{"id":71,"date":"2023-08-05T19:34:58","date_gmt":"2023-08-05T19:34:58","guid":{"rendered":"https:\/\/statorials.org\/tr\/ondalik-dilimler\/"},"modified":"2023-08-05T19:34:58","modified_gmt":"2023-08-05T19:34:58","slug":"ondalik-dilimler","status":"publish","type":"post","link":"https:\/\/statorials.org\/tr\/ondalik-dilimler\/","title":{"rendered":"Ondal\u0131k"},"content":{"rendered":"<p>Bu yaz\u0131da ondal\u0131k say\u0131lar\u0131n ne oldu\u011funu ve nas\u0131l hesapland\u0131klar\u0131n\u0131 a\u00e7\u0131kl\u0131yoruz. Ayr\u0131ca, ondal\u0131k hesaplamalar\u0131n birka\u00e7 ad\u0131m ad\u0131m \u00e7\u00f6z\u00fclm\u00fc\u015f \u00f6rne\u011fini bulacaks\u0131n\u0131z ve buna ek olarak, \u00e7evrimi\u00e7i bir hesap makinesiyle herhangi bir istatistiksel \u00f6rne\u011fin ondal\u0131klar\u0131n\u0131 hesaplayabileceksiniz.<\/p>\n<h2 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"%c2%bfque-son-los-deciles\"><\/span>Ondal\u0131k dilimler nedir?<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p> <strong>\u0130statistikte ondal\u0131k say\u0131lar, s\u0131ral\u0131 bir veri k\u00fcmesini on e\u015fit par\u00e7aya b\u00f6len dokuz de\u011ferdir.<\/strong> B\u00f6ylece birinci, ikinci, \u00fc\u00e7\u00fcnc\u00fc,\u2026 ondal\u0131k dilim numunenin veya pop\u00fclasyonun %10, %20, %30,\u2026&#8217;unu temsil eder.<\/p>\n<p> \u00d6rne\u011fin d\u00f6rd\u00fcnc\u00fc ondal\u0131k de\u011fer, verinin %40&#8217;\u0131ndan y\u00fcksek, ancak geri kalan veriden d\u00fc\u015f\u00fckt\u00fcr.<\/p>\n<p> Ondal\u0131k dilimler b\u00fcy\u00fck D harfi ve ondal\u0131k indeks ile temsil edilir, yani ilk ondal\u0131k dilim D <sub>1<\/sub> , ikinci ondal\u0131k dilim D <sub>2<\/sub> , \u00fc\u00e7\u00fcnc\u00fc ondal\u0131k dilim D <sub>3<\/sub> vb. <\/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\/deciles.png\" alt=\"\" class=\"wp-image-1389\" width=\"414\" height=\"220\" srcset=\"\" sizes=\"auto, \"><\/figure>\n<\/div>\n<p> \ud83d\udc49Herhangi <u style=\"text-decoration-color:#FF8A05;\">bir veri k\u00fcmesi i\u00e7in ondal\u0131k de\u011ferleri hesaplamak i\u00e7in a\u015fa\u011f\u0131daki hesap makinesini kullanabilirsiniz.<\/u><\/p>\n<p> Ondal\u0131k dilimlerin, \u00e7eyrekler, be\u015fte birlik dilimler ve y\u00fczdelik dilimlerle ayn\u0131 \u015fekilde merkezi olmayan konumun bir \u00f6l\u00e7\u00fcs\u00fc oldu\u011funa dikkat edilmelidir. Bu nicelik t\u00fcrlerinin her birinin anlam\u0131n\u0131 web sitemizden kontrol edebilirsiniz.<\/p>\n<p> Ayr\u0131ca be\u015finci ondal\u0131k dilim, t\u00fcm veri setini iki e\u015fit par\u00e7aya b\u00f6ld\u00fc\u011f\u00fc i\u00e7in medyan ve ikinci \u00e7eyre\u011fe e\u015fde\u011ferdir.<\/p>\n<h2 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"como-calcular-los-deciles\"><\/span>Ondal\u0131k say\u0131 nas\u0131l hesaplan\u0131r<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p> Bir dizi istatistiksel verinin <strong>ondal\u0131k konumunu hesaplamak<\/strong> i\u00e7in, ondal\u0131k say\u0131y\u0131 toplam veri say\u0131s\u0131n\u0131n toplam\u0131n\u0131n bir art\u0131s\u0131yla \u00e7arp\u0131n ve sonucu ona b\u00f6l\u00fcn.<\/p>\n<p> Bu nedenle <strong>ondal\u0131k form\u00fcl<\/strong> \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-d84ca1bdd1a62a50e87decde4d360daa_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\cfrac{k\\cdot (n+1)}{10} \\qquad k=1, 2, 3,4,5,6,7,8,9\" title=\"Rendered by QuickLaTeX.com\" height=\"40\" width=\"289\" style=\"vertical-align: -12px;\"><\/p>\n<\/p>\n<p> <strong>L\u00fctfen unutmay\u0131n:<\/strong> Bu form\u00fcl bize ondal\u0131k dilimin de\u011ferini de\u011fil, ondal\u0131k dilimin konumunu s\u00f6yler. Ondal\u0131k 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, ondal\u0131k k\u0131s\u0131m yukar\u0131daki form\u00fcl\u00fcn sa\u011flad\u0131\u011f\u0131 konumda bulunan verilerdir.