{"id":72,"date":"2023-08-05T19:17:23","date_gmt":"2023-08-05T19:17:23","guid":{"rendered":"https:\/\/statorials.org\/tr\/beste-birlik-dilimler\/"},"modified":"2023-08-05T19:17:23","modified_gmt":"2023-08-05T19:17:23","slug":"beste-birlik-dilimler","status":"publish","type":"post","link":"https:\/\/statorials.org\/tr\/beste-birlik-dilimler\/","title":{"rendered":"Be\u015fte birlik dilimler (istatistikler)"},"content":{"rendered":"<p>Bu yaz\u0131da be\u015fte birlik dilimlerin ne oldu\u011funu ve nas\u0131l hesapland\u0131klar\u0131n\u0131 a\u00e7\u0131kl\u0131yoruz. Be\u015fte birlik dilimlerin hesaplanmas\u0131na ili\u015fkin birka\u00e7 \u00e7\u00f6z\u00fclm\u00fc\u015f \u00f6rnek bulacaks\u0131n\u0131z ve ayr\u0131ca \u00e7evrimi\u00e7i bir hesap makinesiyle herhangi bir istatistiksel \u00f6rne\u011fin be\u015fte birlik dilimlerini hesaplayabileceksiniz. <\/p>\n<h2 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"%c2%bfque-son-los-quintiles\"><\/span> Be\u015fte birlikler nedir?<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p> <strong>\u0130statistikte be\u015fte birlik dilimler, bir veri k\u00fcmesini be\u015f e\u015fit par\u00e7aya b\u00f6len d\u00f6rt de\u011ferdir.<\/strong> Dolay\u0131s\u0131yla birinci, ikinci, \u00fc\u00e7\u00fcnc\u00fc ve d\u00f6rd\u00fcnc\u00fc be\u015fte birlik dilimler \u00f6rnek verilerin s\u0131ras\u0131yla %20, %40, %60 ve %80&#8217;ini temsil eder.<\/p>\n<p> Yani, \u00f6rne\u011fin \u00fc\u00e7\u00fcnc\u00fc be\u015fte birlik dilimin de\u011feri, toplanan t\u00fcm verilerin %60&#8217;\u0131ndan daha y\u00fcksek, ancak verilerin geri kalan\u0131ndan daha d\u00fc\u015f\u00fckt\u00fcr.<\/p>\n<p> Be\u015fte birlik dilimlerin sembol\u00fc be\u015fte birlik indeksi olan b\u00fcy\u00fck K harfidir, yani ilk be\u015fte birlik dilim K <sub>1<\/sub> , ikinci be\u015fte birlik dilim K <sub>2<\/sub> , \u00fc\u00e7\u00fcnc\u00fc be\u015fte birlik dilim K <sub>3<\/sub> ve d\u00f6rd\u00fcnc\u00fc be\u015fte birlik dilim K <sub>4&#8217;t\u00fcr<\/sub> . Her ne kadar Q harfiyle de temsil edilebilse de (kartillerle kar\u0131\u015f\u0131kl\u0131k yaratt\u0131\u011f\u0131 i\u00e7in \u00f6nerilmez). <\/p>\n<div class=\"wp-block-image\">\n<figure class=\"aligncenter size-full is-resized\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/statorials.org\/wp-content\/uploads\/2023\/08\/quintiles.png\" alt=\"be\u015fte birlik dilimler\" class=\"wp-image-1425\" width=\"221\" height=\"221\" srcset=\"\" sizes=\"auto, \"><\/figure>\n<\/div>\n<p> \ud83d\udc49Herhangi <u style=\"text-decoration-color:#FF8A05;\">bir veri seti i\u00e7in be\u015flik dilimleri hesaplamak i\u00e7in a\u015fa\u011f\u0131daki hesap makinesini kullanabilirsiniz.<\/u><\/p>\n<p> Be\u015flik dilimler, \u00e7eyreklikler, ondal\u0131k dilimler ve y\u00fczdelik dilimlerle birlikte merkezi olmayan konumun bir \u00f6l\u00e7\u00fcs\u00fcd\u00fcr. Daha fazla ilgileniyorsan\u0131z, bu nicelik t\u00fcrlerinin her birinin ne anlama geldi\u011fini web sitemizden kontrol edebilirsiniz.<\/p>\n<p> Quintile&#8217;nin ba\u015fka bir tan\u0131m\u0131 olabilece\u011fi unutulmamal\u0131d\u0131r. Ekonomide be\u015fte birlik dilimler, bir n\u00fcfusun gelire g\u00f6re s\u0131ralanan y\u00fczdesini temsil eder veya ba\u015fka bir deyi\u015fle, bir n\u00fcfusu gelir d\u00fczeylerine g\u00f6re s\u0131ralar. \u00d6rne\u011fin, ilk be\u015fte birlik dilim bir n\u00fcfustaki insanlar\u0131n en yoksul %20&#8217;sine kar\u015f\u0131l\u0131k gelir, ikinci be\u015fte birlik dilim ise n\u00fcfusun en d\u00fc\u015f\u00fck gelire sahip %40&#8217;\u0131na kar\u015f\u0131l\u0131k gelir, vb. <\/p>\n<h2 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"como-calcular-los-quintiles\"><\/span> Be\u015fte birlik dilimler nas\u0131l hesaplan\u0131r<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p> Bir numunenin veya istatistiksel pop\u00fclasyonun be\u015fte birlik <strong>dilimlerinin konumunu hesaplamak<\/strong> i\u00e7in, be\u015fte birlik dilim say\u0131s\u0131n\u0131 toplam veri say\u0131s\u0131n\u0131n toplam\u0131n\u0131n bir art\u0131s\u0131yla \u00e7arpman\u0131z ve sonucu be\u015fe b\u00f6lmeniz gerekir.