{"id":5052,"date":"2023-07-04T13:29:56","date_gmt":"2023-07-04T13:29:56","guid":{"rendered":"https:\/\/statorials.org\/tr\/standart-sapmanin-avantajlari-dezavantajlari\/"},"modified":"2023-07-04T13:29:56","modified_gmt":"2023-07-04T13:29:56","slug":"standart-sapmanin-avantajlari-dezavantajlari","status":"publish","type":"post","link":"https:\/\/statorials.org\/tr\/standart-sapmanin-avantajlari-dezavantajlari\/","title":{"rendered":"Standart sapma kullanman\u0131n avantajlar\u0131 ve dezavantajlar\u0131"},"content":{"rendered":"<p><\/p>\n<hr>\n<p><span style=\"color: #000000;\">Bir veri setinin <strong>standart sapmas\u0131,<\/strong> bireysel de\u011ferlerin ortalama de\u011ferden tipik sapmas\u0131n\u0131 \u00f6l\u00e7menin bir yoludur.<\/span><\/p>\n<p> <span style=\"color: #000000;\">\u00d6rnek standart sapman\u0131n hesaplanmas\u0131na y\u00f6nelik form\u00fcl <strong><em>(s<\/em><\/strong> ile g\u00f6sterilir):<\/span><\/p>\n<p> <span style=\"color: #000000;\"><strong>s = \u221a <span style=\"border-top: 1px solid black;\">\u03a3(x <sub>ben<\/sub> \u2013 x\u0304) <sup>2<\/sup> \/ (n \u2013 1)<\/span><\/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 bir sembol<\/span><\/li>\n<li> <span style=\"color: #000000;\"><strong>x <sub>i<\/sub><\/strong> : Bir veri k\u00fcmesindeki <sup>i&#8217;inci<\/sup> de\u011fer<\/span><\/li>\n<li> <span style=\"color: #000000;\"><strong>x\u0304<\/strong> : \u00d6rnek \u015fu anlama gelir:<\/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;\"><span style=\"color: #000000;\">Bir veri k\u00fcmesindeki de\u011ferlerin da\u011f\u0131l\u0131m\u0131n\u0131 tan\u0131mlamak i\u00e7in standart sapmay\u0131 kullanman\u0131n iki ana avantaj\u0131 vard\u0131r:<\/span><\/span><\/p>\n<p> <span style=\"color: #000000;\"><strong>Avantaj #1: Standart sapma, hesaplamas\u0131nda bir veri setindeki t\u00fcm g\u00f6zlemleri kullan\u0131r.<\/strong> \u0130statistikte genellikle hesaplamalar\u0131 ger\u00e7ekle\u015ftirmek i\u00e7in bir veri setindeki t\u00fcm g\u00f6zlemleri kullanabilmenin iyi bir \u015fey oldu\u011funu s\u00f6yleriz, \u00e7\u00fcnk\u00fc veri setinde mevcut olan t\u00fcm olas\u0131 &#8220;bilgileri&#8221; kullan\u0131r\u0131z.<\/span><\/p>\n<p> <span style=\"color: #000000;\"><strong>Avantaj #2: Standart sapman\u0131n yorumlanmas\u0131 kolayd\u0131r<\/strong> . Standart sapma, bir veri setindeki &#8220;tipik&#8221; g\u00f6zlemin ortalama de\u011ferden ne kadar uzakta oldu\u011funa dair bize iyi bir fikir veren tek bir de\u011ferdir.<\/span><\/p>\n<p> <span style=\"color: #000000;\">Ancak standart sapmay\u0131 kullanman\u0131n b\u00fcy\u00fck bir dezavantaj\u0131 vard\u0131r:<\/span><\/p>\n<p> <span style=\"color: #000000;\"><strong>Dezavantaj #1: Standart sapma ayk\u0131r\u0131 de\u011ferlerden etkilenebilir<\/strong> . Bir veri setinde a\u015f\u0131r\u0131 ayk\u0131r\u0131 de\u011ferler mevcut oldu\u011funda, standart sapma de\u011ferini \u015fi\u015firebilir ve dolay\u0131s\u0131yla bir veri setindeki de\u011ferlerin da\u011f\u0131l\u0131m\u0131 hakk\u0131nda yan\u0131lt\u0131c\u0131 bir fikir verebilir.