{"id":3163,"date":"2023-07-18T21:59:03","date_gmt":"2023-07-18T21:59:03","guid":{"rendered":"https:\/\/statorials.org\/tr\/sifirin-standart-sapmasi\/"},"modified":"2023-07-18T21:59:03","modified_gmt":"2023-07-18T21:59:03","slug":"sifirin-standart-sapmasi","status":"publish","type":"post","link":"https:\/\/statorials.org\/tr\/sifirin-standart-sapmasi\/","title":{"rendered":"S\u0131f\u0131r\u0131n standart sapmas\u0131 nas\u0131l yorumlan\u0131r?"},"content":{"rendered":"<p><\/p>\n<hr>\n<p><span style=\"color: #000000;\">\u0130statistikte <strong>standart sapma<\/strong> , bir \u00f6rneklemdeki de\u011ferlerin da\u011f\u0131l\u0131m\u0131n\u0131 \u00f6l\u00e7mek i\u00e7in kullan\u0131l\u0131r.<\/span><\/p>\n<p> <span style=\"color: #000000;\">Belirli bir \u00f6rne\u011fin standart sapmas\u0131n\u0131 hesaplamak i\u00e7in a\u015fa\u011f\u0131daki form\u00fcl\u00fc kullanabiliriz:<\/span><\/p>\n<p> <span style=\"color: #000000;\">\u221a <span style=\"border-top: 1px solid black;\">\u03a3(x <sub>i<\/sub> \u2013 x <sub>\u00e7ubuk<\/sub> ) <sup>2<\/sup> \/ (n-1)<\/span><\/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> \u00f6rne\u011fin <sup>i&#8217;inci<\/sup> de\u011feri<\/span><\/li>\n<li> <span style=\"color: #000000;\"><strong>x <sub>\u00e7ubu\u011fu<\/sub> :<\/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;\">Standart sapma de\u011feri ne kadar y\u00fcksek olursa, de\u011ferler bir <a href=\"https:\/\/statorials.org\/tr\/populasyon-ve-ornek\/\" target=\"_blank\" rel=\"noopener\">numunede<\/a> o kadar fazla da\u011f\u0131l\u0131r.<\/span><\/p>\n<p> <span style=\"color: #000000;\">Standart sapma de\u011feri ne kadar d\u00fc\u015f\u00fck olursa de\u011ferler birbirine o kadar yak\u0131n gruplan\u0131r.<\/span><\/p>\n<p> <span style=\"color: #000000;\"><strong><span style=\"color: #000000;\">Bir numunenin standart sapmas\u0131 s\u0131f\u0131r ise numunedeki t\u00fcm de\u011ferlerin birebir ayn\u0131 oldu\u011fu anlam\u0131na gelir.<\/span><\/strong><\/span><\/p>\n<p> <span style=\"color: #000000;\">Yani de\u011ferler aras\u0131nda bo\u015fluk yoktur.<\/span><\/p>\n<p> <span style=\"color: #000000;\"><span style=\"color: #000000;\">A\u015fa\u011f\u0131daki \u00f6rnek s\u0131f\u0131r\u0131n standart sapmas\u0131n\u0131n pratikte nas\u0131l yorumlanaca\u011f\u0131n\u0131 g\u00f6stermektedir.<\/span><\/span><\/p>\n<h3> <span style=\"color: #000000;\"><strong>\u00d6rnek: S\u0131f\u0131r\u0131n standart sapmas\u0131 nas\u0131l yorumlan\u0131r?<\/strong><\/span><\/h3>\n<p> <span style=\"color: #000000;\">10 kertenkeleden olu\u015fan <a href=\"https:\/\/statorials.org\/tr\/ornekleme-yontemleri\/\" target=\"_blank\" rel=\"noopener\">basit ve rastgele bir \u00f6rnek<\/a> toplad\u0131\u011f\u0131m\u0131z\u0131 ve uzunluklar\u0131n\u0131 (in\u00e7 cinsinden) \u00f6l\u00e7t\u00fc\u011f\u00fcm\u00fcz\u00fc varsayal\u0131m:<\/span><\/p>\n<p> <span style=\"color: #000000;\"><strong>Uzunluklar<\/strong> : 7, 7, 7, 7, 7, 7, 7, 7, 7, 7<\/span><\/p>\n<p> <span style=\"color: #000000;\">\u00d6rnekteki kertenkelelerin ortalama uzunlu\u011fu 7 in\u00e7tir.