{"id":1368,"date":"2023-07-26T16:34:08","date_gmt":"2023-07-26T16:34:08","guid":{"rendered":"https:\/\/statorials.org\/tr\/kosullar-merkezi-limit-teoremi\/"},"modified":"2023-07-26T16:34:08","modified_gmt":"2023-07-26T16:34:08","slug":"kosullar-merkezi-limit-teoremi","status":"publish","type":"post","link":"https:\/\/statorials.org\/tr\/kosullar-merkezi-limit-teoremi\/","title":{"rendered":"Merkezi limit teoremi: yerine getirilmesi gereken d\u00f6rt ko\u015ful"},"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><a href=\"https:\/\/statorials.org\/tr\/ornekleme-dagilimi-1\/\" target=\"_blank\" rel=\"noopener noreferrer\">pop\u00fclasyon da\u011f\u0131l\u0131m\u0131<\/a> 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 teoremini uygulamak i\u00e7in d\u00f6rt ko\u015fulun kar\u015f\u0131lanmas\u0131 gerekir:<\/span><\/p>\n<p> <span style=\"color: #000000;\"><strong>1.<\/strong> <strong>Rastgelele\u015ftirme<\/strong> : Veriler rastgele \u00f6rneklenmelidir, b\u00f6ylece pop\u00fclasyonun her bir \u00fcyesinin \u00f6rne\u011fin bir par\u00e7as\u0131 olmak \u00fczere se\u00e7ilme olas\u0131l\u0131\u011f\u0131 e\u015fit olmal\u0131d\u0131r.<\/span><\/p>\n<p> <span style=\"color: #000000;\"><strong>2. Ba\u011f\u0131ms\u0131zl\u0131k:<\/strong> Numunelerin de\u011ferleri birbirinden ba\u011f\u0131ms\u0131z olmal\u0131d\u0131r.<\/span><\/p>\n<p> <span style=\"color: #000000;\"><strong>3. %10 ko\u015fulu:<\/strong> \u00d6rnek de\u011fi\u015ftirilmeden al\u0131nd\u0131\u011f\u0131nda \u00f6rneklem b\u00fcy\u00fckl\u00fc\u011f\u00fc pop\u00fclasyonun %10&#8217;unu ge\u00e7memelidir.<\/span><\/p>\n<p> <span style=\"color: #000000;\"><strong>4. B\u00fcy\u00fck \u00d6rnek Durumu:<\/strong> \u00d6rnek boyutu yeterince b\u00fcy\u00fck olmal\u0131d\u0131r.<\/span><\/p>\n<p> <span style=\"color: #000000;\">Bu e\u011fitimde her bir durumun k\u0131sa bir a\u00e7\u0131klamas\u0131 sa\u011flanmaktad\u0131r.<\/span><\/p>\n<h3> <span style=\"color: #000000;\"><strong>Durum 1: rastgelele\u015ftirme<\/strong><\/span><\/h3>\n<p> <span style=\"color: #000000;\">Merkezi limit teoremini uygulayabilmek i\u00e7in, kulland\u0131\u011f\u0131m\u0131z verilerin <strong>olas\u0131l\u0131k \u00f6rnekleme y\u00f6ntemi<\/strong> kullan\u0131larak pop\u00fclasyondan rastgele \u00f6rneklenmesi gerekir.