{"id":563,"date":"2023-07-29T12:04:41","date_gmt":"2023-07-29T12:04:41","guid":{"rendered":"https:\/\/statorials.org\/tr\/varyansin-nasil-yorumlanacagina-dair-basit-bir-aciklama\/"},"modified":"2023-07-29T12:04:41","modified_gmt":"2023-07-29T12:04:41","slug":"varyansin-nasil-yorumlanacagina-dair-basit-bir-aciklama","status":"publish","type":"post","link":"https:\/\/statorials.org\/tr\/varyansin-nasil-yorumlanacagina-dair-basit-bir-aciklama\/","title":{"rendered":"Varyans\u0131n nas\u0131l yorumlanaca\u011f\u0131na dair basit bir a\u00e7\u0131klama"},"content":{"rendered":"<p><\/p>\n<hr>\n<p><span style=\"color: #000000;\">\u0130statistikte \u00e7o\u011fu zaman de\u011ferlerin bir veri k\u00fcmesinde nas\u0131l &#8220;yay\u0131ld\u0131\u011f\u0131n\u0131&#8221; anlamak isteriz.<\/span> Bunu \u00f6l\u00e7mek i\u00e7in s\u0131kl\u0131kla <span style=\"color: #000000;\">a\u015fa\u011f\u0131daki da\u011f\u0131l\u0131m \u00f6l\u00e7\u00fclerini<\/span> <span style=\"color: #000000;\">kullan\u0131r\u0131z<\/span> :<\/p>\n<ul>\n<li> <span style=\"color: #000000;\"><strong>Aral\u0131k:<\/strong> Bir veri k\u00fcmesindeki en b\u00fcy\u00fck ve en k\u00fc\u00e7\u00fck de\u011ferler aras\u0131ndaki fark.<\/span><\/li>\n<li> <strong><span style=\"color: #000000;\">\u00c7eyrekler aras\u0131 aral\u0131k:<\/span><\/strong> <span style=\"color: #000000;\">bir veri k\u00fcmesinin ilk \u00e7eyre\u011fi ile \u00fc\u00e7\u00fcnc\u00fc \u00e7eyre\u011fi aras\u0131ndaki fark (kartiller, bir veri k\u00fcmesini d\u00f6rt e\u015fit par\u00e7aya b\u00f6len de\u011ferlerdir).<\/span><\/li>\n<li> <strong><span style=\"color: #000000;\">Standart sapma:<\/span><\/strong> <span style=\"color: #000000;\">de\u011ferler ile ortalama aras\u0131ndaki tipik mesafeyi \u00f6l\u00e7menin bir yolu.<\/span><\/li>\n<li> <strong><span style=\"color: #000000;\">Varyans:<\/span><\/strong> <span style=\"color: #000000;\">standart sapman\u0131n karesi.<\/span><\/li>\n<\/ul>\n<p> <span style=\"color: #000000;\">Bu d\u00f6rt \u00f6l\u00e7\u00fcmden <strong>varyans\u0131n<\/strong> sezgisel olarak anla\u015f\u0131lmas\u0131 en zor olan\u0131 olma e\u011filimindedir. Bu makale varyans\u0131n basit bir a\u00e7\u0131klamas\u0131n\u0131 sa\u011flamay\u0131 ama\u00e7lamaktad\u0131r.<\/span><\/p>\n<h2> <span style=\"color: #000000;\"><strong>Standart Sapmay\u0131 Anlamak<\/strong><\/span><\/h2>\n<p> <span style=\"color: #000000;\">Varyans\u0131 anlamadan \u00f6nce, genellikle <strong>\u03c3<\/strong> ile g\u00f6sterilen <strong>standart sapmay\u0131<\/strong> anlamal\u0131y\u0131z.