{"id":2177,"date":"2023-07-23T09:23:03","date_gmt":"2023-07-23T09:23:03","guid":{"rendered":"https:\/\/statorials.org\/tr\/populasyon-varyansina-gore-orneklem-varyansi\/"},"modified":"2023-07-23T09:23:03","modified_gmt":"2023-07-23T09:23:03","slug":"populasyon-varyansina-gore-orneklem-varyansi","status":"publish","type":"post","link":"https:\/\/statorials.org\/tr\/populasyon-varyansina-gore-orneklem-varyansi\/","title":{"rendered":"\u00d6rnek varyans vs. n\u00fcfus varyans\u0131: fark nedir?"},"content":{"rendered":"<p><\/p>\n<hr>\n<p><span style=\"color: #000000;\"><strong>Varyans<\/strong> , bir veri k\u00fcmesindeki de\u011ferlerin da\u011f\u0131l\u0131m\u0131n\u0131 \u00f6l\u00e7menin bir yoludur.<\/span><\/p>\n<p> <span style=\"color: #000000;\"><strong>Pop\u00fclasyon varyans\u0131n\u0131<\/strong> hesaplama form\u00fcl\u00fc \u015f\u00f6yledir:<\/span><\/p>\n<p style=\"text-align: left;\"> <span style=\"color: #000000;\"><strong>\u03c3 <sup>2<\/sup><\/strong> = \u03a3 (x <sub>ben<\/sub> \u2013 \u03bc) <sup>2<\/sup> \/ N<\/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 bir sembol<\/span><\/li>\n<li> <span style=\"color: #000000;\"><strong>\u03bc<\/strong> : N\u00fcfus ortalamas\u0131<\/span><\/li>\n<li> <span style=\"color: #000000;\"><strong>x <sub>i<\/sub><\/strong> : Pop\u00fclasyonun <sup>i&#8217;inci<\/sup> eleman\u0131<\/span><\/li>\n<li> <span style=\"color: #000000;\"><strong>N<\/strong> : N\u00fcfus b\u00fcy\u00fckl\u00fc\u011f\u00fc<\/span><\/li>\n<\/ul>\n<p> <span style=\"color: #000000;\"><strong>\u00d6rnek varyans\u0131n\u0131<\/strong> hesaplama form\u00fcl\u00fc \u015f\u00f6yledir:<\/span><\/p>\n<p style=\"text-align: left;\"> <span style=\"color: #000000;\"><strong>s <sup>2<\/sup><\/strong> = \u03a3 (x <sub>ben<\/sub> \u2013 <span style=\"text-decoration: overline;\">x<\/span> ) <sup>2<\/sup> \/ (n-1)<\/span><\/p>\n<p> <span style=\"color: #000000;\">Alt\u0131n:<\/span><\/p>\n<ul>\n<li> <span style=\"color: #000000;\"><strong><span style=\"text-decoration: overline;\">x<\/span><\/strong> : \u00f6rnek ortalama<\/span><\/li>\n<li> <span style=\"color: #000000;\"><strong>x <sub>i<\/sub><\/strong> : \u00d6rneklemin <sup>i&#8217;inci<\/sup> eleman\u0131<\/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;\">\u0130ki form\u00fcl aras\u0131nda yaln\u0131zca k\u00fc\u00e7\u00fck bir fark oldu\u011funu unutmay\u0131n:<\/span><\/p>\n<p> <span style=\"color: #000000;\">Pop\u00fclasyon varyans\u0131n\u0131 hesaplarken <strong>N&#8217;ye<\/strong> (pop\u00fclasyonun b\u00fcy\u00fckl\u00fc\u011f\u00fc) b\u00f6l\u00fcyoruz.<\/span><\/p>\n<p> <span style=\"color: #000000;\">\u00d6rneklem varyans\u0131n\u0131 hesaplarken <strong>n-1&#8217;e<\/strong> (\u00f6rneklem b\u00fcy\u00fckl\u00fc\u011f\u00fc \u2013 1) b\u00f6l\u00fcyoruz.<\/span><\/p>\n<p> <span style=\"color: #000000;\">\u00d6rneklem varyans\u0131n\u0131 hesaplarken, <a href=\"https:\/\/en.wikipedia.org\/wiki\/Bessel%27s_correction\" target=\"_blank\" rel=\"noopener\">Bessel d\u00fczeltmesi<\/a> ad\u0131 verilen ve n-1&#8217;e b\u00f6lmeyi i\u00e7eren y\u00f6ntemi uyguluyoruz.