{"id":1236,"date":"2023-07-27T04:44:44","date_gmt":"2023-07-27T04:44:44","guid":{"rendered":"https:\/\/statorials.org\/tr\/populasyon-ortalamasiyla-karsilastirildiginda-ornek-ortalamasi\/"},"modified":"2023-07-27T04:44:44","modified_gmt":"2023-07-27T04:44:44","slug":"populasyon-ortalamasiyla-karsilastirildiginda-ornek-ortalamasi","status":"publish","type":"post","link":"https:\/\/statorials.org\/tr\/populasyon-ortalamasiyla-karsilastirildiginda-ornek-ortalamasi\/","title":{"rendered":"\u00d6rnek ortalama ve pop\u00fclasyon ortalamas\u0131: fark nedir?"},"content":{"rendered":"<p><\/p>\n<hr>\n<p><span style=\"color: #000000;\">\u0130statistiklerde s\u0131kl\u0131kla a\u015fa\u011f\u0131daki gibi sorular\u0131 yan\u0131tlamak isteriz:<\/span><\/p>\n<ul>\n<li> <span style=\"color: #000000;\">Belirli bir \u015fehirdeki ortalama hane geliri nedir?<\/span><\/li>\n<li> <span style=\"color: #000000;\">Belirli bir kaplumba\u011fa t\u00fcr\u00fcn\u00fcn ortalama a\u011f\u0131rl\u0131\u011f\u0131 nedir?<\/span><\/li>\n<li> <span style=\"color: #000000;\">Kolej futbol ma\u00e7lar\u0131na ortalama seyirci say\u0131s\u0131 nedir?<\/span><\/li>\n<\/ul>\n<p> <span style=\"color: #000000;\">Her senaryoda, \u00f6l\u00e7mek istedi\u011fimiz t\u00fcm olas\u0131 bireysel unsurlar\u0131 temsil eden bir <a href=\"https:\/\/statorials.org\/tr\/populasyon-ve-ornek\/\" target=\"_blank\" rel=\"noopener noreferrer\">n\u00fcfus<\/a> hakk\u0131ndaki soruyu yan\u0131tlamak istiyoruz.<\/span><\/p>\n<p> <span style=\"color: #000000;\">Ancak, bir pop\u00fclasyondaki her bireye ili\u015fkin veri toplamak yerine, bunun yerine, toplam pop\u00fclasyonun bir b\u00f6l\u00fcm\u00fcn\u00fc temsil eden pop\u00fclasyonun bir \u00f6rne\u011fine ili\u015fkin veri topluyoruz.<\/span><\/p>\n<p> <span style=\"color: #000000;\">\u00d6rne\u011fin toplam pop\u00fclasyonu 800 kaplumba\u011fa olan belirli bir kaplumba\u011fa t\u00fcr\u00fcn\u00fcn ortalama a\u011f\u0131rl\u0131\u011f\u0131n\u0131 bilmek isteyebiliriz.<\/span><\/p>\n<p> <span style=\"color: #000000;\">Pop\u00fclasyondaki her kaplumba\u011fan\u0131n yerini tespit etmek ve tartmak \u00e7ok uzun zaman alaca\u011f\u0131ndan, bunun yerine 30 kaplumba\u011fadan olu\u015fan rastgele basit bir \u00f6rnek topluyor ve a\u011f\u0131rl\u0131klar\u0131n\u0131 \u00f6l\u00e7\u00fcyoruz:<\/span> <\/p>\n<p><img decoding=\"async\" loading=\"lazy\" class=\"aligncenter wp-image-12211 \" src=\"https:\/\/statorials.org\/wp-content\/uploads\/2023\/08\/pop_vs_sample2.png\" alt=\"Ortalama \u00d6rnek \u00d6rnek\" width=\"330\" height=\"443\" srcset=\"\" sizes=\"auto, \"><\/p>\n<p> <span style=\"color: #000000;\">Daha sonra pop\u00fclasyondaki t\u00fcm kaplumba\u011falar\u0131n ortalama a\u011f\u0131rl\u0131\u011f\u0131n\u0131 tahmin etmek i\u00e7in bu kaplumba\u011fa \u00f6rne\u011finin ortalama a\u011f\u0131rl\u0131\u011f\u0131n\u0131 kullanabiliriz.