<\/span><\/p>\n<p> <span style=\"color: #000000;\">Standart sapmay\u0131 hesaplama form\u00fcl\u00fc \u015f\u00f6yledir:<\/span><\/p>\n<p> <span style=\"color: #000000;\"><strong>\u03c3<\/strong> = \u221a(\u03a3 (x <sub>ben<\/sub> \u2013 \u03bc) <sup>2<\/sup> \/ N)<\/span><\/p>\n<p> <span style=\"color: #000000;\">burada \u03bc pop\u00fclasyon ortalamas\u0131d\u0131r, <sub>xi<\/sub> pop\u00fclasyonun <i>i&#8217;inci<\/i> eleman\u0131d\u0131r, N pop\u00fclasyon b\u00fcy\u00fckl\u00fc\u011f\u00fcd\u00fcr ve \u03a3 sadece &#8220;toplam&#8221; anlam\u0131na gelen s\u00fcsl\u00fc bir sembold\u00fcr.<\/span><\/p>\n<p> <span style=\"color: #000000;\">Pratikte standart sapmay\u0131 elle hesaplamaya nadiren ihtiya\u00e7 duyacaks\u0131n\u0131z; bunun yerine istatistik yaz\u0131l\u0131m\u0131 veya hesap makinesi kullanabilirsiniz.<\/span><\/p>\n<p> <span style=\"color: #000000;\">Standart sapma en temel d\u00fczeyde bize bir veri k\u00fcmesindeki veri de\u011ferlerinin da\u011f\u0131l\u0131m\u0131n\u0131 anlat\u0131r. Bunu g\u00f6stermek i\u00e7in a\u015fa\u011f\u0131daki \u00fc\u00e7 veri setini kar\u015f\u0131l\u0131k gelen standart sapmalar\u0131yla birlikte g\u00f6z \u00f6n\u00fcnde bulundurun:<\/span><\/p>\n<p> <span style=\"color: #000000;\">[5, 5, 5] standart sapma = <strong>0<\/strong> (hi\u00e7 yay\u0131lma yok)<\/span><\/p>\n<p> <span style=\"color: #000000;\">[3, 5, 7] standart sapma = <strong>1,63<\/strong> (baz\u0131 sapmalar)<\/span><\/p>\n<p> <span style=\"color: #000000;\">[1, 5, 99] standart sapma = <strong>45,28<\/strong> (\u00e7ok say\u0131da yay\u0131lma)<\/span><\/p>\n<p> <span style=\"color: #000000;\">\u201cStandart sapma\u201d terimi, onu olu\u015fturan iki kelimeye bak\u0131larak anla\u015f\u0131labilir:<\/span><\/p>\n<ul>\n<li> <span style=\"color: #000000;\">\u201csapma\u201d \u2013 bu ortalamaya olan mesafeyi ifade eder.<\/span><\/li>\n<li> <span style=\"color: #000000;\">\u201cstandart\u201d \u2013 bu, bir de\u011fer ile ortalama aras\u0131ndaki \u201cstandart\u201d veya \u201ctipik\u201d mesafeyi ifade eder.<\/span><\/li>\n<\/ul>\n<p> <span style=\"color: #000000;\">Standart sapmay\u0131 anlad\u0131ktan sonra varyans\u0131 anlamak \u00e7ok daha kolayd\u0131r.<\/span><\/p>\n<h2> <span style=\"color: #000000;\"><strong>Bo\u015flu\u011fu Anlamak<\/strong><\/span><\/h2>\n<p> <span style=\"color: #000000;\">Genellikle <strong><sup>\u03c32<\/sup><\/strong> ile g\u00f6sterilen varyans, basit\u00e7e standart sapman\u0131n karesidir. Bir veri k\u00fcmesinin varyans\u0131n\u0131 bulma form\u00fcl\u00fc \u015f\u00f6yledir:<\/span><\/p>\n<p> <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;\">burada \u03bc pop\u00fclasyon ortalamas\u0131d\u0131r, <sub>xi<\/sub> pop\u00fclasyonun <i>i&#8217;inci<\/i> eleman\u0131d\u0131r, N pop\u00fclasyon b\u00fcy\u00fckl\u00fc\u011f\u00fcd\u00fcr ve \u03a3 sadece &#8220;toplam&#8221; anlam\u0131na gelen s\u00fcsl\u00fc bir sembold\u00fcr.<\/span><\/p>\n<p> <span style=\"color: #000000;\">Yani, e\u011fer bir veri setinin standart sapmas\u0131 8 ise varyasyon 8 <sup>2<\/sup> = 64 olacakt\u0131r.