<\/span><\/p>\n<p> <span style=\"color: #000000;\">Matematiksel ayr\u0131nt\u0131lara bo\u011fulmadan, n-1&#8217;e b\u00f6lmek, zaten genellikle ilgilendi\u011fimiz de\u011fer olan pop\u00fclasyon varyans\u0131n\u0131n tarafs\u0131z bir tahminini sa\u011flayabilir.<\/span><\/p>\n<h3> <span style=\"color: #000000;\"><strong>\u00d6rneklem varyans\u0131 ve pop\u00fclasyon varyans\u0131 ne zaman hesaplan\u0131r?<\/strong><\/span><\/h3>\n<p> <span style=\"color: #000000;\">\u00d6rnek varyans\u0131n\u0131 m\u0131 yoksa pop\u00fclasyon varyans\u0131n\u0131 m\u0131 hesaplayaca\u011f\u0131n\u0131zdan emin de\u011filseniz \u015fu genel kural\u0131 akl\u0131n\u0131zda bulundurun:<\/span><\/p>\n<p> <span style=\"color: #000000;\">\u00dczerinde \u00e7al\u0131\u015ft\u0131\u011f\u0131n\u0131z veri seti daha b\u00fcy\u00fck bir pop\u00fclasyondan al\u0131nan bir \u00f6rne\u011fi temsil ediyorsa <strong>\u00f6rnek varyans\u0131n\u0131<\/strong> hesaplaman\u0131z gerekir.<\/span><\/p>\n<p> <span style=\"color: #000000;\">\u00dczerinde \u00e7al\u0131\u015ft\u0131\u011f\u0131n\u0131z veri seti t\u00fcm pop\u00fclasyonu, yani ilgilendi\u011finiz her de\u011feri temsil ediyorsa <strong>pop\u00fclasyon varyans\u0131n\u0131<\/strong> hesaplaman\u0131z gerekir.<\/span><\/p>\n<p> <span style=\"color: #000000;\">A\u015fa\u011f\u0131daki \u00f6rneklerde \u00f6rneklem varyans\u0131n\u0131n pop\u00fclasyon varyans\u0131na g\u00f6re hesaplanmas\u0131na y\u00f6nelik farkl\u0131 senaryolar g\u00f6sterilmektedir.<\/span><\/p>\n<h3> <span style=\"color: #000000;\"><strong>\u00d6rnek: \u00d6rnek Varyans\u0131n Hesaplanmas\u0131<\/strong><\/span><\/h3>\n<p> <span style=\"color: #000000;\">Bir botanik\u00e7inin belirli bir bitki t\u00fcr\u00fcn\u00fcn boy de\u011fi\u015fimini hesaplamak istedi\u011fini varsayal\u0131m. Bir b\u00f6lgede binlerce ayr\u0131 bitki bulundu\u011fundan, 20 bitkiden olu\u015fan basit ve rastgele bir \u00f6rnek almaya ve her birinin y\u00fcksekli\u011fini \u00f6l\u00e7meye karar verir.<\/span> <\/p>\n<p><img decoding=\"async\" loading=\"lazy\" class=\" wp-image-20106 aligncenter\" src=\"https:\/\/statorials.org\/wp-content\/uploads\/2023\/08\/popsamp1.png\" alt=\"\" width=\"407\" height=\"401\" srcset=\"\" sizes=\"auto, \"><\/p>\n<p> <span style=\"color: #000000;\">Bu senaryoda botanik\u00e7inin <strong>\u00f6rnek varyans\u0131n\u0131<\/strong> hesaplamas\u0131 gerekir \u00e7\u00fcnk\u00fc bitki pop\u00fclasyonunun tamam\u0131n\u0131n varyans\u0131yla ilgilenmektedir ancak bu \u00f6rne\u011fi sadece ger\u00e7ek pop\u00fclasyon varyans\u0131n\u0131 tahmin etmek i\u00e7in kullanmaktad\u0131r.<\/span><\/p>\n<h3> <span style=\"color: #000000;\"><strong>\u00d6rnek: pop\u00fclasyon varyans\u0131n\u0131n hesaplanmas\u0131<\/strong><\/span><\/h3>\n<p> <span style=\"color: #000000;\">Bir \u00f6\u011fretmenin s\u0131n\u0131f\u0131ndaki 20 \u00f6\u011frencinin s\u0131nav puanlar\u0131n\u0131n varyans\u0131n\u0131 hesaplamak istedi\u011fini varsayal\u0131m.