<\/p>\n<p> Bu nedenle, <strong>be\u015fte birlik dilimlerin form\u00fcl\u00fc<\/strong> \u015f\u00f6yledir:<\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/statorials.org\/wp-content\/ql-cache\/quicklatex.com-4315101111b7c44489c8731dd15ad2e8_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\cfrac{k\\cdot (n+1)}{5} \\qquad k=1, 2, 3,4\" title=\"Rendered by QuickLaTeX.com\" height=\"40\" width=\"206\" style=\"vertical-align: -12px;\"><\/p>\n<\/p>\n<p> <strong>L\u00fctfen unutmay\u0131n:<\/strong> Bu form\u00fcl\u00fcn sonucu bize be\u015fte birlik dilimin de\u011ferini de\u011fil konumunu s\u00f6yler. Bu nedenle be\u015fte birlik k\u0131s\u0131m, form\u00fcl taraf\u0131ndan elde edilen konumda bulunan veriler olacakt\u0131r.<\/p>\n<p> Ancak bazen bu form\u00fcl\u00fcn sonucu bize ondal\u0131k say\u0131 verir, bu nedenle sonucun ondal\u0131k say\u0131 olup olmad\u0131\u011f\u0131na ba\u011fl\u0131 olarak iki durumu ay\u0131rmam\u0131z gerekir:<\/p>\n<ul>\n<li> Form\u00fcl\u00fcn sonucu <strong>ondal\u0131k k\u0131sm\u0131 olmayan bir say\u0131<\/strong> ise, be\u015fte birlik k\u0131s\u0131m yukar\u0131daki form\u00fcl\u00fcn sa\u011flad\u0131\u011f\u0131 konumda bulunan verilerdir.<\/li>\n<li> Form\u00fcl sonucu <strong>ondal\u0131k k\u0131sm\u0131 olan bir say\u0131ysa<\/strong> , be\u015fte birlik de\u011fer a\u015fa\u011f\u0131daki ifade kullan\u0131larak hesaplan\u0131r:<\/li>\n<\/ul>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/statorials.org\/wp-content\/ql-cache\/quicklatex.com-76531b97b13949b0ffb9426b6a96751a_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"K=x_i+d\\cdot (x_{i+1}-x_i)\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"183\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<p> Burada <em>x <sub>i<\/sub><\/em> ve <em>x <sub>i+1,<\/sub><\/em> birinci form\u00fclle elde edilen say\u0131n\u0131n aralar\u0131nda bulundu\u011fu konumlar\u0131n say\u0131lar\u0131d\u0131r ve <em>d<\/em> , birinci form\u00fclle elde edilen say\u0131n\u0131n ondal\u0131k k\u0131sm\u0131d\u0131r.<\/p>\n<p> Bir veri setinin be\u015fte birlik dilimlerini belirlemek i\u00e7in bu kadar \u00e7ok ad\u0131m g\u00f6rd\u00fc\u011f\u00fcn\u00fczde korktuysan\u0131z endi\u015felenmeyin, asl\u0131nda olduk\u00e7a basit. A\u015fa\u011f\u0131daki iki \u00f6rne\u011fi okuyun, mutlaka \u00e7ok daha iyi anlayacaks\u0131n\u0131z.<\/p>\n<p> <strong>Not<\/strong> : \u0130statistik toplulu\u011fu be\u015fte birlik dilimlerin nas\u0131l hesapland\u0131\u011f\u0131 konusunda hala tam olarak bir fikir birli\u011fine varmam\u0131\u015ft\u0131r; bu nedenle bunu biraz farkl\u0131 a\u00e7\u0131klayan bir kitap bulabilirsiniz. <\/p>\n<h2 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"ejemplos-del-calculo-de-quintiles\"><\/span> Be\u015fte birlik dilimleri hesaplama \u00f6rnekleri<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p> A\u015fa\u011f\u0131da size bir veri serisinden be\u015fte birlik dilimlerin nas\u0131l elde edilece\u011fine dair ad\u0131m ad\u0131m \u00e7\u00f6z\u00fclm\u00fc\u015f iki al\u0131\u015ft\u0131rma b\u0131rak\u0131yoruz. Yani iki olas\u0131 durumu g\u00f6rebilirsiniz; ilk al\u0131\u015ft\u0131rmada sonu\u00e7lar ondal\u0131k de\u011fildir, ikinci al\u0131\u015ft\u0131rmada ise \u00f6yledir.