{"id":691,"date":"2023-07-29T02:11:57","date_gmt":"2023-07-29T02:11:57","guid":{"rendered":"https:\/\/statorials.org\/tr\/merkezi-limit-teoremi-excel\/"},"modified":"2023-07-29T02:11:57","modified_gmt":"2023-07-29T02:11:57","slug":"merkezi-limit-teoremi-excel","status":"publish","type":"post","link":"https:\/\/statorials.org\/tr\/merkezi-limit-teoremi-excel\/","title":{"rendered":"Excel&#39;de merkezi limit teoremi nas\u0131l uygulan\u0131r?"},"content":{"rendered":"<p><\/p>\n<hr>\n<p><span style=\"color: #000000;\"><a href=\"https:\/\/statorials.org\/tr\/merkezi-limit-teoremi\/\" target=\"_blank\" rel=\"noopener\">Merkezi limit teoremi,<\/a> pop\u00fclasyon da\u011f\u0131l\u0131m\u0131 normal <em>olmasa bile,<\/em> \u00f6rneklem b\u00fcy\u00fckl\u00fc\u011f\u00fc yeterince b\u00fcy\u00fckse, bir \u00f6rneklem ortalamas\u0131n\u0131n \u00f6rnekleme da\u011f\u0131l\u0131m\u0131n\u0131n yakla\u015f\u0131k olarak normal oldu\u011funu belirtir.<\/span><\/p>\n<p> <span style=\"color: #000000;\">Merkezi limit teoremi ayr\u0131ca \u00f6rnekleme da\u011f\u0131l\u0131m\u0131n\u0131n a\u015fa\u011f\u0131daki \u00f6zelliklere sahip olaca\u011f\u0131n\u0131 belirtir:<\/span><\/p>\n<p> <span style=\"color: #000000;\"><strong>1.<\/strong> \u00d6rnekleme da\u011f\u0131l\u0131m\u0131n\u0131n ortalamas\u0131 n\u00fcfus da\u011f\u0131l\u0131m\u0131n\u0131n ortalamas\u0131na e\u015fit olacakt\u0131r:<\/span><\/p>\n<p style=\"text-align: center;\"> <span style=\"color: #000000;\"><strong>x = \u00b5<\/strong><\/span><\/p>\n<p> <span style=\"color: #000000;\"><strong>2.<\/strong> \u00d6rnekleme da\u011f\u0131l\u0131m\u0131n\u0131n standart sapmas\u0131, pop\u00fclasyon standart sapmas\u0131n\u0131n \u00f6rneklem b\u00fcy\u00fckl\u00fc\u011f\u00fcne b\u00f6l\u00fcnmesine e\u015fit olacakt\u0131r:<\/span><\/p>\n<p style=\"text-align: center;\"> <span style=\"color: #000000;\"><strong>s = \u03c3 \/ <span style=\"text-decoration: overline;\">\u221an<\/span><\/strong><\/span><\/p>\n<p> <span style=\"color: #000000;\">Bu derste Excel&#8217;deki merkezi limit teoreminin belirli bir da\u011f\u0131l\u0131ma nas\u0131l uygulanaca\u011f\u0131n\u0131 a\u00e7\u0131kl\u0131yoruz.<\/span><\/p>\n<h2> <strong>Excel&#8217;de Merkezi Limit Teoremini Uygulamak<\/strong><\/h2>\n<p> <span style=\"color: #000000;\">Ortalamas\u0131 <strong>8<\/strong> ve standart sapmas\u0131 <strong>4<\/strong> olan bir da\u011f\u0131l\u0131ma sahip oldu\u011fumuzu varsayal\u0131m. \u00d6rneklem b\u00fcy\u00fckl\u00fc\u011f\u00fc <strong>15<\/strong> olan \u00f6rnekleme da\u011f\u0131l\u0131m\u0131n\u0131n hem ortalamas\u0131n\u0131 hem de standart sapmas\u0131n\u0131 bulmak i\u00e7in Excel&#8217;de a\u015fa\u011f\u0131daki form\u00fclleri kullanabiliriz:<\/span> <\/p>\n<p><img decoding=\"async\" loading=\"lazy\" class=\"aligncenter wp-image-6637 \" src=\"https:\/\/statorials.org\/wp-content\/uploads\/2023\/08\/centrallimexcel1.png\" alt=\"Excel'de Merkezi Limit Teoremi \u00d6rne\u011fi\" width=\"537\" height=\"324\" srcset=\"\" sizes=\"auto, \"><\/p>\n<p> <span style=\"color: #000000;\">\u00d6rnekleme da\u011f\u0131l\u0131m\u0131n\u0131n ortalamas\u0131, n\u00fcfus da\u011f\u0131l\u0131m\u0131n\u0131n ortalamas\u0131na yani <strong>8&#8217;e<\/strong> e\u015fittir.