<\/span><\/p>\n<p> <span style=\"color: #000000;\">Veya bir veri setinin standart sapmas\u0131 10 ise varyasyon 10 <sup>2<\/sup> = 100 olacakt\u0131r.<\/span><\/p>\n<p> <span style=\"color: #000000;\">Veya bir veri setinin standart sapmas\u0131 3,7 ise varyasyon 3,7 <sup>2<\/sup> = 13,69 olacakt\u0131r.<\/span><\/p>\n<p> <span style=\"color: #000000;\">Bir veri setinde de\u011ferler ne kadar da\u011f\u0131n\u0131ksa varyans da o kadar y\u00fcksek olur. Bunu g\u00f6stermek i\u00e7in a\u015fa\u011f\u0131daki \u00fc\u00e7 veri setini kar\u015f\u0131l\u0131k gelen varyanslar\u0131yla birlikte g\u00f6z \u00f6n\u00fcnde bulundurun:<\/span><\/p>\n<p> <span style=\"color: #000000;\">[5, 5, 5] varyans = <strong>0<\/strong> (hi\u00e7 yay\u0131lma yok)<\/span><\/p>\n<p> <span style=\"color: #000000;\">[3, 5, 7] varyans = <b>2,67<\/b> (baz\u0131 sapmalar)<\/span><\/p>\n<p> <span style=\"color: #000000;\">[1, 5, 99] varyans = <b>2.050,67<\/b> (\u00e7ok say\u0131da yay\u0131lma)<\/span><\/p>\n<h2> <span style=\"color: #000000;\"><strong>Standart sapma yerine varyans\u0131 ne zaman kullan\u0131rs\u0131n\u0131z?<\/strong><\/span><\/h2>\n<p> <span style=\"color: #000000;\">Yukar\u0131daki standart sapma ve varyans a\u00e7\u0131klamalar\u0131n\u0131 okuduktan sonra, bir veri k\u00fcmesini tan\u0131mlamak i\u00e7in ne zaman standart sapma yerine varyans\u0131 kullanaca\u011f\u0131n\u0131z\u0131 merak ediyor olabilirsiniz.<\/span><\/p>\n<p> <span style=\"color: #000000;\">Sonu\u00e7ta standart sapma bize bir de\u011fer ile ortalama aras\u0131ndaki ortalama mesafeyi s\u00f6ylerken, varyans bize bu de\u011ferin karesini verir. Standart sapman\u0131n anla\u015f\u0131lmas\u0131 ve yorumlanmas\u0131 \u00e7ok daha kolay gibi g\u00f6r\u00fcn\u00fcyor.<\/span><\/p>\n<p> <span style=\"color: #000000;\">Ger\u00e7ekte, bir veri k\u00fcmesindeki de\u011ferlerin da\u011f\u0131l\u0131m\u0131n\u0131 tan\u0131mlamak i\u00e7in neredeyse her zaman standart sapmay\u0131 kullanacaks\u0131n\u0131z.<\/span><\/p>\n<p> <span style=\"color: #000000;\">Ancak varyans, <a href=\"https:\/\/statorials.org\/tr\/tek-yonlu-anova\/\" target=\"_blank\" rel=\"noopener\">ANOVA<\/a> veya <a href=\"https:\/\/statorials.org\/tr\/dogrusal-regresyon-1\/\" target=\"_blank\" rel=\"noopener\">regresyon<\/a> gibi bir teknik kullan\u0131ld\u0131\u011f\u0131nda ve bir modelin toplam varyans\u0131n\u0131 belirli fakt\u00f6rlere g\u00f6re a\u00e7\u0131klamaya \u00e7al\u0131\u015f\u0131rken yararl\u0131 olabilir.<\/span><\/p>\n<p> <span style=\"color: #000000;\">\u00d6rne\u011fin, test puanlar\u0131ndaki farkl\u0131l\u0131\u011f\u0131n ne kadar\u0131n\u0131n IQ ile, ne kadar\u0131n\u0131n \u00e7al\u0131\u015f\u0131lan saatlerle a\u00e7\u0131klanabilece\u011fini anlamak isteyebilirsiniz.