<\/p>\n<h3 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"ejemplo-1\"><\/span> \u00f6rnek 1<span class=\"ez-toc-section-end\"><\/span><\/h3>\n<ul>\n<li> A\u015fa\u011f\u0131daki veri serilerinin be\u015fte birlik dilimlerini hesaplay\u0131n: <\/li>\n<\/ul>\n<div class=\"wp-block-image\">\n<figure class=\"aligncenter size-full is-resized\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/statorials.org\/wp-content\/uploads\/2023\/08\/serie-de-donnees-ordonnees.png\" alt=\"s\u0131ral\u0131 veri\" class=\"wp-image-1428\" width=\"337\" height=\"257\" srcset=\"\" sizes=\"auto, \"><\/figure>\n<\/div>\n<p> Yukar\u0131daki a\u00e7\u0131klamada g\u00f6rd\u00fc\u011f\u00fcn\u00fcz gibi be\u015fte birlik dilimlerin konumunu bulma form\u00fcl\u00fc \u015f\u00f6yledir:<\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/statorials.org\/wp-content\/ql-cache\/quicklatex.com-4315101111b7c44489c8731dd15ad2e8_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\cfrac{k\\cdot (n+1)}{5} \\qquad k=1, 2, 3,4\" title=\"Rendered by QuickLaTeX.com\" height=\"40\" width=\"206\" style=\"vertical-align: -12px;\"><\/p>\n<\/p>\n<p> <em>n<\/em> parametresi, 49 olan toplam veri say\u0131s\u0131n\u0131 ifade eder, dolay\u0131s\u0131yla ilk be\u015fte birlik k\u0131sm\u0131n konumunu bulmak i\u00e7in <em>n&#8217;yi<\/em> 49 ile ve <em>k&#8217;yi<\/em> 1 ile de\u011fi\u015ftirmemiz gerekir:<\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/statorials.org\/wp-content\/ql-cache\/quicklatex.com-2edc2929c85f11304b6832d974956393_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\cfrac{1\\cdot (49+1)}{5}=10 \\quad \\color{orange}\\bm{\\longrightarrow}\\color{black}\\quad K_1=205\" title=\"Rendered by QuickLaTeX.com\" height=\"40\" width=\"356\" style=\"vertical-align: -12px;\"><\/p>\n<\/p>\n<p> Form\u00fclden 10 say\u0131s\u0131n\u0131 elde ettik; bu, be\u015fte birlik dilimin s\u0131ral\u0131 listenin onuncu konumunda oldu\u011fu anlam\u0131na gelir ve bu da 205 verisine kar\u015f\u0131l\u0131k gelir.<\/p>\n<p> \u0130kinci be\u015fte birlik k\u0131sm\u0131 hesaplamak i\u00e7in ayn\u0131 form\u00fcl\u00fc kullanmal\u0131s\u0131n\u0131z ancak <em>k&#8217;yi<\/em> 2 ile de\u011fi\u015ftirmelisiniz:<\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/statorials.org\/wp-content\/ql-cache\/quicklatex.com-44df54a81f195da80ceed0f32fad4b63_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\cfrac{2\\cdot (49+1)}{5}=20 \\quad \\color{orange}\\bm{\\longrightarrow}\\color{black}\\quad K_2=236\" title=\"Rendered by QuickLaTeX.com\" height=\"40\" width=\"357\" style=\"vertical-align: -12px;\"><\/p>\n<\/p>\n<p> Bu nedenle ikinci be\u015fte birlik s\u0131ral\u0131 listenin 20 numaral\u0131 pozisyonundad\u0131r, yani 236 de\u011ferindedir.<\/p>\n<p> Yine, be\u015fte birlik dilim 3&#8217;\u00fc belirlemek i\u00e7in i\u015flemi tekrarl\u0131yoruz, ancak mant\u0131ksal olarak \u015fimdi <em>k&#8217;yi<\/em> 3 ile de\u011fi\u015ftiriyoruz:<\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/statorials.org\/wp-content\/ql-cache\/quicklatex.com-38e005f63293c6b0b57c942b4aa7b3d9_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\cfrac{3\\cdot (49+1)}{5}=30 \\quad \\color{orange}\\bm{\\longrightarrow}\\color{black}\\quad K_3=266\" title=\"Rendered by QuickLaTeX.com\" height=\"40\" width=\"357\" style=\"vertical-align: -12px;\"><\/p>\n<\/p>\n<p> Dolay\u0131s\u0131yla \u00fc\u00e7\u00fcnc\u00fc be\u015fte birlik dilim, 266&#8217;ya kar\u015f\u0131l\u0131k gelen 30. konumda yer alan verilerdir.<\/p>\n<p> Son olarak d\u00f6rd\u00fcnc\u00fc be\u015fte birlik k\u0131sm\u0131 hesaplamak i\u00e7in form\u00fcl\u00fc tekrar uyguluyoruz:<\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/statorials.org\/wp-content\/ql-cache\/quicklatex.com-d4ed563c423f11c9ccf06c8c7c644886_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\cfrac{4\\cdot (49+1)}{5}=40 \\quad \\color{orange}\\bm{\\longrightarrow}\\color{black}\\quad K_4=286\" title=\"Rendered by QuickLaTeX.com\" height=\"40\" width=\"357\" style=\"vertical-align: -12px;\"><\/p>\n<\/p>\n<p> D\u00f6rd\u00fcnc\u00fc be\u015fte birlik dilim bu nedenle 40 konumundad\u0131r, yani d\u00f6rd\u00fcnc\u00fc be\u015fte birlik dilim 286&#8217;d\u0131r.