<\/span><\/p>\n<p> <span style=\"color: #000000;\">\u0130statistikte iki t\u00fcr <a href=\"https:\/\/statorials.org\/tr\/ornekleme-yontemleri\/\" target=\"_blank\" rel=\"noopener\">\u00f6rnekleme y\u00f6ntemi<\/a> vard\u0131r:<\/span><\/p>\n<p> <span style=\"color: #000000;\"><strong>1. Olas\u0131l\u0131kl\u0131 \u00d6rnekleme Y\u00f6ntemleri:<\/strong> Bir pop\u00fclasyonun her \u00fcyesinin, \u00f6rne\u011fin bir par\u00e7as\u0131 olmak \u00fczere se\u00e7ilme olas\u0131l\u0131\u011f\u0131n\u0131n e\u015fit oldu\u011fu \u00f6rnekleme y\u00f6ntemleri. \u00d6rnekler \u015funlar\u0131 i\u00e7erir:<\/span><\/p>\n<ul>\n<li> <span style=\"color: #000000;\">Basit rastgele \u00f6rnek<\/span><\/li>\n<li> <span style=\"color: #000000;\">Tabakal\u0131 rastgele \u00f6rnek<\/span><\/li>\n<li> <span style=\"color: #000000;\">K\u00fcmelenmi\u015f rastgele \u00f6rnek<\/span><\/li>\n<li> <span style=\"color: #000000;\">Sistematik rastgele \u00f6rnekleme<\/span><\/li>\n<\/ul>\n<p> <span style=\"color: #000000;\"><strong>2. Olas\u0131l\u0131ks\u0131z \u00f6rnekleme y\u00f6ntemleri:<\/strong> Bir pop\u00fclasyonun her \u00fcyesinin, \u00f6rne\u011fin bir par\u00e7as\u0131 olmak \u00fczere se\u00e7ilme olas\u0131l\u0131\u011f\u0131n\u0131n ayn\u0131 olmad\u0131\u011f\u0131 \u00f6rnekleme y\u00f6ntemleri. \u00d6rnekler \u015funlar\u0131 i\u00e7erir:<\/span><\/p>\n<ul>\n<li> <span style=\"color: #000000;\">Kolayl\u0131k \u00f6rne\u011fi<\/span><\/li>\n<li> <a href=\"https:\/\/statorials.org\/tr\/gonullu-yanit-ornegi\/\" target=\"_blank\" rel=\"noopener\">G\u00f6n\u00fcll\u00fc yan\u0131t \u00f6rne\u011fi<\/a><\/li>\n<li> <a href=\"https:\/\/statorials.org\/tr\/kartopu-orneklemesi-1\/\" target=\"_blank\" rel=\"noopener\">Kartopu \u00d6rne\u011fi<\/a><\/li>\n<li> <span style=\"color: #000000;\">Saf numune<\/span><\/li>\n<\/ul>\n<p> <span style=\"color: #000000;\">Numuneyi elde etmek i\u00e7in olas\u0131l\u0131kl\u0131 \u00f6rnekleme y\u00f6nteminin kullan\u0131lmas\u0131 \u00f6nemlidir, \u00e7\u00fcnk\u00fc bu <a href=\"https:\/\/statorials.org\/tr\/temsili-ornek-1\/\" target=\"_blank\" rel=\"noopener\">, pop\u00fclasyonun temsili bir \u00f6rne\u011fini<\/a> elde etme \u015fans\u0131n\u0131 en \u00fcst d\u00fczeye \u00e7\u0131kar\u0131r.<\/span><\/p>\n<h3> <span style=\"color: #000000;\"><strong>Durum 2: Ba\u011f\u0131ms\u0131zl\u0131k<\/strong><\/span><\/h3>\n<p> <span style=\"color: #000000;\">Merkezi limit teoremini uygulayabilmek i\u00e7in \u00f6rnekteki de\u011ferlerin her birinin birbirinden ba\u011f\u0131ms\u0131z oldu\u011funu da varsaymam\u0131z gerekir.<\/span> <span style=\"color: #000000;\">Ba\u015fka bir deyi\u015fle bir olay\u0131n meydana gelmesi di\u011fer bir olay\u0131n meydana gelmesini etkilemez.<\/span><\/p>\n<p> <span style=\"color: #000000;\">Olas\u0131l\u0131kl\u0131 \u00f6rnekleme y\u00f6ntemi kulland\u0131\u011f\u0131m\u0131zda bu varsay\u0131m \u00e7o\u011funlukla kar\u015f\u0131lan\u0131r, \u00e7\u00fcnk\u00fc bu t\u00fcr \u00f6rnekleme y\u00f6ntemleri <a href=\"https:\/\/statorials.org\/tr\/istatistikte-gozlem\/\" target=\"_blank\" rel=\"noopener\">, hangi g\u00f6zlemlerin<\/a> \u00f6rne\u011fe dahil edilece\u011fini birbirinden tamamen ba\u011f\u0131ms\u0131z olarak se\u00e7er.