<\/span><\/p>\n<p> <span style=\"color: #000000;\">A\u015fa\u011f\u0131daki \u00f6rnekler standart sapma kullanman\u0131n avantajlar\u0131 ve dezavantajlar\u0131 hakk\u0131nda daha fazla bilgi sa\u011flar.<\/span><\/p>\n<h2> <span style=\"color: #000000;\"><strong>Avantaj #1: Standart sapma t\u00fcm g\u00f6zlemleri kullan\u0131r<\/strong><\/span><\/h2>\n<p> <span style=\"color: #000000;\">Bir s\u0131n\u0131ftaki \u00f6\u011frencilerin s\u0131nav puanlar\u0131n\u0131n da\u011f\u0131l\u0131m\u0131n\u0131 g\u00f6steren a\u015fa\u011f\u0131daki veri setine sahip oldu\u011fumuzu varsayal\u0131m:<\/span><\/p>\n<p> <span style=\"color: #000000;\">Derecelendirmeler: 68, 70, 71, 75, 78, 82, 83, 83, 85, 90, 91, 91, 92<\/span><\/p>\n<p> <span style=\"color: #000000;\"><strong>Bu veri setinin \u00f6rnek standart sapmas\u0131n\u0131n 8,46 oldu\u011funu bulmak i\u00e7in bir hesap makinesi veya istatistik yaz\u0131l\u0131m\u0131 kullanabiliriz.<\/strong><\/span><\/p>\n<p> <span style=\"color: #000000;\">Bu \u00f6rnekte standart sapma kullanman\u0131n avantaj\u0131, de\u011ferlerin tipik &#8220;da\u011f\u0131l\u0131m\u0131n\u0131&#8221; bulmak i\u00e7in veri setindeki t\u00fcm olas\u0131 g\u00f6zlemleri kullanmam\u0131zd\u0131r.<\/span><\/p>\n<p> <span style=\"color: #000000;\">Bunun aksine, bu veri setindeki de\u011ferlerin da\u011f\u0131l\u0131m\u0131n\u0131 \u00f6l\u00e7mek i\u00e7in \u00e7eyrekler aras\u0131 aral\u0131k gibi ba\u015fka bir metrik kullanabiliriz.<\/span><\/p>\n<p> <span style=\"color: #000000;\"><strong>\u00c7eyrekler aras\u0131 aral\u0131\u011f\u0131n 17,5 oldu\u011funu<\/strong> bulmak i\u00e7in bir hesap makinesi kullanabiliriz. Bu, veri k\u00fcmesindeki de\u011ferlerin ortadaki %50&#8217;lik k\u0131sm\u0131 aras\u0131ndaki bo\u015flu\u011fu temsil eder.<\/span><\/p>\n<p> <span style=\"color: #000000;\">\u015eimdi veri k\u00fcmesindeki en d\u00fc\u015f\u00fck de\u011feri \u00e7ok daha d\u00fc\u015f\u00fck olacak \u015fekilde de\u011fi\u015ftirdi\u011fimizi varsayal\u0131m:<\/span><\/p>\n<p> <span style=\"color: #000000;\">Derecelendirmeler: 22, 70, 71, 75, 78, 82, 83, 83, 85, 90, 91, 91, 92<\/span><\/p>\n<p> <span style=\"color: #000000;\"><strong>\u00d6rnek standart sapman\u0131n 18,37 oldu\u011funu<\/strong> bulmak i\u00e7in bir hesap makinesi kullanabiliriz.<\/span><\/p>\n<p> <span style=\"color: #000000;\"><span style=\"color: #000000;\">Ancak ortadaki %50&#8217;lik de\u011ferlerin hi\u00e7biri etkilenmedi\u011finden <strong>\u00e7eyrekler aras\u0131 aral\u0131k hala 17,5&#8217;tir<\/strong> .