<\/p>\n<h3 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"ejemplo-2\"><\/span> \u00d6rnek 2<span class=\"ez-toc-section-end\"><\/span><\/h3>\n<ul>\n<li> A\u015fa\u011f\u0131daki tabloda toplanan istatistiksel verilerin d\u00f6rtte birlik dilimini hesaplay\u0131n:. <\/li>\n<\/ul>\n<div class=\"wp-block-image\">\n<figure class=\"aligncenter size-full is-resized\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/statorials.org\/wp-content\/uploads\/2023\/08\/exemple-de-donnees-triees-resolu.png\" alt=\"\u00f6rnek veri\" class=\"wp-image-1396\" width=\"344\" height=\"231\" srcset=\"\" sizes=\"auto, \"><\/figure>\n<\/div>\n<p> \u00d6nceki \u00f6rnekte oldu\u011fu gibi, be\u015fte birlik dilimlerin konumlar\u0131n\u0131 elde etmek i\u00e7in a\u015fa\u011f\u0131daki form\u00fcl\u00fc kullanman\u0131z gerekir:<\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/statorials.org\/wp-content\/ql-cache\/quicklatex.com-4315101111b7c44489c8731dd15ad2e8_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\cfrac{k\\cdot (n+1)}{5} \\qquad k=1, 2, 3,4\" title=\"Rendered by QuickLaTeX.com\" height=\"40\" width=\"206\" style=\"vertical-align: -12px;\"><\/p>\n<\/p>\n<p> Bu durumda \u00f6rneklem b\u00fcy\u00fckl\u00fc\u011f\u00fc 42 g\u00f6zlemdir, dolay\u0131s\u0131yla ilk be\u015fte birlik dilimin konumunu bulmak i\u00e7in <em>n<\/em> parametresini 42 ve <em>k<\/em> parametresini 1 ile de\u011fi\u015ftirmemiz gerekir:<\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/statorials.org\/wp-content\/ql-cache\/quicklatex.com-39dd28bf3391d3cb9c08c67a243cd753_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\cfrac{1\\cdot (42+1)}{5}=8,6\" title=\"Rendered by QuickLaTeX.com\" height=\"40\" width=\"133\" style=\"vertical-align: -12px;\"><\/p>\n<\/p>\n<p> Ancak ilk \u00f6rnekten farkl\u0131 olarak bu sefer form\u00fcl bize ondal\u0131k bir say\u0131 veriyor, dolay\u0131s\u0131yla tam be\u015fte birlik k\u0131sm\u0131 hesaplamak i\u00e7in a\u015fa\u011f\u0131daki form\u00fcl\u00fc uygulamam\u0131z gerekiyor:<\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/statorials.org\/wp-content\/ql-cache\/quicklatex.com-76531b97b13949b0ffb9426b6a96751a_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"K=x_i+d\\cdot (x_{i+1}-x_i)\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"183\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<p> \u0130lk form\u00fclden elde edilen say\u0131 8,6&#8217;d\u0131r, yani ilk be\u015fte birlik dilim s\u0131ras\u0131yla 78 ve 79 olan sekizinci ve dokuzuncu veriler aras\u0131ndad\u0131r. Dolay\u0131s\u0131yla <em>x <sub>i<\/sub><\/em> 78, <em>x <sub>i+1<\/sub><\/em> 79 ve <em>d<\/em> elde edilen say\u0131n\u0131n ondal\u0131k k\u0131sm\u0131 yani 0,6&#8217;d\u0131r.<\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/statorials.org\/wp-content\/ql-cache\/quicklatex.com-50a6db57f083891c734f60d31634fbda_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"K_1=78+0,6\\cdot (79-78)=78,6\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"253\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<p> \u015eimdi ikinci be\u015fte birlik k\u0131sm\u0131 bulmak i\u00e7in ayn\u0131 i\u015flemi tekrar yap\u0131yoruz. \u0130lk \u00f6nce konumunu hesapl\u0131yoruz:<\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/statorials.org\/wp-content\/ql-cache\/quicklatex.com-234797a0f4b3d3b9a367edb5750f5796_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\cfrac{2\\cdot (42+1)}{5}=17,2\" title=\"Rendered by QuickLaTeX.com\" height=\"40\" width=\"141\" style=\"vertical-align: -12px;\"><\/p>\n<\/p>\n<p> Ancak