{"id":1458,"date":"2023-07-26T07:43:59","date_gmt":"2023-07-26T07:43:59","guid":{"rendered":"https:\/\/statorials.org\/tr\/ornekleme-degiskenligi\/"},"modified":"2023-07-26T07:43:59","modified_gmt":"2023-07-26T07:43:59","slug":"ornekleme-degiskenligi","status":"publish","type":"post","link":"https:\/\/statorials.org\/tr\/ornekleme-degiskenligi\/","title":{"rendered":"\u00d6rnekleme de\u011fi\u015fkenli\u011fi nedir? tan\u0131m ve \u00f6rnek"},"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 eyaletteki 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;\">Bununla birlikte, 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 <strong>\u00f6rne\u011fine<\/strong> 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 <a href=\"https:\/\/statorials.org\/tr\/ornekleme-yontemleri\/\" target=\"_blank\" rel=\"noopener\">basit ve rastgele bir \u00f6rnek<\/a> toplay\u0131p bunlar\u0131 tart\u0131yoruz:<\/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<p> <span style=\"color: #000000;\"><strong>\u00d6rnekleme de\u011fi\u015fkenli\u011fi,<\/strong> ortalaman\u0131n \u00f6rnekten \u00f6rne\u011fe de\u011fi\u015fece\u011fi ger\u00e7e\u011fini ifade eder.<\/span><\/p>\n<p> <span style=\"color: #000000;\">\u00d6rne\u011fin, 30 kaplumba\u011fadan olu\u015fan rastgele bir \u00f6rnekte, \u00f6rnek ortalamas\u0131 350 pound olabilir. Ba\u015fka bir rastgele numunede numune arac\u0131 345 pound olabilir. Yine ba\u015fka bir numunede numune ortalamas\u0131 355 pound olabilir.<\/span> <\/p>\n<p><img decoding=\"async\" loading=\"lazy\" class=\"aligncenter wp-image-14437 \" src=\"https:\/\/statorials.org\/wp-content\/uploads\/2023\/08\/echantillonnagevariabilite1.png\" alt=\"\" width=\"220\" height=\"502\" srcset=\"\" sizes=\"auto, \"><\/p>\n<p> <span style=\"color: #000000;\">\u00d6rnek ortalamalar aras\u0131nda <strong>de\u011fi\u015fkenlik<\/strong> vard\u0131r.<\/span><\/p>\n<h3> <span style=\"color: #000000;\"><strong>\u00d6rnekleme de\u011fi\u015fkenli\u011fi nas\u0131l \u00f6l\u00e7\u00fcl\u00fcr?<\/strong><\/span><\/h3>\n<p> <span style=\"color: #000000;\">Uygulamada, bir pop\u00fclasyon parametresini tahmin etmek i\u00e7in yaln\u0131zca tek bir \u00f6rnek topluyoruz. \u00d6rne\u011fin, t\u00fcm kaplumba\u011fa pop\u00fclasyonunun ortalama a\u011f\u0131rl\u0131\u011f\u0131n\u0131 tahmin etmek i\u00e7in yaln\u0131zca 30 deniz kaplumba\u011fas\u0131ndan olu\u015fan tek bir \u00f6rnek toplayaca\u011f\u0131z.<\/span><\/p>\n<p> <span style=\"color: #000000;\">Bu, yaln\u0131zca bir \u00f6rnek ortalamas\u0131n\u0131 ( <span style=\"border-top: 1px solid black;\">x<\/span> ) hesaplayaca\u011f\u0131m\u0131z ve bunu pop\u00fclasyon ortalamas\u0131n\u0131 (\u03bc) tahmin etmek i\u00e7in kullanaca\u011f\u0131m\u0131z anlam\u0131na gelir.<\/span><\/p>\n<p> <span style=\"color: #000000;\"><strong>\u00d6rnek ortalama = <span style=\"border-top: 1px solid black;\">x<\/span><\/strong><\/span><\/p>\n<p> <span style=\"color: #000000;\">Ancak numune ortalamalar\u0131n\u0131n numuneden numuneye de\u011fi\u015fti\u011fini biliyoruz. Dolay\u0131s\u0131yla, bu de\u011fi\u015fkenli\u011fi hesaba katmak i\u00e7in \u00f6rnek ortalamas\u0131n\u0131n standart sapmas\u0131n\u0131 tahmin etmek amac\u0131yla a\u015fa\u011f\u0131daki form\u00fcl\u00fc kullanabiliriz:<\/span><\/p>\n<p> <span style=\"color: #000000;\"><strong>\u00d6rneklem ortalamas\u0131n\u0131n standart sapmas\u0131 = s\/ <span style=\"border-top: 1px solid black;\">\u221an<\/span><\/strong><\/span><\/p>\n<p> <span style=\"color: #000000;\">Alt\u0131n:<\/span><\/p>\n<ul>\n<li> <span style=\"color: #000000;\"><strong>s:<\/strong> numunenin standart sapmas\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;\">\u00d6rne\u011fin, 