<\/span><\/p>\n<p> <span style=\"color: #000000;\">Bunu bilerek, bu veri seti i\u00e7in \u00f6rnek standart sapmay\u0131\/sapmalar\u0131 hesaplayabiliriz:<\/span><\/p>\n<ul>\n<li> <span style=\"color: #000000;\">s = \u221a <span style=\"border-top: 1px solid black;\">\u03a3(x <sub>ben<\/sub> \u2013 x <sub>\u00e7ubuk<\/sub> ) <sup>2<\/sup> \/ (n-1)<\/span><\/span><\/li>\n<li> <span style=\"color: #000000;\"><span style=\"border-top: 1px solid black;\">s = \u221a ((7 \u2013 7) <sup>2<\/sup> + (7 \u2013 7) <sup>2<\/sup> + (7 \u2013 7) <sup>2<\/sup> + \u2026 + (7 \u2013 7) <sup>2<\/sup> \/ (10-1)<\/span><\/span><\/li>\n<li> <span style=\"color: #000000;\">s = \u221a <span style=\"border-top: 1px solid black;\">0 <sup>2<\/sup> + 0 <sup>2<\/sup> + 0 <sup>2<\/sup> + \u2026 + 0 <sup>2\/9<\/sup><\/span><\/span><\/li>\n<li> <span style=\"color: #000000;\">s = <strong>0<\/strong><\/span><\/li>\n<\/ul>\n<p> <span style=\"color: #000000;\">\u00d6rneklem standart sapmas\u0131 <strong>0<\/strong> olarak \u00e7\u0131k\u0131yor.<\/span><\/p>\n<p> <span style=\"color: #000000;\"><span style=\"color: #000000;\">Her kertenkele tam olarak ayn\u0131 uzunlukta oldu\u011fundan veri setindeki de\u011ferlerin da\u011f\u0131l\u0131m\u0131 tam olarak s\u0131f\u0131rd\u0131r.<\/span><\/span><\/p>\n<h3> <span style=\"color: #000000;\"><strong>Ger\u00e7ek d\u00fcnyada standart sapma hi\u00e7 s\u0131f\u0131r olacak m\u0131?<\/strong><\/span><\/h3>\n<p> <span style=\"color: #000000;\"><span style=\"color: #000000;\">Ger\u00e7ek d\u00fcnyadaki bir veri k\u00fcmesinin standart sapmas\u0131n\u0131n s\u0131f\u0131r olmas\u0131 tamamen m\u00fcmk\u00fcnd\u00fcr, ancak bu nadirdir.<\/span><\/span><\/p>\n<p> <span style=\"color: #000000;\">S\u0131f\u0131r standart sapmayla kar\u015f\u0131la\u015fabilece\u011finiz en muhtemel senaryo, nadir olaylar i\u00e7in k\u00fc\u00e7\u00fck numuneler toplarken olacakt\u0131r.<\/span><\/p>\n<p> <span style=\"color: #000000;\">\u00d6rne\u011fin, belirli bir \u015fehirde bir haftal\u0131k s\u00fcre boyunca trafik kazalar\u0131n\u0131n say\u0131s\u0131na ili\u015fkin veri toplad\u0131\u011f\u0131n\u0131z\u0131 varsayal\u0131m.<\/span><\/p>\n<p> <span style=\"color: #000000;\">A\u015fa\u011f\u0131daki verileri toplaman\u0131z tamamen m\u00fcmk\u00fcnd\u00fcr:<\/span> <\/p>\n<p><img decoding=\"async\" loading=\"lazy\" class=\" wp-image-26867 aligncenter\" src=\"https:\/\/statorials.org\/wp-content\/uploads\/2023\/08\/sd0.jpg\" alt=\"\" width=\"185\" height=\"242\" srcset=\"\" sizes=\"auto, \"><\/p>\n<p> <span style=\"color: #000000;\">Bu senaryoda ortalama g\u00fcnl\u00fck kaza say\u0131s\u0131 s\u0131f\u0131r olaca\u011f\u0131 gibi standart sapma da s\u0131f\u0131r olacakt\u0131r.