<\/span><\/p>\n<p> <span style=\"color: #000000;\">\u00d6rnekleme da\u011f\u0131l\u0131m\u0131n\u0131n standart sapmas\u0131, pop\u00fclasyon standart sapmas\u0131n\u0131n \u00f6rneklem b\u00fcy\u00fckl\u00fc\u011f\u00fcne b\u00f6l\u00fcnmesine e\u015fittir veya: 4 \/\u221a15 = <strong>1,0328<\/strong> .<\/span><\/p>\n<p> <span style=\"color: #000000;\">Olas\u0131l\u0131kla ilgili sorular\u0131 yan\u0131tlamak i\u00e7in merkezi limit teoremini de kullanabiliriz. \u00d6rne\u011fin, belirli bir pop\u00fclasyonun ortalamas\u0131 <strong>8<\/strong> ve standart sapmas\u0131 <strong>4<\/strong> ise, belirli bir \u00f6rneklem b\u00fcy\u00fckl\u00fc\u011f\u00fcn\u00fcn <strong>15<\/strong> olmas\u0131 olas\u0131l\u0131\u011f\u0131 nedir? <b>&nbsp;<\/b> ortalamas\u0131 <strong>7&#8217;den<\/strong> k\u00fc\u00e7\u00fck veya ona e\u015fit mi?<\/span><\/p>\n<p> <span style=\"color: #000000;\">Bu soruyu yan\u0131tlamak i\u00e7in Excel&#8217;de a\u015fa\u011f\u0131daki s\u00f6zdizimini kullanan <strong>NORM.DA\u011e()<\/strong> i\u015flevini kullanabiliriz:<\/span><\/p>\n<p> <span style=\"color: #000000;\"><strong>NORM.DA\u011e(x, ortalama, standart_sapma, k\u00fcm\u00fclatif)<\/strong><\/span><\/p>\n<p> <span style=\"color: #000000;\">Alt\u0131n:<\/span><\/p>\n<ul>\n<li> <span style=\"color: #000000;\"><strong>x:<\/strong> \u00f6rnek, test etmek istedi\u011finiz anlam\u0131na gelir<\/span><\/li>\n<li> <span style=\"color: #000000;\"><strong>ortalama:<\/strong> \u00f6rnekleme da\u011f\u0131l\u0131m\u0131n\u0131n beklenen ortalamas\u0131<\/span><\/li>\n<li> <span style=\"color: #000000;\"><strong>standard_dev:<\/strong> \u00f6rnekleme da\u011f\u0131l\u0131m\u0131n\u0131n beklenen standart sapmas\u0131<\/span><\/li>\n<li> <span style=\"color: #000000;\"><strong>k\u00fcm\u00fclatif:<\/strong> DO\u011eRU normal CDF de\u011ferini d\u00f6nd\u00fcr\u00fcr; FALSE, normal PDF&#8217;nin de\u011ferini d\u00f6nd\u00fcr\u00fcr. Bizim durumumuzda her zaman TRUE&#8217;yu kullanaca\u011f\u0131z.<\/span><\/li>\n<\/ul>\n<p> <span style=\"color: #000000;\">Bu fonksiyon, \u00f6rnek ortalamas\u0131n\u0131n belirli bir de\u011ferden k\u00fc\u00e7\u00fck veya ona e\u015fit olma olas\u0131l\u0131\u011f\u0131n\u0131 d\u00f6nd\u00fcrecektir.<\/span><\/p>\n<p> <span style=\"color: #000000;\">Bu \u00f6rnekte kullanaca\u011f\u0131m\u0131z form\u00fcl \u015fu \u015fekildedir:<\/span> <\/p>\n<p><img decoding=\"async\" loading=\"lazy\" class=\"aligncenter wp-image-6640 \" src=\"https:\/\/statorials.org\/wp-content\/uploads\/2023\/08\/centrallimexcel2.png\" alt=\"Excel'de Merkezi Limit Teoremi Olas\u0131l\u0131\u011f\u0131\" width=\"587\" height=\"301\" srcset=\"\" sizes=\"auto, \"><\/p>\n<p> <span style=\"color: #000000;\">Bu bize ortalamas\u0131 <strong>8<\/strong> ve standart sapmas\u0131 <strong>4<\/strong> olan bir pop\u00fclasyon i\u00e7in belirli b\u00fcy\u00fckl\u00fckteki bir \u00f6rne\u011fin <strong>15<\/strong> olma olas\u0131l\u0131\u011f\u0131n\u0131n oldu\u011funu s\u00f6yler. <b>&nbsp;<\/b> ortalamas\u0131 <strong>7<\/strong> veya <strong>0,1665&#8217;ten<\/strong> k\u00fc\u00e7\u00fck veya ona e\u015fittir.<\/span><\/p>\n<p> <span style=\"color: #000000;\">Belirli bir \u00f6rnek boyutunun belirli bir say\u0131dan <em>daha b\u00fcy\u00fck<\/em> bir ortalamaya sahip olma olas\u0131l\u0131\u011f\u0131n\u0131 da basit\u00e7e form\u00fcl <strong>1 \u2013 NORM.DA\u011e()<\/strong> kullanarak bulabiliriz.