form\u00fclden 17 ile 18 aras\u0131nda bir ondal\u0131k say\u0131 elde ederiz, b\u00f6ylece ikinci be\u015fte birlik k\u0131s\u0131m, de\u011ferleri s\u0131ral\u0131 listenin s\u0131ras\u0131yla 109 ve 112&#8217;sine kar\u015f\u0131l\u0131k gelen on yedinci ve on sekizinci konumlar aras\u0131nda olacakt\u0131r. Bu nedenle, tam be\u015fte birlik de\u011feri belirlemek i\u00e7in s\u00fcre\u00e7te ikinci form\u00fcl\u00fc uyguluyoruz:<\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/statorials.org\/wp-content\/ql-cache\/quicklatex.com-f2e1ce59b20f303488c325836285c2c8_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"K_2=109+0,2\\cdot (112-109)=109,6\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"289\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<p> \u00dc\u00e7\u00fcnc\u00fc be\u015fte birlik k\u0131sm\u0131 elde etmek i\u00e7in y\u00f6ntemi tekrarl\u0131yoruz, \u00f6nce konumunu belirliyoruz:<\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/statorials.org\/wp-content\/ql-cache\/quicklatex.com-27ffb4409dd927f39d65db9dee1edfd0_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\cfrac{3\\cdot (42+1)}{5}=25,8\" title=\"Rendered by QuickLaTeX.com\" height=\"40\" width=\"142\" style=\"vertical-align: -12px;\"><\/p>\n<\/p>\n<p> Hesaplanan 25,8 say\u0131s\u0131, be\u015fte birlik de\u011ferin, de\u011ferleri 134 ve 141 olan yirmi be\u015finci ve yirmi alt\u0131nc\u0131 konumlar aras\u0131nda olaca\u011f\u0131 anlam\u0131na gelir. Bu nedenle tam be\u015fte birlik de\u011ferin hesaplanmas\u0131 \u015fu \u015fekildedir:<\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/statorials.org\/wp-content\/ql-cache\/quicklatex.com-d2bfcc289eeacbbc0a667f6b994541ef_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"K_3=134+0,8\\cdot (141-134)=139,6\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"289\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<p> Son olarak 4&#8217;\u00fcnc\u00fc dilimin hesaplanmas\u0131 i\u00e7in ayn\u0131 i\u015flemi son kez tekrarl\u0131yoruz. \u0130lk \u00f6nce konumunu buluyoruz:<\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/statorials.org\/wp-content\/ql-cache\/quicklatex.com-027c1e4027a019e60dedc93a67a2cb51_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\cfrac{4\\cdot (42+1)}{5}=34,4\" title=\"Rendered by QuickLaTeX.com\" height=\"40\" width=\"142\" style=\"vertical-align: -12px;\"><\/p>\n<\/p>\n<p> Bu nedenle d\u00f6rd\u00fcnc\u00fc be\u015fte birlik dilimin kesin de\u011feri 34 ile 35 aras\u0131nda olacakt\u0131r ve konumlar\u0131 172 ve 179 numaral\u0131 verilere kar\u015f\u0131l\u0131k gelir. Bu nedenle d\u00f6rd\u00fcnc\u00fc be\u015fte birli\u011fin hesaplanmas\u0131 \u015fu \u015fekildedir: <\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/statorials.org\/wp-content\/ql-cache\/quicklatex.com-6176c604adba400f1d6df2d3dbf85ebb_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"K_4=172+0,4\\cdot (179-172)=174,8\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"289\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<h2 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"calculadora-de-quintiles\"><\/span> Be\u015flik Hesap Makinesi<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p> Be\u015fte birlik dilimleri hesaplamak i\u00e7in a\u015fa\u011f\u0131daki hesap makinesine istatistiksel veri k\u00fcmesini girin. Veriler bir bo\u015flukla ayr\u0131lmal\u0131 ve ondal\u0131k ay\u0131r\u0131c\u0131 olarak nokta kullan\u0131larak girilmelidir. <\/p>\n<form action=\"\" method=\"post\"><textarea name=\"datos\" style=\"border:1.5px solid #4FC3F7; border-radius:15px;\" placeholder=\"3 4 9 7 2 3.4 1 5.2 11 6 ...