<\/li>\n<li> Form\u00fcl\u00fcn sonucu <strong>ondal\u0131k k\u0131sm\u0131 olan bir say\u0131<\/strong> ise, ondal\u0131k de\u011fer a\u015fa\u011f\u0131daki form\u00fcl 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-dea1a6ff3ec04aca29983e36653e2f4b_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"D=x_i+d\\cdot (x_{i+1}-x_i)\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"182\" 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> \u015eimdi istatistiksel bir \u00f6rne\u011fin ondal\u0131k rakamlar\u0131n\u0131 alman\u0131n karma\u015f\u0131k oldu\u011funu d\u00fc\u015f\u00fcnebilirsiniz, ancak pratikte olduk\u00e7a basittir. A\u015fa\u011f\u0131daki iki \u00f6rne\u011fi okursan\u0131z mutlaka \u00e7ok daha iyi anlayacaks\u0131n\u0131z.<\/p>\n<p> <strong>Not<\/strong> : Bilim camias\u0131 ondal\u0131k say\u0131lar\u0131n nas\u0131l hesaplanaca\u011f\u0131 konusunda tam olarak fikir birli\u011fine varmam\u0131\u015ft\u0131r, dolay\u0131s\u0131yla bunu biraz farkl\u0131 a\u00e7\u0131klayan istatistik kitaplar\u0131n\u0131 bulabilirsiniz. <\/p>\n<h2 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"ejemplo-del-calculo-de-deciles\"><\/span> Ondal\u0131k hesaplama \u00f6rne\u011fi<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p> Yukar\u0131da g\u00f6rd\u00fc\u011f\u00fcn\u00fcz gibi ondal\u0131k say\u0131lar\u0131n hesaplanmas\u0131, ilk form\u00fcl\u00fcn bize verdi\u011fi say\u0131n\u0131n ondal\u0131k olup olmamas\u0131na ba\u011fl\u0131d\u0131r, bu y\u00fczden a\u015fa\u011f\u0131da her durum i\u00e7in bir tane olmak \u00fczere iki \u00e7\u00f6z\u00fcml\u00fc \u00f6rnek haz\u0131rlad\u0131k. Her durumda, ondal\u0131k dilimlerin bile\u015fimi hakk\u0131nda herhangi bir sorunuz varsa, bunlar\u0131 yorumlarda sorabilece\u011finizi unutmay\u0131n.<\/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 veriler g\u00f6z \u00f6n\u00fcne al\u0131nd\u0131\u011f\u0131nda, en k\u00fc\u00e7\u00fckten en b\u00fcy\u00fc\u011fe, numunenin birinci, \u00fc\u00e7\u00fcnc\u00fc ve sekizinci dilimini bulun. <\/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.png\" alt=\"s\u0131ral\u0131 veri \u00f6rne\u011fi\" class=\"wp-image-1395\" width=\"331\" height=\"192\" srcset=\"\" sizes=\"auto, \"><\/figure>\n<\/div>\n<p> Bu al\u0131\u015ft\u0131rmadaki veriler zaten s\u0131ralanm\u0131\u015ft\u0131r, bu nedenle s\u0131ray\u0131 de\u011fi\u015ftirmeye gerek yoktur, aksi takdirde \u00f6nce verileri en k\u00fc\u00e7\u00fckten en b\u00fcy\u00fc\u011fe do\u011fru s\u0131ralamak zorunda kal\u0131r\u0131z.<\/p>\n<p> Yukar\u0131da a\u00e7\u0131kland\u0131\u011f\u0131 gibi ondal\u0131k say\u0131lar\u0131n konumlar\u0131n\u0131 bulmay\u0131 m\u00fcmk\u00fcn k\u0131lan form\u00fcl 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-9d776d64e6cae271e22b1044a785e7ff_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\cfrac{k\\cdot (n+1)}{10} \\qquad k=1,2,3,4,5,6,7,8,9\" title=\"Rendered by QuickLaTeX.com\" height=\"40\" width=\"289\" style=\"vertical-align: -12px;\"><\/p>\n<\/p>\n<p> Bu al\u0131\u015ft\u0131rman\u0131n \u00f6rneklem b\u00fcy\u00fckl\u00fc\u011f\u00fc 29 g\u00f6zlemdir, dolay\u0131s\u0131yla ilk ondal\u0131k dilimin konumunu hesaplamak i\u00e7in <em>n<\/em> yerine 29 ve <em>k<\/em> yerine 1 koymal\u0131s\u0131n\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-5e09eac1617e712e646cca0f85a3a29e_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\cfrac{1\\cdot (29+1)}{10}=3\\quad \\color{orange}\\bm{\\longrightarrow}\\color{black}\\quad D_1=85\" title=\"Rendered by QuickLaTeX.com\" height=\"40\" width=\"338\" style=\"vertical-align: -12px;\"><\/p>\n<\/p>\n<p> Form\u00fcl\u00fcn sonucu 3 oldu\u011fundan ilk ondal\u0131k dilim s\u0131ral\u0131 listenin \u00fc\u00e7\u00fcnc\u00fc konumunda olacakt\u0131r ve bu de\u011fer 85&#8217;e kar\u015f\u0131l\u0131k gelir.