<\/span><\/p>\n<p> <span style=\"color: #000000;\">E\u011fer varyasyonun %36&#8217;s\u0131 IQ&#8217;dan ve %64&#8217;\u00fc \u00e7al\u0131\u015fma saatinden kaynaklan\u0131yorsa, bunu anlamak kolayd\u0131r. Ancak 6 ve 8&#8217;lik standart sapmalar\u0131 kullan\u0131rsak, bu \u00e7ok daha az sezgisel olur ve problem ba\u011flam\u0131nda pek bir anlam ifade etmez.<\/span><\/p>\n<p> <span style=\"color: #000000;\">Standart sapma yerine varyans kullanman\u0131n daha iyi olabilece\u011fi ba\u015fka bir durum da teorik istatistiksel \u00e7al\u0131\u015fma yapt\u0131\u011f\u0131n\u0131z zamand\u0131r.<\/span><\/p>\n<p> <span style=\"color: #000000;\">Bu durumda karek\u00f6k i\u015fareti kullanman\u0131z gerekmedi\u011fi i\u00e7in hesaplama s\u0131ras\u0131nda varyans\u0131 kullanmak \u00e7ok daha kolayd\u0131r.<\/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 varyans hakk\u0131nda ek bilgi sa\u011flar:<\/span><\/p>\n<p> <a href=\"https:\/\/statorials.org\/tr\/populasyon-varyansina-gore-orneklem-varyansi\/\" target=\"_blank\" rel=\"noopener\">\u00d6rneklem varyans\u0131 ve pop\u00fclasyon varyans\u0131: fark nedir?<\/a><br \/><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><\/p>\n","protected":false},"excerpt":{"rendered":"<p>\u0130statistikte \u00e7o\u011fu zaman de\u011ferlerin bir veri k\u00fcmesinde nas\u0131l &#8220;yay\u0131ld\u0131\u011f\u0131n\u0131&#8221; anlamak isteriz. Bunu \u00f6l\u00e7mek i\u00e7in s\u0131kl\u0131kla a\u015fa\u011f\u0131daki da\u011f\u0131l\u0131m \u00f6l\u00e7\u00fclerini kullan\u0131r\u0131z : Aral\u0131k: Bir veri k\u00fcmesindeki en b\u00fcy\u00fck ve en k\u00fc\u00e7\u00fck de\u011ferler aras\u0131ndaki fark. \u00c7eyrekler aras\u0131 aral\u0131k: bir veri k\u00fcmesinin ilk \u00e7eyre\u011fi ile \u00fc\u00e7\u00fcnc\u00fc \u00e7eyre\u011fi aras\u0131ndaki fark (kartiller, bir veri k\u00fcmesini d\u00f6rt e\u015fit par\u00e7aya b\u00f6len de\u011ferlerdir). 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-563","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>Varyans\u0131n nas\u0131l yorumlanaca\u011f\u0131na dair basit bir a\u00e7\u0131klama - Statorials<\/title>\n<meta name=\"description\" content=\"Burada varyans\u0131n nas\u0131l yorumlanaca\u011f\u0131na dair basit bir a\u00e7\u0131klamay\u0131 birka\u00e7 \u00f6rnekle birlikte bulabilirsiniz.\" \/>\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\/varyansin-nasil-yorumlanacagina-dair-basit-bir-aciklama\/\" \/>\n<meta property=\"og:locale\" content=\"tr_TR\" \/>\n<meta property=\"og:type\" content=\"article\" \/>\n<meta property=\"og:title\" content=\"Varyans\u0131n nas\u0131l yorumlanaca\u011f\u0131na dair basit bir a\u00e7\u0131klama - 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