<\/span><\/p>\n<h3> <span style=\"color: #000000;\"><strong>Durum 3: %10 ko\u015fulu<\/strong><\/span><\/h3>\n<p> <span style=\"color: #000000;\">\u00d6rnek de\u011fi\u015ftirilmeden al\u0131nd\u0131\u011f\u0131nda (ki bu neredeyse her zaman b\u00f6yledir), \u00f6rneklem b\u00fcy\u00fckl\u00fc\u011f\u00fc toplam pop\u00fclasyonun %10&#8217;unu ge\u00e7memelidir.<\/span><\/p>\n<p> <span style=\"color: #000000;\">\u00d6rne\u011fin:<\/span><\/p>\n<ul>\n<li> <span style=\"color: #000000;\">Pop\u00fclasyon b\u00fcy\u00fckl\u00fc\u011f\u00fcm\u00fcz 500 ki\u015fi ise \u00f6rneklem b\u00fcy\u00fckl\u00fc\u011f\u00fcm\u00fcz\u00fcn 50 ki\u015fiyi ge\u00e7memesi gerekiyor.<\/span><\/li>\n<li> <span style=\"color: #000000;\">Pop\u00fclasyon b\u00fcy\u00fckl\u00fc\u011f\u00fcm\u00fcz 1.000 ki\u015fi ise \u00f6rneklemimizin 100 ki\u015fiyi ge\u00e7memesi gerekiyor.<\/span><\/li>\n<li> <span style=\"color: #000000;\">E\u011fer pop\u00fclasyon b\u00fcy\u00fckl\u00fc\u011f\u00fcm\u00fcz 50.000 ki\u015fi ise \u00f6rneklem b\u00fcy\u00fckl\u00fc\u011f\u00fcm\u00fcz\u00fcn 5.000 ki\u015fiyi ge\u00e7memesi gerekiyor.<\/span><\/li>\n<\/ul>\n<p> <span style=\"color: #000000;\">Ve benzeri.<\/span><\/p>\n<h3> <span style=\"color: #000000;\"><strong>Durum 4: B\u00fcy\u00fck numune ko\u015fulu<\/strong><\/span><\/h3>\n<p> <span style=\"color: #000000;\">Son olarak merkezi limit teoremini uygulayabilmek i\u00e7in \u00f6rneklem b\u00fcy\u00fckl\u00fc\u011f\u00fcm\u00fcz\u00fcn yeterince b\u00fcy\u00fck olmas\u0131 gerekir.<\/span><\/p>\n<p> <span style=\"color: #000000;\">Genellikle &#8220;yeterince b\u00fcy\u00fck&#8221; ifadesinin 30 veya daha fazla oldu\u011funu d\u00fc\u015f\u00fcn\u00fcyoruz. Ancak bu say\u0131, n\u00fcfus da\u011f\u0131l\u0131m\u0131n\u0131n temel \u015fekline ba\u011fl\u0131 olarak biraz de\u011fi\u015febilir.<\/span><\/p>\n<p> <span style=\"color: #000000;\">\u00d6zellikle:<\/span><\/p>\n<ul>\n<li> <span style=\"color: #000000;\">N\u00fcfus da\u011f\u0131l\u0131m\u0131 simetrikse, 15 kadar k\u00fc\u00e7\u00fck bir \u00f6rneklem b\u00fcy\u00fckl\u00fc\u011f\u00fc bazen yeterli olabilir.<\/span><\/li>\n<li> <span style=\"color: #000000;\">N\u00fcfus da\u011f\u0131l\u0131m\u0131 \u00e7arp\u0131ksa genellikle en az 30 ki\u015fiden olu\u015fan bir \u00f6rneklem gereklidir.<\/span><\/li>\n<li> <span style=\"color: #000000;\">N\u00fcfus da\u011f\u0131l\u0131m\u0131 a\u015f\u0131r\u0131 derecede \u00e7arp\u0131ksa 40 veya daha fazla ki\u015fiden olu\u015fan bir \u00f6rneklem gerekli olabilir.