaki-alani-bulun\/","title":{"rendered":"Z puan\u0131n\u0131n sa\u011f\u0131ndaki alan nas\u0131l bulunur (\u00f6rneklerle)"},"content":{"rendered":"<p><\/p>\n<hr>\n<p><span style=\"color: #000000;\">\u0130statistiklerde <a href=\"https:\/\/statorials.org\/tr\/z-puanlarini-yorumlama\/\" target=\"_blank\" rel=\"noopener\">z-puan\u0131<\/a> bize<\/span> <span style=\"color: #000000;\">belirli bir de\u011ferin pop\u00fclasyon ortalamas\u0131ndan ka\u00e7 standart sapma oldu\u011funu s\u00f6yler.<\/span><\/p>\n<p> <span style=\"color: #000000;\">Belirli bir de\u011fere ili\u015fkin z-puan\u0131n\u0131 hesaplamak i\u00e7in a\u015fa\u011f\u0131daki form\u00fcl\u00fc kullan\u0131r\u0131z:<\/span><\/p>\n<p style=\"text-align: center;\"> <span style=\"color: #000000;\"><strong>z = (x \u2013 \u03bc) \/ \u03c3<\/strong><\/span><\/p>\n<p> <span style=\"color: #000000;\">Alt\u0131n:<\/span><\/p>\n<ul>\n<li> <span style=\"color: #000000;\"><strong>x<\/strong> : Bireysel verilerin de\u011feri<\/span><\/li>\n<li> <span style=\"color: #000000;\"><strong>\u03bc<\/strong> : N\u00fcfus ortalamas\u0131<\/span><\/li>\n<li> <span style=\"color: #000000;\"><strong>\u03c3<\/strong> : N\u00fcfus standart sapmas\u0131<\/span><\/li>\n<\/ul>\n<p> <span style=\"color: #000000;\">Belirli bir z-puan\u0131n\u0131n sa\u011f\u0131nda yer alan normal da\u011f\u0131l\u0131m alt\u0131ndaki alan\u0131 bulmak i\u00e7in iki y\u00f6ntemden birini kullanabiliriz:<\/span><\/p>\n<p> <span style=\"color: #000000;\"><strong>1.<\/strong> z tablosunu kullan\u0131n.<\/span><\/p>\n<p> <span style=\"color: #000000;\"><strong>2.<\/strong> <a href=\"https:\/\/statorials.org\/tr\/z-puani-hesaplayicinin-sagindaki-alan\/\" target=\"_blank\" rel=\"noopener\">Z-puan\u0131 hesaplay\u0131c\u0131s\u0131n\u0131n sa\u011f\u0131ndaki kutuyu kullan\u0131n.<\/a><\/span><\/p>\n<p> <span style=\"color: #000000;\">A\u015fa\u011f\u0131daki \u00f6rnekler bu y\u00f6ntemlerin her birinin pratikte nas\u0131l kullan\u0131laca\u011f\u0131n\u0131 g\u00f6stermektedir.<\/span><\/p>\n<h3> <span style=\"color: #000000;\"><strong>\u00d6rnek 1: Negatif Z puan\u0131n\u0131n sa\u011f\u0131ndaki alan<\/strong><\/span><\/h3>\n<p> <span style=\"color: #000000;\">Belirli bir yunus t\u00fcr\u00fcn\u00fcn a\u011f\u0131rl\u0131\u011f\u0131, ortalama \u03bc = 300 pound ve standart sapma \u03c3 = 15 pound ile normal olarak da\u011f\u0131t\u0131l\u0131r. Yunuslar\u0131n yakla\u015f\u0131k y\u00fczde ka\u00e7\u0131 284 poundun \u00fczerindedir?<\/span><\/p>\n<p> <span style=\"color: #000000;\">284 poundluk bir a\u011f\u0131rl\u0131\u011f\u0131n z-puan\u0131 \u015fu \u015fekilde hesaplanacakt\u0131r: z = (284 \u2013 300) \/ 15 = <strong>-1,07<\/strong><\/span><\/p>\n<p> <span style=\"color: #000000;\">Bu z-puan\u0131n\u0131n sa\u011f\u0131ndaki alan\u0131 bulmak i\u00e7in iki y\u00f6ntemden birini kullanabiliriz:<\/span><\/p>\n<p> <span style=\"color: #000000;\"><strong>Y\u00f6ntem 1: z tablosunu kullan\u0131n.