<\/span><\/span><\/p>\n<p> <span style=\"color: #000000;\">Bu, \u00f6rnek standart sapman\u0131n, di\u011fer da\u011f\u0131l\u0131m \u00f6l\u00e7\u00fcmlerinden farkl\u0131 olarak, hesaplamas\u0131nda veri k\u00fcmesindeki t\u00fcm g\u00f6zlemleri hesaba katt\u0131\u011f\u0131n\u0131 g\u00f6sterir.<\/span><\/p>\n<h2> <span style=\"color: #000000;\"><strong>Avantaj #2: Standart sapman\u0131n yorumlanmas\u0131 kolayd\u0131r<\/strong><\/span><\/h2>\n<p> <span style=\"color: #000000;\">Bir s\u0131n\u0131ftaki \u00f6\u011frencilerin s\u0131nav puanlar\u0131n\u0131n da\u011f\u0131l\u0131m\u0131n\u0131 g\u00f6steren a\u015fa\u011f\u0131daki veri k\u00fcmesini hat\u0131rlay\u0131n:<\/span><\/p>\n<p> <span style=\"color: #000000;\">Derecelendirmeler: 68, 70, 71, 75, 78, 82, 83, 83, 85, 90, 91, 91, 92<\/span><\/p>\n<p> <span style=\"color: #000000;\">Bu veri setinin \u00f6rnek standart sapmas\u0131n\u0131n <strong>8,46<\/strong> oldu\u011funu bulmak i\u00e7in bir hesap makinesi kulland\u0131k.<\/span><\/p>\n<p> <span style=\"color: #000000;\">Bunu yorumlamak kolayd\u0131r \u00e7\u00fcnk\u00fc bu basit\u00e7e &#8220;tipik&#8221; bir s\u0131nav puan\u0131n\u0131n ortalama s\u0131nav puan\u0131na g\u00f6re yakla\u015f\u0131k 8,46 sapmas\u0131 anlam\u0131na gelir.<\/span><\/p>\n<p> <span style=\"color: #000000;\">\u00d6te yandan, di\u011fer da\u011f\u0131l\u0131m \u00f6l\u00e7\u00fclerinin yorumlanmas\u0131 o kadar kolay de\u011fildir.<\/span><\/p>\n<p> <span style=\"color: #000000;\">\u00d6rne\u011fin, bir <strong>varyasyon katsay\u0131s\u0131,<\/strong> standart sapman\u0131n \u00f6rnek ortalamas\u0131na oran\u0131n\u0131 temsil eden ba\u015fka bir da\u011f\u0131l\u0131m \u00f6l\u00e7\u00fcs\u00fcd\u00fcr.<\/span><\/p>\n<p> <span style=\"color: #000000;\">De\u011fi\u015fim katsay\u0131s\u0131: s\/x\u0304<\/span><\/p>\n<p> <span style=\"color: #000000;\"><span style=\"color: #000000;\">Bu \u00f6rnekte ortalama s\u0131nav puan\u0131 81,46 oldu\u011fundan varyasyon katsay\u0131s\u0131 \u015fu \u015fekilde hesaplan\u0131r: 8,46 \/ 81,46 = <strong>0,104<\/strong> .<\/span><\/span><\/p>\n<p> <span style=\"color: #000000;\">Bu, \u00f6rnek standart sapman\u0131n \u00f6rnek ortalamaya oran\u0131n\u0131 temsil eder; bu, birden \u00e7ok veri k\u00fcmesindeki de\u011ferlerin da\u011f\u0131l\u0131m\u0131n\u0131 kar\u015f\u0131la\u015ft\u0131rmak i\u00e7in yararl\u0131 olabilir, ancak kendi ba\u015f\u0131na bir metrik olarak yorumlanmas\u0131 \u00e7ok kolay de\u011fildir.<\/span><\/p>\n<h2> <span style=\"color: #000000;\"><strong>Dezavantaj #1: Standart sapma ayk\u0131r\u0131 de\u011ferlerden etkilenebilir<\/strong><\/span><\/h2>\n<p> <span style=\"color: #000000;\">Bir \u015firketteki 10 \u00e7al\u0131\u015fan\u0131n (bin dolar cinsinden) maa\u015f bilgilerini i\u00e7eren a\u015fa\u011f\u0131daki veri setine sahip oldu\u011fumuzu varsayal\u0131m:<\/span><\/p>\n<p> <span style=\"color: #000000;\">Maa\u015flar: 44, 48, 57, 68, 70, 71, 73, 79, 84, 94<\/span><\/p>\n<p> <span style=\"color: #000000;\">Maa\u015flar\u0131n \u00f6rnek standart sapmas\u0131 yakla\u015f\u0131k <strong>15,57&#8217;dir<\/strong> .