\" required=\"\" oninvalid=\"this.setCustomValidity('Introduce los datos aqu\u00ed')\" oninput=\"this.setCustomValidity('')\"><\/textarea><\/p>\n<div style=\"text-align:center\"><input align=\"center\" style=\"border-radius:30px; margin: 20px\" type=\"submit\" name=\"submit\" value=\"Be\u015fte birlik dilimleri hesapla\"><\/div>\n<\/form>\n<h2 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"quintiles-en-datos-agrupados\"><\/span> Grupland\u0131r\u0131lm\u0131\u015f verilerdeki be\u015fte birlik dilimler<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p> <strong>Veriler aral\u0131klar halinde grupland\u0131r\u0131ld\u0131\u011f\u0131nda be\u015fte birlik dilimleri hesaplamak<\/strong> i\u00e7in \u00f6ncelikle a\u015fa\u011f\u0131daki form\u00fcl\u00fc kullanarak aral\u0131\u011f\u0131n\u0131 veya s\u0131n\u0131f\u0131n\u0131 bulman\u0131z gerekir:<\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/statorials.org\/wp-content\/ql-cache\/quicklatex.com-4315101111b7c44489c8731dd15ad2e8_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\cfrac{k\\cdot (n+1)}{5} \\qquad k=1, 2, 3,4\" title=\"Rendered by QuickLaTeX.com\" height=\"40\" width=\"206\" style=\"vertical-align: -12px;\"><\/p>\n<\/p>\n<p> Bu nedenle be\u015fte birlik dilim, mutlak frekans\u0131 \u00f6nceki ifadeyle elde edilen say\u0131dan hemen b\u00fcy\u00fck olan aral\u0131kta olacakt\u0131r.<\/p>\n<p> Ve be\u015fte birli\u011fin ait oldu\u011fu aral\u0131\u011f\u0131 bildi\u011fimizde, be\u015fte birli\u011fin tam de\u011ferini bulmak i\u00e7in a\u015fa\u011f\u0131daki form\u00fcl\u00fc uygulamam\u0131z gerekir:<\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/statorials.org\/wp-content\/ql-cache\/quicklatex.com-0078153fc3eff2a156082edfd49fc248_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"K_k=L_i+ \\cfrac{\\displaystyle\\frac{k\\cdot (n+1)}{5}-F_{i-1}}{f_i}\\cdot I_i \\qquad k=1,2,3,4\" title=\"Rendered by QuickLaTeX.com\" height=\"61\" width=\"380\" style=\"vertical-align: -16px;\"><\/p>\n<\/p>\n<p> Alt\u0131n:<\/p>\n<ul>\n<li> <em>L <sub>i<\/sub><\/em> be\u015fte birlik dilimin bulundu\u011fu aral\u0131\u011f\u0131n alt s\u0131n\u0131r\u0131d\u0131r.<\/li>\n<li> <em>n<\/em> , toplam g\u00f6zlem say\u0131s\u0131d\u0131r.<\/li>\n<li> <em>F <sub>i-1<\/sub><\/em> \u00f6nceki aral\u0131\u011f\u0131n k\u00fcm\u00fclatif mutlak frekans\u0131d\u0131r.<\/li>\n<li> <em>f <sub>i,<\/sub><\/em> be\u015fte birlik dilimin bulundu\u011fu aral\u0131\u011f\u0131n mutlak frekans\u0131d\u0131r.<\/li>\n<li> <em>I <sub>i<\/sub><\/em> be\u015fte birlik aral\u0131\u011f\u0131n geni\u015fli\u011fidir.<\/li>\n<\/ul>\n<p> Bunun nas\u0131l yap\u0131ld\u0131\u011f\u0131n\u0131 g\u00f6rebilirsiniz; burada, aral\u0131klar halinde grupland\u0131r\u0131lm\u0131\u015f a\u015fa\u011f\u0131daki veri serilerinin be\u015fte birlik dilimlerinin hesaplanmas\u0131na ili\u015fkin \u00e7\u00f6z\u00fclm\u00fc\u015f bir \u00f6rnek verilmi\u015ftir: <\/p>\n<div class=\"wp-block-image\">\n<figure class=\"aligncenter size-full is-resized\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/statorials.org\/wp-content\/uploads\/2023\/08\/ensemble-de-donnees-regroupees-par-intervalles.png\" alt=\"aral\u0131klarla grupland\u0131r\u0131lm\u0131\u015f veri k\u00fcmesi\" class=\"wp-image-1431\" width=\"231\" height=\"231\" srcset=\"\" sizes=\"auto, \"><\/figure>\n<\/div>\n<p> Veriler grupland\u0131r\u0131lm\u0131\u015f oldu\u011fundan, be\u015fte birlik dilimleri hesaplamak i\u00e7in a\u015fa\u011f\u0131daki y\u00f6ntemi kullanmam\u0131z gerekir: \u00f6nce be\u015fte birlik dilimin d\u00fc\u015ft\u00fc\u011f\u00fc aral\u0131\u011f\u0131 belirleyin, ard\u0131ndan be\u015fte birlik dilimin tam de\u011ferini bulun.