<\/p>\n<p> \u015eimdi ayn\u0131 i\u015flemi \u00fc\u00e7\u00fcnc\u00fc ondal\u0131k dilimle tekrar uyguluyoruz. <em>K&#8217;y\u0131<\/em> 3 ile de\u011fi\u015ftirerek 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-80334025fcaf39a38569f709ba84d228_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\cfrac{3\\cdot (29+1)}{10}=9\\quad \\color{orange}\\bm{\\longrightarrow}\\color{black}\\quad D_3=97\" title=\"Rendered by QuickLaTeX.com\" height=\"40\" width=\"339\" style=\"vertical-align: -12px;\"><\/p>\n<\/p>\n<p> Bu nedenle \u00fc\u00e7\u00fcnc\u00fc ondal\u0131k dilim dokuzuncu konumdaki \u00f6\u011fe olacakt\u0131r, yani 97.<\/p>\n<p> Son olarak ayn\u0131 i\u015flemi yap\u0131yoruz ancak sekizinci ondal\u0131k dilimi belirlemek i\u00e7in form\u00fcle 8 koyuyoruz:<\/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-c523f9d6aba2e305690a3a7214545f4f_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\cfrac{8\\cdot (29+1)}{10}=24\\quad \\color{orange}\\bm{\\longrightarrow}\\color{black}\\quad D_8=131\" title=\"Rendered by QuickLaTeX.com\" height=\"40\" width=\"356\" style=\"vertical-align: -12px;\"><\/p>\n<\/p>\n<p> Sekizinci ondal\u0131k dilim, s\u0131ral\u0131 veri listesinin 24. pozisyonundaki say\u0131 olacakt\u0131r, dolay\u0131s\u0131yla sekizinci ondal\u0131k dilim 131 olacakt\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 tablodaki verilerden 4, 7 ve 9 ondal\u0131klar\u0131n\u0131 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=\"\" class=\"wp-image-1396\" width=\"344\" height=\"231\" srcset=\"\" sizes=\"auto, \"><\/figure>\n<\/div>\n<p> \u00d6nceki \u00f6rnekte oldu\u011fu gibi, ondal\u0131k say\u0131lar\u0131n 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-9d776d64e6cae271e22b1044a785e7ff_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\cfrac{k\\cdot (n+1)}{10} \\qquad k=1,2,3,4,5,6,7,8,9\" title=\"Rendered by QuickLaTeX.com\" height=\"40\" width=\"289\" style=\"vertical-align: -12px;\"><\/p>\n<\/p>\n<p> Bu durumda \u00f6rneklem b\u00fcy\u00fckl\u00fc\u011f\u00fc 42&#8217;dir, dolay\u0131s\u0131yla d\u00f6rd\u00fcnc\u00fc ondal\u0131k dilimin konumunu bulmak i\u00e7in <em>n<\/em> parametresini 42 ve <em>k<\/em> parametresini 4 ile de\u011fi\u015ftirmeniz 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-714bf70e19bccae368d9ce894d5c17c2_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\cfrac{4\\cdot (42+1)}{10}=17,2\" title=\"Rendered by QuickLaTeX.com\" height=\"40\" width=\"141\" style=\"vertical-align: -12px;\"><\/p>\n<\/p>\n<p> Ancak bu sefer form\u00fclden ondal\u0131k bir say\u0131 ald\u0131k, dolay\u0131s\u0131yla tam ondal\u0131k de\u011feri 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-dea1a6ff3ec04aca29983e36653e2f4b_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"D=x_i+d\\cdot (x_{i+1}-x_i)\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"182\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<p> \u0130lk form\u00fclden elde edilen say\u0131 17,2&#8217;dir, yani d\u00f6rd\u00fcnc\u00fc ondal\u0131k dilim, s\u0131ras\u0131yla 109 ve 112 olan on yedinci ve on sekizinci say\u0131lar aras\u0131ndad\u0131r. Bu nedenle <em>x <sub>i<\/sub><\/em> 109, <em>x <sub>i+ 1<\/sub><\/em> 112 ve <em>d<\/em> ondal\u0131k k\u0131s\u0131md\u0131r. elde edilen say\u0131n\u0131n 0,2&#8217;si.