<\/span><\/li>\n<\/ul>\n<p> <span style=\"color: #000000;\">N\u00fcfus da\u011f\u0131l\u0131m\u0131n\u0131n \u015fekline ba\u011fl\u0131 olarak, merkezi limit teoreminin uygulanmas\u0131 i\u00e7in 30&#8217;dan b\u00fcy\u00fck veya k\u00fc\u00e7\u00fck bir \u00f6rneklem b\u00fcy\u00fckl\u00fc\u011f\u00fcne ihtiyac\u0131n\u0131z olabilir.<\/span><\/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 teoremini uygulamak i\u00e7in d\u00f6rt ko\u015fulun kar\u015f\u0131lanmas\u0131 gerekir: 1. Rastgelele\u015ftirme : Veriler rastgele \u00f6rneklenmelidir, b\u00f6ylece pop\u00fclasyonun her bir \u00fcyesinin \u00f6rne\u011fin bir par\u00e7as\u0131 olmak \u00fczere se\u00e7ilme olas\u0131l\u0131\u011f\u0131 e\u015fit olmal\u0131d\u0131r. 2. Ba\u011f\u0131ms\u0131zl\u0131k: Numunelerin de\u011ferleri birbirinden [&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-1368","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>Merkezi limit teoremi: yerine getirilmesi gereken d\u00f6rt ko\u015ful<\/title>\n<meta name=\"description\" content=\"Bu e\u011fitimde merkezi limit teoremini uygulamak i\u00e7in kar\u015f\u0131lanmas\u0131 gereken d\u00f6rt ko\u015ful a\u00e7\u0131klanmaktad\u0131r.\" \/>\n<meta name=\"robots\" content=\"index, follow, max-snippet:-1, max-image-preview:large, max-video-preview:-1\" \/>\n<link rel=\"canonical\" href=\"https:\/\/statorials.org\/tr\/kosullar-merkezi-limit-teoremi\/\" \/>\n<meta property=\"og:locale\" content=\"tr_TR\" \/>\n<meta property=\"og:type\" content=\"article\" \/>\n<meta property=\"og:title\" content=\"Merkezi limit teoremi: yerine getirilmesi gereken d\u00f6rt ko\u015ful\" \/>\n<meta property=\"og:description\" content=\"Bu e\u011fitimde merkezi limit teoremini uygulamak i\u00e7in kar\u015f\u0131lanmas\u0131 gereken d\u00f6rt ko\u015ful a\u00e7\u0131klanmaktad\u0131r.\" \/>\n<meta property=\"og:url\" content=\"https:\/\/statorials.org\/tr\/kosullar-merkezi-limit-teoremi\/\" \/>\n<meta property=\"og:site_name\" content=\"Statorials\" \/>\n<meta property=\"article:published_time\" content=\"2023-07-26T16:34:08+00:00\" \/>\n<meta name=\"author\" content=\"Dr.benjamin anderson\" \/>\n<meta name=\"twitter:card\" content=\"summary_large_image\" \/>\n<meta name=\"twitter:label1\" content=\"Yazan:\" \/>\n\t<meta name=\"twitter:data1\" content=\"Dr.benjamin anderson\" \/>\n\t<meta name=\"twitter:label2\" content=\"Tahmini okuma s\u00fcresi\" \/>\n\t<meta name=\"twitter:data2\" content=\"3 dakika\" \/>\n<script type=\"application\/ld+json\" class=\"yoast-schema-graph\">{\"@context\":\"https:\/\/schema.org\",\"@graph\":[{\"@type\":\"WebPage\",\"@id\":\"https:\/\/statorials.org\/tr\/kosullar-merkezi-limit-teoremi\/\",\"url\":\"https:\/\/statorials.org\/tr\/kosullar-merkezi-limit-teoremi\/\",\"name\":\"Merkezi