<\/p>\n<p> Bu nedenle, ilk be\u015fte birlik dilimin bulundu\u011fu aral\u0131\u011f\u0131 bulmak i\u00e7in a\u015fa\u011f\u0131daki form\u00fcl\u00fc kullan\u0131r\u0131z:<\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/statorials.org\/wp-content\/ql-cache\/quicklatex.com-a21562998b07e3b0e3177461ddecd31c_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\cfrac{k\\cdot (n+1)}{5}\" title=\"Rendered by QuickLaTeX.com\" height=\"40\" width=\"78\" style=\"vertical-align: -12px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/statorials.org\/wp-content\/ql-cache\/quicklatex.com-d40b057bca7ebd308d9b0064c0bf31ac_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\cfrac{1\\cdot (150+1)}{5} =30,2 \\quad \\color{orange}\\bm{\\longrightarrow}\\color{black}\\quad [150,200)\" title=\"Rendered by QuickLaTeX.com\" height=\"40\" width=\"382\" style=\"vertical-align: -12px;\"><\/p>\n<\/p>\n<p> \u0130lk y\u00fczdelik dilim, k\u00fcm\u00fclatif mutlak frekans\u0131 30,2&#8217;den hemen b\u00fcy\u00fck olan aral\u0131kta olacakt\u0131r; bu durumda, k\u00fcm\u00fclatif mutlak frekans\u0131 42 olan aral\u0131k [150,200) olacakt\u0131r. Ve y\u00fczdelik dilim aral\u0131\u011f\u0131n\u0131 bildi\u011fimizde, denklemin ikinci form\u00fcl\u00fcn\u00fc uygular\u0131z. Kesin de\u011ferini belirlemek i\u00e7in s\u00fcre\u00e7:<\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/statorials.org\/wp-content\/ql-cache\/quicklatex.com-5f7a280d1eb985e88acc079defadcbd3_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"K_k=L_i+ \\cfrac{\\displaystyle\\frac{k\\cdot (n+1)}{5}-F_{i-1}}{f_i}\\cdot I_i \" title=\"Rendered by QuickLaTeX.com\" height=\"61\" width=\"252\" style=\"vertical-align: -16px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/statorials.org\/wp-content\/ql-cache\/quicklatex.com-8475977437a578994a573dedc8feb1b5_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"K_1=150+\\cfrac{\\displaystyle\\frac{1\\cdot (150+1)}{5}-18}{24}\\cdot 50=175,42\" title=\"Rendered by QuickLaTeX.com\" height=\"57\" width=\"338\" style=\"vertical-align: -12px;\"><\/p>\n<\/p>\n<p> \u015eimdi ikinci be\u015fte birlik k\u0131sm\u0131 elde etmek i\u00e7in ayn\u0131 prosed\u00fcr\u00fc tekrarl\u0131yoruz, \u00f6nce onun i\u00e7inde bulundu\u011fu aral\u0131\u011f\u0131 hesapl\u0131yoruz:<\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/statorials.org\/wp-content\/ql-cache\/quicklatex.com-b9c2b7b61979ea392041fd0d4ddd7ee4_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\cfrac{2\\cdot (150+1)}{5} =60,4 \\quad \\color{orange}\\bm{\\longrightarrow}\\color{black}\\quad [200,250)\" title=\"Rendered by QuickLaTeX.com\" height=\"40\" width=\"382\" style=\"vertical-align: -12px;\"><\/p>\n<\/p>\n<p> 60,4&#8217;\u00fcn hemen \u00fczerindeki k\u00fcm\u00fclatif mutlak frekans 75&#8217;tir, dolay\u0131s\u0131yla ikinci be\u015fte birlik aral\u0131k [200 250] olur. Bu nedenle, tam be\u015fte birlik de\u011feri hesaplamak i\u00e7in kar\u015f\u0131l\u0131k gelen de\u011ferleri ikinci form\u00fclde yerine koyar\u0131z:<\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/statorials.org\/wp-content\/ql-cache\/quicklatex.com-808754bc9bc24696f42284175556b3d1_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"K_2=200+\\cfrac{\\displaystyle\\frac{2\\cdot (150+1)}{5}-42}{33}\\cdot 50=227,88\" title=\"Rendered by QuickLaTeX.com\" height=\"57\" width=\"339\" style=\"vertical-align: -12px;\"><\/p>\n<\/p>\n<p> Be\u015fte birlik 3&#8217;\u00fc elde etmek i\u00e7in ayn\u0131 i\u015flemi \u00fc\u00e7\u00fcnc\u00fc kez yap\u0131yoruz. \u0130lk \u00f6nce be\u015fte birli\u011fin bulundu\u011fu aral\u0131\u011f\u0131 belirliyoruz:<\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/statorials.org\/wp-content\/ql-cache\/quicklatex.com-9dcb5226afadcf5a30c11657505dbc58_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\cfrac{3\\cdot (150+1)}{5} =90,6 \\quad \\color{orange}\\bm{\\longrightarrow}\\color{black}\\quad [250,300)\" title=\"Rendered by QuickLaTeX.com\" height=\"40\" width=\"382\" style=\"vertical-align: -12px;\"><\/p>\n<\/p>\n<p> Be\u015flik dilim [250,300) aral\u0131\u011f\u0131ndad\u0131r \u00e7\u00fcnk\u00fc k\u00fcm\u00fclatif mutlak frekans\u0131 (102) 90,6&#8217;n\u0131n hemen \u00fczerindedir. \u00dc\u00e7\u00fcnc\u00fc be\u015fte birlik dilimin kesin de\u011ferinin hesaplanmas\u0131 bu nedenle a\u015fa\u011f\u0131daki gibidir:<\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/statorials.org\/wp-content\/ql-cache\/quicklatex.com-23a4e65bb979c2b6a8c1fbd689bd4b57_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"K_3=250+\\cfrac{\\displaystyle\\frac{3\\cdot (150+1)}{5}-75}{27}\\cdot 50=278,89\" title=\"Rendered by QuickLaTeX.com\" height=\"57\" width=\"339\" style=\"vertical-align: -12px;\"><\/p>\n<\/p>\n<p> Sonunda d\u00f6rd\u00fcnc\u00fc be\u015fte birlik k\u0131sm\u0131 bulaca\u011f\u0131z. Her zaman oldu\u011fu gibi \u00f6nce aral\u0131\u011f\u0131n\u0131 buluyoruz:<\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/statorials.org\/wp-content\/ql-cache\/quicklatex.com-395cf1fb8712219c061f3d214fd06049_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\cfrac{4\\cdot (150+1)}{5} =120,8 \\quad \\color{orange}\\bm{\\longrightarrow}\\color{black}\\quad [300,350)\" title=\"Rendered by QuickLaTeX.com\" height=\"40\" width=\"390\" style=\"vertical-align: -12px;\"><\/p>\n<\/p>\n<p> Mutlak frekans\u0131 120,8&#8217;den hemen b\u00fcy\u00fck olan aral\u0131k [300,350] olup de\u011feri 130&#8217;dur. Dolay\u0131s\u0131yla d\u00f6rd\u00fcnc\u00fc be\u015fte birlik dilimin tam de\u011feri \u015fu \u015fekilde olacakt\u0131r:<\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/statorials.org\/wp-content\/ql-cache\/quicklatex.com-ca36008a796d3e129075f54ba4a0fe90_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"K_4=300+\\cfrac{\\displaystyle\\frac{4\\cdot (150+1)}{5}-102}{28}\\cdot 50=333,57\" title=\"Rendered by QuickLaTeX.com\" height=\"57\" width=\"348\" style=\"vertical-align: -12px;\"><\/p><\/p>\n","protected":false},"excerpt":{"rendered":"<p>Bu yaz\u0131da be\u015fte birlik dilimlerin ne oldu\u011funu ve nas\u0131l hesapland\u0131klar\u0131n\u0131 a\u00e7\u0131kl\u0131yoruz. Be\u015fte birlik dilimlerin hesaplanmas\u0131na ili\u015fkin birka\u00e7 \u00e7\u00f6z\u00fclm\u00fc\u015f \u00f6rnek bulacaks\u0131n\u0131z ve ayr\u0131ca \u00e7evrimi\u00e7i bir hesap makinesiyle herhangi bir istatistiksel \u00f6rne\u011fin be\u015fte birlik dilimlerini hesaplayabileceksiniz. Be\u015fte birlikler nedir? \u0130statistikte be\u015fte birlik dilimler, bir veri k\u00fcmesini be\u015f e\u015fit par\u00e7aya b\u00f6len d\u00f6rt de\u011ferdir. Dolay\u0131s\u0131yla birinci, ikinci, \u00fc\u00e7\u00fcnc\u00fc ve [&hellip;]<\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[14],"tags":[],"class_list":["post-72","post","type-post","status-publish","format-standard","hentry","category-istatistik"],"yoast_head":"<!-- This site is optimized with the Yoast SEO plugin v21.3 - https:\/\/yoast.com\/wordpress\/plugins\/seo\/ -->\n<title>\u25b7 Be\u015fli gruplar: bunlar nelerdir, form\u00fcl, \u00f6rnekler, hesap makinesi,...<\/title>\n<meta name=\"description\" content=\"Be\u015fte birlikler nedir - Be\u015fte birlikler nas\u0131l hesaplan\u0131r - Grupland\u0131r\u0131lm\u0131\u015f verilerde be\u015fte birlikler - Pratik \u00f6rnekler - Be\u015fte birlik hesaplay\u0131c\u0131\" \/>\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\/beste-birlik-dilimler\/\" \/>\n<meta property=\"og:locale\" content=\"tr_TR\" \/>\n<meta property=\"og:type\" content=\"article\" \/>\n<meta property=\"og:title\" content=\"\u25b7 Be\u015fli gruplar: bunlar nelerdir, form\u00fcl, \u00f6rnekler, hesap makinesi,...\" \/>\n<meta property=\"og:description\" content=\"Be\u015fte birlikler nedir - 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