<\/span> <\/p>\n<p><img decoding=\"async\" loading=\"lazy\" class=\" wp-image-20107 aligncenter\" src=\"https:\/\/statorials.org\/wp-content\/uploads\/2023\/08\/varsamp.png\" alt=\"\" width=\"63\" height=\"360\" srcset=\"\" sizes=\"auto, \"><\/p>\n<p> <span style=\"color: #000000;\">Bu senaryoda \u00f6\u011fretmenin <strong>pop\u00fclasyon varyans\u0131n\u0131<\/strong> hesaplamas\u0131 gerekir \u00e7\u00fcnk\u00fc \u00fczerinde \u00e7al\u0131\u015ft\u0131\u011f\u0131 veri seti (20 s\u0131nav sonucu) ilgilenilen pop\u00fclasyonun tamam\u0131n\u0131 temsil eder.<\/span><\/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, farkl\u0131 istatistiksel yaz\u0131l\u0131mlarda \u00f6rnek varyans\u0131n\u0131n ve pop\u00fclasyon varyans\u0131n\u0131n nas\u0131l hesaplanaca\u011f\u0131n\u0131 a\u00e7\u0131klamaktad\u0131r:<\/span><\/p>\n<p><a href=\"https:\/\/statorials.org\/tr\/ornek-populasyon-varyansi-excel\/\" target=\"_blank\" rel=\"noopener\">Excel&#8217;de \u00d6rnek ve Pop\u00fclasyon Varyans\u0131 Nas\u0131l Hesaplan\u0131r?<\/a><br \/> <a href=\"https:\/\/statorials.org\/tr\/rdeki-varyans\/\" target=\"_blank\" rel=\"noopener\">R&#8217;de \u00f6rnek ve pop\u00fclasyon varyans\u0131 nas\u0131l hesaplan\u0131r?<\/a><br \/> <a href=\"https:\/\/statorials.org\/tr\/ornek-populasyon-varyansi-pitonu\/\" target=\"_blank\" rel=\"noopener\">Python&#8217;da \u00f6rnek ve pop\u00fclasyon varyans\u0131 nas\u0131l hesaplan\u0131r<\/a><\/p>\n","protected":false},"excerpt":{"rendered":"<p>Varyans , bir veri k\u00fcmesindeki de\u011ferlerin da\u011f\u0131l\u0131m\u0131n\u0131 \u00f6l\u00e7menin bir yoludur. Pop\u00fclasyon varyans\u0131n\u0131 hesaplama form\u00fcl\u00fc \u015f\u00f6yledir: \u03c3 2 = \u03a3 (x ben \u2013 \u03bc) 2 \/ N Alt\u0131n: \u03a3 : \u201cToplam\u201d anlam\u0131na gelen bir sembol \u03bc : N\u00fcfus ortalamas\u0131 x i : Pop\u00fclasyonun i&#8217;inci eleman\u0131 N : N\u00fcfus b\u00fcy\u00fckl\u00fc\u011f\u00fc \u00d6rnek varyans\u0131n\u0131 hesaplama form\u00fcl\u00fc \u015f\u00f6yledir: s 2 [&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-2177","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>\u00d6rneklem varyans\u0131 ve pop\u00fclasyon varyans\u0131: fark nedir? - Statorials<\/title>\n<meta name=\"description\" content=\"Bu e\u011fitimde \u00f6rnek varyans ile pop\u00fclasyon varyans\u0131 aras\u0131ndaki fark\u0131n yan\u0131 s\u0131ra bunlar\u0131n ne zaman kullan\u0131laca\u011f\u0131 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\/populasyon-varyansina-gore-orneklem-varyansi\/\" \/>\n<meta property=\"og:locale\" content=\"tr_TR\" \/>\n<meta property=\"og:type\" content=\"article\" \/>\n<meta property=\"og:title\" content=\"\u00d6rneklem varyans\u0131 ve pop\u00fclasyon varyans\u0131: fark nedir? 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