<\/strong><\/span><\/p>\n<p> <span style=\"color: #000000;\">Z-puan\u0131n\u0131n sa\u011f\u0131ndaki alan\u0131 bulmak i\u00e7in z-tablosunda <strong>-1,07<\/strong> de\u011ferini arayabiliriz:<\/span> <\/p>\n<p><img decoding=\"async\" loading=\"lazy\" class=\" wp-image-19234 aligncenter\" src=\"https:\/\/statorials.org\/wp-content\/uploads\/2023\/08\/zonegauche2.png\" alt=\"\" width=\"592\" height=\"473\" srcset=\"\" sizes=\"auto, \"><\/p>\n<p> <span style=\"color: #000000;\">Bu, z = -1,07&#8217;nin solundaki alan\u0131 temsil eder. B\u00f6ylece sa\u011fdaki alan \u015fu \u015fekilde hesaplan\u0131r: 1 \u2013 0,1423 = veya <strong>0,8577<\/strong> .<\/span><\/p>\n<p> <span style=\"color: #000000;\">Senaryomuza uyguland\u0131\u011f\u0131nda bu, yunuslar\u0131n yakla\u015f\u0131k <strong>%85,77&#8217;sinin<\/strong> 284 pound&#8217;dan daha a\u011f\u0131r oldu\u011fu anlam\u0131na gelir.<\/span><\/p>\n<p> <span style=\"color: #000000;\"><strong>Y\u00f6ntem 2: Z puan\u0131 hesaplay\u0131c\u0131n\u0131n sa\u011f\u0131ndaki kutuyu kullan\u0131n<\/strong><\/span><\/p>\n<p> <span style=\"color: #000000;\">Z = -1,07&#8217;nin sa\u011f\u0131ndaki alan\u0131n <strong>0,8577<\/strong> oldu\u011funu bulmak i\u00e7in <a href=\"https:\/\/statorials.org\/tr\/z-puani-hesaplayicinin-sagindaki-alan\/\" target=\"_blank\" rel=\"noopener\">Z puan\u0131 hesaplay\u0131c\u0131s\u0131n\u0131n sa\u011f\u0131ndaki alan\u0131<\/a> da kullanabiliriz.<\/span> <\/p>\n<p><img decoding=\"async\" loading=\"lazy\" class=\" wp-image-19240 aligncenter\" src=\"https:\/\/statorials.org\/wp-content\/uploads\/2023\/08\/zonedroite1.png\" alt=\"\" width=\"514\" height=\"368\" srcset=\"\" sizes=\"auto, \"><\/p>\n<h3> <span style=\"color: #000000;\"><strong>\u00d6rnek 2: Pozitif Z puan\u0131n\u0131n sa\u011f\u0131ndaki alan<\/strong><\/span><\/h3>\n<p> <span style=\"color: #000000;\">Belirli bir s\u0131navdaki puanlar ortalama \u03bc = 85 ve standart sapma \u03c3 = 8 ile normal olarak da\u011f\u0131t\u0131l\u0131r. \u00d6\u011frencilerin yakla\u015f\u0131k y\u00fczde ka\u00e7\u0131 s\u0131navda 87&#8217;nin \u00fczerinde puan al\u0131yor?<\/span><\/p>\n<p> <span style=\"color: #000000;\">87 puanl\u0131k s\u0131nav puan\u0131n\u0131n z puan\u0131 \u015fu \u015fekilde hesaplanacakt\u0131r: z = (87 \u2013 85) \/ 8 = <strong>0,25.<\/strong><\/span><\/p>\n<p> <span style=\"color: #000000;\">Bu z-puan\u0131n\u0131n sa\u011f\u0131ndaki alan\u0131 bulmak i\u00e7in iki y\u00f6ntemden birini kullanabiliriz:<\/span><\/p>\n<p> <span style=\"color: #000000;\"><strong>Y\u00f6ntem 1: z tablosunu kullan\u0131n.<\/strong><\/span><\/p>\n<p> <span style=\"color: #000000;\">Z-puan\u0131n\u0131n sa\u011f\u0131ndaki alan\u0131 bulmak i\u00e7in z-tablosunda <strong>0,25<\/strong> de\u011ferini aramam\u0131z yeterlidir:<\/span> <\/p>\n<p><img decoding=\"async\" loading=\"lazy\" class=\"aligncenter wp-image-7555 \" src=\"https:\/\/statorials.org\/wp-content\/uploads\/2023\/08\/ztable1.png\" alt=\"Z tablosunu okuma \u00f6rne\u011fi\" width=\"616\" height=\"350\" srcset=\"\" sizes=\"auto, \"><\/p>\n<p> <span style=\"color: #000000;\">z = 0,25&#8217;in solundaki alan\u0131 temsil eder. B\u00f6ylece sa\u011fdaki alan \u015fu \u015fekilde hesaplan\u0131r: 1 \u2013 0,5987 = <strong>0,4013<\/strong> . Senaryomuza uyguland\u0131\u011f\u0131nda bu, \u00f6\u011frencilerin yakla\u015f\u0131k <strong>%40,13&#8217;\u00fcn\u00fcn<\/strong> bu s\u0131navda 87&#8217;nin \u00fczerinde puan ald\u0131\u011f\u0131 anlam\u0131na gelir.