<\/span><\/p>\n<h3> <span style=\"color: #000000;\"><strong>\u00d6rnek ortalama nas\u0131l hesaplan\u0131r<\/strong><\/span><\/h3>\n<p> <span style=\"color: #000000;\">Genellikle <span style=\"text-decoration: overline;\">x<\/span> ile g\u00f6sterilen \u00f6rnek ortalamas\u0131n\u0131 hesaplama form\u00fcl\u00fc a\u015fa\u011f\u0131daki gibidir:<\/span><\/p>\n<p> <span style=\"color: #000000;\"><strong><span style=\"text-decoration: overline;\">x<\/span> = \u03a3x <sub>ben<\/sub> \/ n<\/strong><\/span><\/p>\n<p> <span style=\"color: #000000;\">Alt\u0131n:<\/span><\/p>\n<ul>\n<li> <span style=\"color: #000000;\"><strong>\u03a3:<\/strong> \u201ctoplam\u201d anlam\u0131na gelen karma\u015f\u0131k bir Yunan sembol\u00fc<\/span><\/li>\n<li> <span style=\"color: #000000;\"><strong>x <sub>i<\/sub> :<\/strong> Veri k\u00fcmesindeki i&#8217;inci g\u00f6zlemin de\u011feri<\/span><\/li>\n<li> <span style=\"color: #000000;\"><strong>n:<\/strong> \u00d6rneklem b\u00fcy\u00fckl\u00fc\u011f\u00fc<\/span><\/li>\n<\/ul>\n<p> <span style=\"color: #000000;\">\u00d6rne\u011fin, a\u015fa\u011f\u0131daki a\u011f\u0131rl\u0131klara (pound cinsinden) sahip 10 kaplumba\u011fadan olu\u015fan bir \u00f6rnek toplad\u0131\u011f\u0131m\u0131z\u0131 varsayal\u0131m:<\/span><\/p>\n<ul>\n<li> <span style=\"color: #000000;\">70, 80, 80, 85, 90, 95, 110, 120, 140, 150<\/span><\/li>\n<\/ul>\n<p> <span style=\"color: #000000;\">\u00d6rnek ortalama \u015fu \u015fekilde hesaplanacakt\u0131r:<\/span><\/p>\n<ul>\n<li> <span style=\"color: #000000;\"><strong><span style=\"text-decoration: overline;\">x<\/span><\/strong> = (70+ 80+80+85+90+95+110+120+140+150) \/ 10 = <strong>102<\/strong><\/span><\/li>\n<\/ul>\n<h3> <span style=\"color: #000000;\"><strong>\u00d6rnek ortalaman\u0131n neden tarafs\u0131z oldu\u011fu<\/strong><\/span><\/h3>\n<p> <span style=\"color: #000000;\">\u0130statistik jargonunda, \u00f6rnek ortalaman\u0131n bir <strong>istatistik<\/strong> , pop\u00fclasyon ortalamas\u0131n\u0131n ise bir <strong>parametre<\/strong> oldu\u011funu s\u00f6yleyebiliriz.<\/span><\/p>\n<p> <span style=\"color: #000000;\">\u0130\u015fte iki terim aras\u0131ndaki fark:<\/span><\/p>\n<p> <span style=\"color: #000000;\"><strong>\u0130statistik<\/strong> , bir numunenin belirli \u00f6zelliklerini tan\u0131mlayan bir say\u0131d\u0131r.<\/span><\/p>\n<p> <span style=\"color: #000000;\"><strong>Parametre,<\/strong> bir pop\u00fclasyonun karakteristi\u011fini tan\u0131mlayan bir say\u0131d\u0131r.<\/span><\/p>\n<p> <span style=\"color: #000000;\">Parametre asl\u0131nda \u00f6l\u00e7mek istedi\u011fimiz de\u011ferdir ancak istatistik elde edilmesi \u00e7ok daha kolay oldu\u011fundan parametrenin de\u011ferini tahmin etmek i\u00e7in kulland\u0131\u011f\u0131m\u0131z de\u011ferdir.