<\/span><\/p>\n<p> <span style=\"color: #000000;\">Veya belki de bir i\u015fletme i\u00e7in pahal\u0131 bir \u00fcr\u00fcn\u00fcn 6 ayl\u0131k d\u00f6nemdeki ayl\u0131k sat\u0131\u015f say\u0131s\u0131na ili\u015fkin a\u015fa\u011f\u0131daki verileri topluyorsunuz:<\/span> <\/p>\n<p><img decoding=\"async\" loading=\"lazy\" class=\" wp-image-26868 aligncenter\" src=\"https:\/\/statorials.org\/wp-content\/uploads\/2023\/08\/sd0_1.jpg\" alt=\"\" width=\"182\" height=\"216\" srcset=\"\" sizes=\"auto, \"><\/p>\n<p> <span style=\"color: #000000;\">\u00dcr\u00fcn \u00e7ok pahal\u0131 oldu\u011fu i\u00e7in \u015firketin ayda yaln\u0131zca iki tane satt\u0131\u011f\u0131 ortaya \u00e7\u0131kt\u0131.<\/span><\/p>\n<p> <span style=\"color: #000000;\">Bu senaryoda ayl\u0131k ortalama sat\u0131lan \u00fcr\u00fcn say\u0131s\u0131 iki, sat\u0131lan ayl\u0131k \u00fcr\u00fcnlerin standart sapmas\u0131 ise s\u0131f\u0131rd\u0131r.<\/span><\/p>\n<p> <span style=\"color: #000000;\"><strong>Ger\u00e7ek bir veri setinde s\u0131f\u0131r standart sapmayla kar\u015f\u0131la\u015ft\u0131\u011f\u0131n\u0131zda bunun, veri setindeki her de\u011ferin tamamen ayn\u0131 oldu\u011fu anlam\u0131na geldi\u011fini bilin.<\/strong><\/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 istatistiklerde standart sapma hakk\u0131nda ek bilgi sa\u011flar:<\/span><\/p>\n<p> <a href=\"https:\/\/statorials.org\/tr\/standart-sapma-neden-onemlidir\/\" target=\"_blank\" rel=\"noopener\">Standart sapma neden \u00f6nemlidir?<\/a><br \/><a href=\"https:\/\/statorials.org\/tr\/standart-sapma-ve-standart-hata\/\" target=\"_blank\" rel=\"noopener\">Standart sapma ve standart hata: fark nedir?<\/a><br \/> <a href=\"https:\/\/statorials.org\/tr\/ceyrekler-arasi-aralik-ve-standart-sapma\/\" target=\"_blank\" rel=\"noopener\">Standart sapma ve \u00e7eyrekler aras\u0131 aral\u0131k: fark nedir?<\/a><\/p>\n","protected":false},"excerpt":{"rendered":"<p>\u0130statistikte standart sapma , bir \u00f6rneklemdeki de\u011ferlerin da\u011f\u0131l\u0131m\u0131n\u0131 \u00f6l\u00e7mek i\u00e7in kullan\u0131l\u0131r. Belirli bir \u00f6rne\u011fin standart sapmas\u0131n\u0131 hesaplamak i\u00e7in a\u015fa\u011f\u0131daki form\u00fcl\u00fc kullanabiliriz: \u221a \u03a3(x i \u2013 x \u00e7ubuk ) 2 \/ (n-1) Alt\u0131n: \u03a3: \u201ctoplam\u201d anlam\u0131na gelen bir sembol x i : \u00f6rne\u011fin i&#8217;inci de\u011feri x \u00e7ubu\u011fu : \u00d6rnek \u015fu anlama gelir: n: \u00d6rneklem b\u00fcy\u00fckl\u00fc\u011f\u00fc Standart [&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-3163","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>S\u0131f\u0131r\u0131n standart sapmas\u0131 nas\u0131l yorumlan\u0131r - Statorials<\/title>\n<meta name=\"description\" content=\"Bu e\u011fitimde, 1&#039;in standart sapmas\u0131n\u0131n nas\u0131l yorumlanaca\u011f\u0131 \u00e7e\u015fitli \u00f6rneklerle 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\/sifirin-standart-sapmasi\/\" \/>\n<meta property=\"og:locale\" content=\"tr_TR\" \/>\n<meta property=\"og:type\" content=\"article\" \/>\n<meta property=\"og:title\" content=\"S\u0131f\u0131r\u0131n standart sapmas\u0131 nas\u0131l yorumlan\u0131r - 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