30 deniz kaplumba\u011fas\u0131ndan olu\u015fan bir \u00f6rnek ald\u0131\u011f\u0131m\u0131z\u0131 ve \u00f6rne\u011fin ortalama a\u011f\u0131rl\u0131\u011f\u0131n\u0131n 350 pound ve \u00f6rne\u011fin standart sapmas\u0131n\u0131n 12 pound oldu\u011funu buldu\u011fumuzu varsayal\u0131m. Bu say\u0131lara dayanarak \u015funlar\u0131 hesaplayabiliriz:<\/span><\/p>\n<p> <span style=\"color: #000000;\"><strong>\u00d6rnek ortalama =<\/strong> 350 kitap<\/span><\/p>\n<p> <span style=\"color: #000000;\"><strong>\u00d6rnek ortalaman\u0131n standart sapmas\u0131 =<\/strong> 12 \/ \u221a <span style=\"border-top: 1px solid black;\">30<\/span> = 2,19 pound<\/span><\/p>\n<p> <span style=\"color: #000000;\">Bu, t\u00fcm kaplumba\u011falar\u0131n ger\u00e7ek pop\u00fclasyon ortalama a\u011f\u0131rl\u0131\u011f\u0131na ili\u015fkin en iyi tahminimizin 350 pound oldu\u011fu anlam\u0131na gelir, ancak \u00f6rnek ortalamas\u0131n\u0131n yakla\u015f\u0131k 2,19 poundluk bir standart sapma ile de\u011fi\u015fmesini beklemeliyiz.<\/span><\/p>\n<p> <span style=\"color: #000000;\">\u00d6rnek ortalamas\u0131n\u0131n standart sapmas\u0131n\u0131n ilgin\u00e7 bir \u00f6zelli\u011fi, daha b\u00fcy\u00fck \u00f6rnek boyutlar\u0131 kulland\u0131k\u00e7a do\u011fal olarak k\u00fc\u00e7\u00fclmesidir.<\/span><\/p>\n<p> <span style=\"color: #000000;\">\u00d6rne\u011fin, 100 deniz kaplumba\u011fas\u0131ndan olu\u015fan bir numune ald\u0131\u011f\u0131m\u0131z\u0131 ve numunenin ortalama a\u011f\u0131rl\u0131\u011f\u0131n\u0131n 350 pound ve numunenin standart sapmas\u0131n\u0131n 12 pound oldu\u011funu buldu\u011fumuzu varsayal\u0131m. \u00d6rnek ortalamas\u0131n\u0131n standart sapmas\u0131 daha sonra a\u015fa\u011f\u0131daki \u015fekilde hesaplanacakt\u0131r:<\/span><\/p>\n<p> <span style=\"color: #000000;\"><strong>\u00d6rnek ortalaman\u0131n standart sapmas\u0131 =<\/strong> 12 \/ \u221a <span style=\"border-top: 1px solid black;\">100<\/span> = 1,2 pound<\/span><\/p>\n<p> <span style=\"color: #000000;\">\u00d6rnek ortalamas\u0131na ili\u015fkin en iyi tahminimiz h\u00e2l\u00e2 350 pound olacakt\u0131r, ancak 100 deniz kaplumba\u011fas\u0131ndan olu\u015fan bir \u00f6rnekten 100 deniz kaplumba\u011fas\u0131ndan olu\u015fan bir sonraki \u00f6rne\u011fine kadar olan ortalaman\u0131n yaln\u0131zca 1,2 poundluk bir standart sapma ile de\u011fi\u015fmesini bekleyebiliriz.<\/span><\/p>\n<p> <span style=\"color: #000000;\">Ba\u015fka bir deyi\u015fle, numune boyutlar\u0131 daha b\u00fcy\u00fck oldu\u011funda numune ortalamalar\u0131 aras\u0131nda daha az de\u011fi\u015fkenlik olur.<\/span><\/p>\n<h3> <span style=\"color: #000000;\"><strong>Ek kaynaklar<\/strong><\/span><\/h3>\n<p> <a href=\"https:\/\/statorials.org\/tr\/ornekleme-dagilimi-1\/\" target=\"_blank\" rel=\"noopener\">\u00d6rnekleme da\u011f\u0131l\u0131m\u0131 nedir?<\/a><br \/> <a href=\"https:\/\/statorials.org\/tr\/merkezi-limit-teoremi\/\" target=\"_blank\" rel=\"noopener\">Merkezi Limit Teoremine Giri\u015f<\/a><br \/> <a href=\"https:\/\/statorials.org\/tr\/merkezi-limit-teoremi-hesaplayicisi\/\" target=\"_blank\" rel=\"noopener\">Merkezi Limit Teoremi Hesaplay\u0131c\u0131<\/a><\/p>\n","protected":false},"excerpt":{"rendered":"<p>\u0130statistiklerde s\u0131kl\u0131kla a\u015fa\u011f\u0131daki gibi sorular\u0131 yan\u0131tlamak isteriz: Belirli bir eyaletteki 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. Bununla birlikte, bir pop\u00fclasyondaki her bireye ili\u015fkin veri toplamak yerine, bunun [&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-1458","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>\u00d6rnekleme de\u011fi\u015fkenli\u011fi nedir? 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