<\/span><\/p>\n<p> <span style=\"color: #000000;\">Bir \u00f6rnek elde etmek i\u00e7in<a href=\"https:\/\/statorials.org\/tr\/ornekleme-yontemleri\/\" target=\"_blank\" rel=\"noopener noreferrer\">basit rastgele \u00f6rnekleme<\/a> gibi bir y\u00f6ntem kulland\u0131\u011f\u0131m\u0131zda, \u00f6rnek ortalamas\u0131n\u0131n pop\u00fclasyon ortalamas\u0131n\u0131n <strong>tarafs\u0131z bir tahmincisi<\/strong> oldu\u011funu s\u00f6yleriz.<\/span><\/p>\n<p> <span style=\"color: #000000;\">Ba\u015fka bir deyi\u015fle, \u00f6rneklem ortalamas\u0131n\u0131n ger\u00e7ek pop\u00fclasyon ortalamas\u0131n\u0131 oldu\u011fundan az veya fazla tahmin edece\u011fine inanmam\u0131z i\u00e7in hi\u00e7bir nedenimiz yok.<\/span><\/p>\n<p> <span style=\"color: #000000;\">Bunun nedeni, basit rastgele \u00f6rnekleme gibi bir y\u00f6ntem kulland\u0131\u011f\u0131m\u0131zda, pop\u00fclasyonun her \u00fcyesinin \u00f6rne\u011fe dahil olma \u015fans\u0131n\u0131n e\u015fit olmas\u0131d\u0131r; bu da, \u00f6rne\u011fin, genel pop\u00fclasyonun &#8220;mini versiyonu&#8221; olma ihtimalinin y\u00fcksek oldu\u011fu anlam\u0131na gelir. .<\/span><\/p>\n<p> <span style=\"color: #000000;\">Numunenin <a href=\"https:\/\/statorials.org\/tr\/temsili-ornek-1\/\" target=\"_blank\" rel=\"noopener noreferrer\">genel pop\u00fclasyonu temsil<\/a> etti\u011fini s\u00f6yleyebiliriz; bu, numune b\u00fcy\u00fckl\u00fc\u011f\u00fcn\u00fcn yeterince b\u00fcy\u00fck oldu\u011fu varsay\u0131larak, numune ortalamas\u0131n\u0131n pop\u00fclasyon ortalamas\u0131n\u0131n iyi bir tahmini olmas\u0131 gerekti\u011fi anlam\u0131na gelir.<\/span><\/p>\n<h3> <span style=\"color: #000000;\"><strong>\u00d6rnek ortalamayla g\u00fcven aral\u0131klar\u0131n\u0131n kullan\u0131lmas\u0131 hakk\u0131nda<\/strong><\/span><\/h3>\n<p> <span style=\"color: #000000;\">Her ne kadar \u00f6rnek ortalamas\u0131 pop\u00fclasyon ortalamas\u0131n\u0131n tarafs\u0131z bir tahminini sa\u011flasa da, pop\u00fclasyon ortalamas\u0131n\u0131 <em>tam olarak<\/em> e\u015fle\u015ftirmesi pek olas\u0131 de\u011fildir.<\/span><\/p>\n<p> <span style=\"color: #000000;\">\u00d6rne\u011fin, bir kaplumba\u011fa pop\u00fclasyonunun ortalama a\u011f\u0131rl\u0131\u011f\u0131n\u0131 tahmin etmek i\u00e7in bir kaplumba\u011fa \u00f6rne\u011fini kullanmak istersek, d\u00fc\u015f\u00fck a\u011f\u0131rl\u0131kl\u0131 kaplumba\u011falarla dolu bir \u00f6rne\u011fi veya belki de a\u011f\u0131r kaplumba\u011falarla dolu bir \u00f6rne\u011fi se\u00e7ebiliriz.<\/span><\/p>\n<p> <span style=\"color: #000000;\">N\u00fcfus ortalamas\u0131na ili\u015fkin tahminimiz etraf\u0131ndaki bu belirsizli\u011fi yakalamak i\u00e7in bir<a href=\"https:\/\/statorials.org\/tr\/guvenilirlik-araligi\/\" target=\"_blank\" rel=\"noopener noreferrer\">g\u00fcven aral\u0131\u011f\u0131<\/a> olu\u015fturabiliriz.<\/span><\/p>\n<p> <span style=\"color: #000000;\">G\u00fcven aral\u0131\u011f\u0131, belirli bir g\u00fcven d\u00fczeyine sahip bir pop\u00fclasyon parametresini i\u00e7ermesi muhtemel bir de\u011fer aral\u0131\u011f\u0131d\u0131r.