<\/span><\/p>\n<p> <span style=\"color: #000000;\"><strong>Y\u00f6ntem 2: Z puan\u0131 hesaplay\u0131c\u0131n\u0131n sa\u011f\u0131ndaki kutuyu kullan\u0131n<\/strong><\/span><\/p>\n<p> <span style=\"color: #000000;\">Z = 0,25&#8217;in sa\u011f\u0131ndaki alan\u0131n <strong>0,4013<\/strong> oldu\u011funu bulmak i\u00e7in <a href=\"https:\/\/statorials.org\/tr\/z-puani-hesaplayicinin-sagindaki-alan\/\" target=\"_blank\" rel=\"noopener\">Z puan\u0131 hesaplay\u0131c\u0131s\u0131n\u0131n sa\u011f\u0131ndaki alan\u0131<\/a> da kullanabiliriz.<\/span> <\/p>\n<p><img decoding=\"async\" loading=\"lazy\" class=\" wp-image-19241 aligncenter\" src=\"https:\/\/statorials.org\/wp-content\/uploads\/2023\/08\/zonedroite2.png\" alt=\"\" width=\"503\" height=\"358\" srcset=\"\" sizes=\"auto, \"><\/p>\n<h3> <span style=\"color: #000000;\"><strong>Ek kaynaklar<\/strong><\/span><\/h3>\n<p> <span style=\"color: #000000;\">A\u015fa\u011f\u0131daki e\u011fitimler z puanlar\u0131n\u0131n kullan\u0131m\u0131na ili\u015fkin ek bilgiler sa\u011flar:<\/span><\/p>\n<p> <a href=\"https:\/\/statorials.org\/tr\/znin-sol-bolgesini-bulun\/\" target=\"_blank\" rel=\"noopener\">Z-Skorunun solundaki alan nas\u0131l bulunur?<\/a><br \/> <a href=\"https:\/\/statorials.org\/tr\/verilen-alanin-z-puanini-bulun\/\" target=\"_blank\" rel=\"noopener\">Belirli bir alanda Z puanlar\u0131 nas\u0131l bulunur?<\/a><br \/> \u0130yi bir Z-Skoru olarak kabul edilen \u015fey nedir?<br \/> <a href=\"https:\/\/statorials.org\/tr\/z-puanindan-elle-elde-edilen-p-degeri\/\" target=\"_blank\" rel=\"noopener\">Z puan\u0131ndan P de\u011feri manuel olarak nas\u0131l hesaplan\u0131r?<\/a><\/p>\n","protected":false},"excerpt":{"rendered":"<p>\u0130statistiklerde z-puan\u0131 bize belirli bir de\u011ferin pop\u00fclasyon ortalamas\u0131ndan ka\u00e7 standart sapma oldu\u011funu s\u00f6yler. Belirli bir de\u011fere ili\u015fkin z-puan\u0131n\u0131 hesaplamak i\u00e7in a\u015fa\u011f\u0131daki form\u00fcl\u00fc kullan\u0131r\u0131z: z = (x \u2013 \u03bc) \/ \u03c3 Alt\u0131n: x : Bireysel verilerin de\u011feri \u03bc : N\u00fcfus ortalamas\u0131 \u03c3 : N\u00fcfus standart sapmas\u0131 Belirli bir z-puan\u0131n\u0131n sa\u011f\u0131nda yer alan normal da\u011f\u0131l\u0131m alt\u0131ndaki alan\u0131 [&hellip;]<\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[11],"tags":[],"class_list":["post-2065","post","type-post","status-publish","format-standard","hentry","category-rehber"],"yoast_head":"<!-- This site is optimized with the Yoast SEO plugin v21.3 - https:\/\/yoast.com\/wordpress\/plugins\/seo\/ -->\n<title>Z Skorunun Sa\u011f\u0131ndaki Alan Nas\u0131l Bulunur (\u00d6rneklerle) \u2013 Statorials<\/title>\n<meta name=\"description\" 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