limit teoremi: yerine getirilmesi gereken d\u00f6rt ko\u015ful\",\"isPartOf\":{\"@id\":\"https:\/\/statorials.org\/tr\/#website\"},\"datePublished\":\"2023-07-26T16:34:08+00:00\",\"dateModified\":\"2023-07-26T16:34:08+00:00\",\"author\":{\"@id\":\"https:\/\/statorials.org\/tr\/#\/schema\/person\/365dc158a39a7c8ae256355451e3de48\"},\"description\":\"Bu e\u011fitimde merkezi limit teoremini uygulamak i\u00e7in kar\u015f\u0131lanmas\u0131 gereken d\u00f6rt ko\u015ful a\u00e7\u0131klanmaktad\u0131r.\",\"breadcrumb\":{\"@id\":\"https:\/\/statorials.org\/tr\/kosullar-merkezi-limit-teoremi\/#breadcrumb\"},\"inLanguage\":\"tr\",\"potentialAction\":[{\"@type\":\"ReadAction\",\"target\":[\"https:\/\/statorials.org\/tr\/kosullar-merkezi-limit-teoremi\/\"]}]},{\"@type\":\"BreadcrumbList\",\"@id\":\"https:\/\/statorials.org\/tr\/kosullar-merkezi-limit-teoremi\/#breadcrumb\",\"itemListElement\":[{\"@type\":\"ListItem\",\"position\":1,\"name\":\"Ev\",\"item\":\"https:\/\/statorials.org\/tr\/\"},{\"@type\":\"ListItem\",\"position\":2,\"name\":\"Merkezi limit teoremi: yerine getirilmesi gereken d\u00f6rt ko\u015ful\"}]},{\"@type\":\"WebSite\",\"@id\":\"https:\/\/statorials.org\/tr\/#website\",\"url\":\"https:\/\/statorials.org\/tr\/\",\"name\":\"Statorials\",\"description\":\"\u0130statistik okuryazarl\u0131\u011f\u0131 rehberiniz!\",\"potentialAction\":[{\"@type\":\"SearchAction\",\"target\":{\"@type\":\"EntryPoint\",\"urlTemplate\":\"https:\/\/statorials.org\/tr\/?s={search_term_string}\"},\"query-input\":\"required name=search_term_string\"}],\"inLanguage\":\"tr\"},{\"@type\":\"Person\",\"@id\":\"https:\/\/statorials.org\/tr\/#\/schema\/person\/365dc158a39a7c8ae256355451e3de48\",\"name\":\"Dr.benjamin anderson\",\"image\":{\"@type\":\"ImageObject\",\"inLanguage\":\"tr\",\"@id\":\"https:\/\/statorials.org\/tr\/#\/schema\/person\/image\/\",\"url\":\"https:\/\/statorials.org\/tr\/wp-content\/uploads\/2023\/10\/Dr.-Benjamin-Anderson-96x96.jpg\",\"contentUrl\":\"https:\/\/statorials.org\/tr\/wp-content\/uploads\/2023\/10\/Dr.-Benjamin-Anderson-96x96.jpg\",\"caption\":\"Dr.benjamin anderson\"},\"description\":\"Merhaba, ben Benjamin, emekli bir istatistik profes\u00f6r\u00fc ve Statorials \u00f6\u011fretmenine d\u00f6n\u00fc\u015ft\u00fcm. \u0130statistik alan\u0131ndaki kapsaml\u0131 deneyimim ve uzmanl\u0131\u011f\u0131mla, \u00f6\u011frencilerimi Statorials arac\u0131l\u0131\u011f\u0131yla g\u00fc\u00e7lendirmek i\u00e7in bilgilerimi payla\u015fmaya can at\u0131yorum. 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