<\/span><\/p>\n<p> <span style=\"color: #000000;\">\u00d6rne\u011fin, 30 kaplumba\u011fadan olu\u015fan bir \u00f6rnek toplayabiliriz ve bu \u00f6rne\u011fin ortalama a\u011f\u0131rl\u0131\u011f\u0131n\u0131n 102 pound oldu\u011funu bulabiliriz. Daha sonra %95&#8217;lik bir g\u00fcven aral\u0131\u011f\u0131 olu\u015fturursak aral\u0131\u011f\u0131n \u015fu \u015fekilde oldu\u011funu bulabiliriz:<\/span><\/p>\n<p> <span style=\"color: #000000;\"><strong>%95 g\u00fcven aral\u0131\u011f\u0131 = [98,5, 105,5]<\/strong><\/span><\/p>\n<p> <span style=\"color: #000000;\">Bunu, [98.5, 105.5] g\u00fcven aral\u0131\u011f\u0131n\u0131n kaplumba\u011fa pop\u00fclasyonunun ger\u00e7ek ortalama a\u011f\u0131rl\u0131\u011f\u0131n\u0131 i\u00e7erme ihtimalinin %95 oldu\u011fu \u015feklinde yorumlayabiliriz.<\/span><\/p>\n<p> <span style=\"color: #000000;\">Bu g\u00fcven aral\u0131\u011f\u0131 basit \u00f6rnek ortalamas\u0131ndan daha kullan\u0131\u015fl\u0131d\u0131r \u00e7\u00fcnk\u00fc bize ger\u00e7ek pop\u00fclasyon ortalamas\u0131n\u0131n muhtemelen i\u00e7inde yer ald\u0131\u011f\u0131 bir de\u011fer <em>aral\u0131\u011f\u0131<\/em> verir.<\/span><\/p>\n<h3> <span style=\"color: #000000;\"><strong>Ek kaynaklar<\/strong><\/span><\/h3>\n<p> <a href=\"https:\/\/statorials.org\/tr\/populasyon-ve-ornek\/\" target=\"_blank\" rel=\"noopener noreferrer\">N\u00fcfus vs. \u00f6rnek: fark nedir?<\/a><br \/> <a href=\"https:\/\/statorials.org\/tr\/istatistik-ve-parametre\/\" target=\"_blank\" rel=\"noopener noreferrer\">\u0130statistik vs. parametreler: fark nedir?<\/a><br \/><a href=\"https:\/\/statorials.org\/tr\/guvenilirlik-araligi\/\" target=\"_blank\" rel=\"noopener noreferrer\">G\u00fcven Aral\u0131klar\u0131na Giri\u015f<\/a><\/p>\n","protected":false},"excerpt":{"rendered":"<p>\u0130statistiklerde s\u0131kl\u0131kla a\u015fa\u011f\u0131daki gibi sorular\u0131 yan\u0131tlamak isteriz: Belirli bir \u015fehirdeki ortalama hane geliri nedir? Belirli bir kaplumba\u011fa t\u00fcr\u00fcn\u00fcn ortalama a\u011f\u0131rl\u0131\u011f\u0131 nedir? Kolej futbol ma\u00e7lar\u0131na ortalama seyirci say\u0131s\u0131 nedir? Her senaryoda, \u00f6l\u00e7mek istedi\u011fimiz t\u00fcm olas\u0131 bireysel unsurlar\u0131 temsil eden bir n\u00fcfus hakk\u0131ndaki soruyu yan\u0131tlamak istiyoruz. Ancak, bir pop\u00fclasyondaki her bireye ili\u015fkin veri toplamak yerine, bunun yerine, [&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-1236","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>\u00d6rnek ortalama ve pop\u00fclasyon ortalamas\u0131: fark nedir?<\/title>\n<meta name=\"description\" content=\"\u00d6rnek ortalamas\u0131 ile pop\u00fclasyon ortalamas\u0131 aras\u0131ndaki fark\u0131n \u00f6rneklerle basit bir a\u00e7\u0131klamas\u0131.\" \/>\n<meta name=\"robots\" content=\"index, follow, max-snippet:-1, max-image-preview:large, max-video-preview:-1\" \/>\n<link rel=\"canonical\" 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