<\/span><\/p>\n<p> <span style=\"color: #000000;\">\u015eimdi, tamamen ayn\u0131 veri setine sahip oldu\u011fumuzu, ancak en y\u00fcksek maa\u015f\u0131n <em>\u00e7ok<\/em> daha y\u00fcksek oldu\u011funu varsayal\u0131m:<\/span><\/p>\n<p> <span style=\"color: #000000;\">Maa\u015flar: 44, 48, 57, 68, 70, 71, 73, 79, 84, 895<\/span><\/p>\n<p> <span style=\"color: #000000;\">Bu veri setindeki maa\u015flar\u0131n \u00f6rnek standart sapmas\u0131 yakla\u015f\u0131k <strong>262,47&#8217;dir<\/strong> .<\/span><\/p>\n<p> <span style=\"color: #000000;\">Yaln\u0131zca tek bir a\u015f\u0131r\u0131 ayk\u0131r\u0131 de\u011ferin dahil edilmesiyle standart sapma b\u00fcy\u00fck \u00f6l\u00e7\u00fcde etkileniyor ve art\u0131k &#8220;tipik&#8221; maa\u015f da\u011f\u0131l\u0131m\u0131 konusunda yan\u0131lt\u0131c\u0131 bir fikir veriyor.<\/span><\/p>\n<p> <span style=\"color: #000000;\"><strong>Not<\/strong> : Bir veri setinde ayk\u0131r\u0131 de\u011ferler mevcut oldu\u011funda, \u00e7eyrekler aras\u0131 aral\u0131k, ayk\u0131r\u0131 de\u011ferlerden etkilenmedi\u011finden daha iyi bir da\u011f\u0131l\u0131m \u00f6l\u00e7\u00fcm\u00fc sa\u011flayabilir.<\/span><\/p>\n<h2> <span style=\"color: #000000;\"><strong>Ek kaynaklar<\/strong><\/span><\/h2>\n<p> <span style=\"color: #000000;\">A\u015fa\u011f\u0131daki e\u011fitimler istatistikte standart sapman\u0131n kullan\u0131m\u0131na ili\u015fkin ek bilgiler sa\u011flar:<\/span><\/p>\n<p> <span style=\"color: #000000;\"><a href=\"https:\/\/statorials.org\/tr\/ceyrekler-arasi-aralik-ve-standart-sapma\/\" target=\"_blank\" rel=\"noopener\">\u00c7eyrekler aras\u0131 aral\u0131k ve standart sapma: fark<\/a><br \/> <a href=\"https:\/\/statorials.org\/tr\/standart-sapmaya-gore-degisim-katsayisi\/\" target=\"_blank\" rel=\"noopener\">Standart sapmaya kar\u015f\u0131 varyasyon katsay\u0131s\u0131: fark<\/a><br \/> <a href=\"https:\/\/statorials.org\/tr\" target=\"_blank\" rel=\"noopener\">N\u00fcfus vs. \u00d6rnek Standart Sapma: Her Biri Ne Zaman Kullan\u0131lmal\u0131<\/a><\/span><\/p>\n","protected":false},"excerpt":{"rendered":"<p>Bir veri setinin standart sapmas\u0131, bireysel de\u011ferlerin ortalama de\u011ferden tipik sapmas\u0131n\u0131 \u00f6l\u00e7menin bir yoludur. \u00d6rnek standart sapman\u0131n hesaplanmas\u0131na y\u00f6nelik form\u00fcl (s ile g\u00f6sterilir): s = \u221a \u03a3(x ben \u2013 x\u0304) 2 \/ (n \u2013 1) Alt\u0131n: \u03a3 : \u201cToplam\u201d anlam\u0131na gelen bir sembol x i : Bir veri k\u00fcmesindeki i&#8217;inci de\u011fer x\u0304 : \u00d6rnek \u015fu [&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-5052","post","type-post","status-publish","format-standard","hentry","category-rehber"],"yoast_head":"<!-- This site is optimized with 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