<\/span><\/p>\n<p> <span style=\"color: #000000;\">\u00d6rne\u011fin, a\u015fa\u011f\u0131daki form\u00fcl, 15 ki\u015filik belirli bir \u00f6rneklem b\u00fcy\u00fckl\u00fc\u011f\u00fcn\u00fcn 7&#8217;den <em>b\u00fcy\u00fck<\/em> bir ortalamaya sahip olma olas\u0131l\u0131\u011f\u0131n\u0131n nas\u0131l belirlenece\u011fini g\u00f6sterir:<\/span> <\/p>\n<p><img decoding=\"async\" loading=\"lazy\" class=\"aligncenter wp-image-6641 \" src=\"https:\/\/statorials.org\/wp-content\/uploads\/2023\/08\/centrallimexcel3.png\" alt=\"Excel'de Merkezi Limit Teoremi\" width=\"619\" height=\"312\" srcset=\"\" sizes=\"auto, \"><\/p>\n<p> <span style=\"color: #000000;\">Son olarak, <strong>NORM.DA\u011e(daha b\u00fcy\u00fck say\u0131) \u2013 NORM.DA\u011e(daha k\u00fc\u00e7\u00fck say\u0131)<\/strong> form\u00fcl\u00fcn\u00fc kullanarak belirli bir \u00f6rneklem b\u00fcy\u00fckl\u00fc\u011f\u00fcn\u00fcn iki say\u0131 <em>aras\u0131nda<\/em> bir ortalamaya sahip olma olas\u0131l\u0131\u011f\u0131n\u0131 bulabiliriz.<\/span><\/p>\n<p> <span style=\"color: #000000;\">\u00d6rne\u011fin, a\u015fa\u011f\u0131daki form\u00fcl, belirli bir \u00f6rneklem b\u00fcy\u00fckl\u00fc\u011f\u00fc olan 15&#8217;in ortalamas\u0131n\u0131n 7 ile 9 aras\u0131nda olmas\u0131 olas\u0131l\u0131\u011f\u0131n\u0131n nas\u0131l bulunaca\u011f\u0131n\u0131 g\u00f6sterir:<\/span> <\/p>\n<p><img decoding=\"async\" loading=\"lazy\" class=\"aligncenter wp-image-6642 \" src=\"https:\/\/statorials.org\/wp-content\/uploads\/2023\/08\/centrallimexcel4.png\" alt=\"Excel'de Merkezi Limit Teoremi ile \u00d6rnekleme Da\u011f\u0131l\u0131m\u0131\" width=\"663\" height=\"293\" srcset=\"\" sizes=\"auto, \"><\/p>\n<h3> <span style=\"color: #000000;\"><strong>Ek kaynaklar<\/strong><\/span><\/h3>\n<p> <a href=\"https:\/\/statorials.org\/tr\/merkezi-limit-teoremi-hesaplayicisi\/\" target=\"_blank\" rel=\"noopener\">Merkezi Limit Teoremi Hesaplay\u0131c\u0131<\/a><br \/> <a href=\"https:\/\/statorials.org\/tr\/excelin-temel-kurali\/\" target=\"_blank\" rel=\"noopener\">Excel&#8217;de temel kural nas\u0131l uygulan\u0131r?<\/a><br \/> <a href=\"https:\/\/statorials.org\/tr\/can-egrisi-excel\/\" target=\"_blank\" rel=\"noopener\">Excel&#8217;de \u00c7an E\u011frisi Nas\u0131l Olu\u015fturulur<\/a><\/p>\n","protected":false},"excerpt":{"rendered":"<p>Merkezi limit teoremi, pop\u00fclasyon da\u011f\u0131l\u0131m\u0131 normal olmasa bile, \u00f6rneklem b\u00fcy\u00fckl\u00fc\u011f\u00fc yeterince b\u00fcy\u00fckse, bir \u00f6rneklem ortalamas\u0131n\u0131n \u00f6rnekleme da\u011f\u0131l\u0131m\u0131n\u0131n yakla\u015f\u0131k olarak normal oldu\u011funu belirtir. Merkezi limit teoremi ayr\u0131ca \u00f6rnekleme da\u011f\u0131l\u0131m\u0131n\u0131n a\u015fa\u011f\u0131daki \u00f6zelliklere sahip olaca\u011f\u0131n\u0131 belirtir: 1. \u00d6rnekleme da\u011f\u0131l\u0131m\u0131n\u0131n ortalamas\u0131 n\u00fcfus da\u011f\u0131l\u0131m\u0131n\u0131n ortalamas\u0131na e\u015fit olacakt\u0131r: x = \u00b5 2. \u00d6rnekleme da\u011f\u0131l\u0131m\u0131n\u0131n standart sapmas\u0131, pop\u00fclasyon standart sapmas\u0131n\u0131n \u00f6rneklem b\u00fcy\u00fckl\u00fc\u011f\u00fcne [&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-691","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>Excel&#039;de Merkezi 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