<\/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-2a5171108fff2844d26149c6dcefa32d_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"D_4=109+0,2\\cdot (112-109)=109,6\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"288\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<p> Yedinci ondal\u0131k dilimi bulmak i\u00e7in ayn\u0131 i\u015flemi tekrarl\u0131yoruz. \u0130lk \u00f6nce ondal\u0131k dilimin 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-23131fe357456930ce15c391c168d2b5_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\cfrac{7\\cdot (42+1)}{10}=30,1\" title=\"Rendered by QuickLaTeX.com\" height=\"40\" width=\"141\" style=\"vertical-align: -12px;\"><\/p>\n<\/p>\n<p> Form\u00fclden 30.1 say\u0131s\u0131n\u0131 elde ettik, bu da ondal\u0131k dilimin 30 ile 31 konumlar\u0131 aras\u0131nda olaca\u011f\u0131 anlam\u0131na gelir, de\u011ferleri 154 ve 159&#8217;dur. Bu nedenle tam ondal\u0131k hesaplama \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-1dd52ed78001ad05dae7fcb3e4d6c57d_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"D_7=154+0,1\\cdot (159-154)=154,5\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"287\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<p> Son olarak dokuzuncu ondal\u0131k dilimi elde etmek i\u00e7in ayn\u0131 y\u00f6ntemi tekrar uyguluyoruz. Ondal\u0131\u011f\u0131n 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-3ec4e5393a5a3cbc2c0ec323d0f518a8_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\cfrac{9\\cdot (42+1)}{10}=38,7\" title=\"Rendered by QuickLaTeX.com\" height=\"40\" width=\"142\" style=\"vertical-align: -12px;\"><\/p>\n<\/p>\n<p> Elde edilen say\u0131 ondal\u0131kt\u0131r ve 38 ile 39 aras\u0131ndad\u0131r ve konumlar\u0131 189 ile 196 de\u011ferlerine kar\u015f\u0131l\u0131k gelir. Dolay\u0131s\u0131yla ondal\u0131k 9&#8217;un 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-3239505467e98ad92e388a7d37741a4c_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"D_9=189+0,7\\cdot (196-189)=193,9\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"288\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<h2 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"calculadora-de-deciles\"><\/span> Ondal\u0131k Hesaplay\u0131c\u0131<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p> Ondal\u0131klar\u0131 hesaplamak i\u00e7in a\u015fa\u011f\u0131daki hesap makinesine bir istatistiksel veri seti tak\u0131n. 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=\"Ondal\u0131k de\u011ferleri hesapla\"><\/div>\n<\/form>\n<h2 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"deciles-en-datos-agrupados\"><\/span> Grupland\u0131r\u0131lm\u0131\u015f verilerdeki ondal\u0131k say\u0131lar<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p> <strong>Veriler aral\u0131klar halinde grupland\u0131r\u0131ld\u0131\u011f\u0131nda ondal\u0131k dilimleri hesaplamak<\/strong> i\u00e7in \u00f6ncelikle a\u015fa\u011f\u0131daki form\u00fcl\u00fc kullanarak ondal\u0131k dilimin d\u00fc\u015ft\u00fc\u011f\u00fc aral\u0131\u011f\u0131 veya b\u00f6lmeyi bulmam\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-ffd7077d6e9c8bc8fab60d60512a739a_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\cfrac{k\\cdot (n+1)}{10} \\qquad k=1, 2, 3,3,4,5,6,7,8,9\" title=\"Rendered by QuickLaTeX.com\" height=\"40\" width=\"306\" style=\"vertical-align: -12px;\"><\/p>\n<\/p>\n<p> Dolay\u0131s\u0131yla ondal\u0131k dilim, mutlak frekans\u0131 \u00f6nceki ifadede elde edilen say\u0131dan hemen b\u00fcy\u00fck olan aral\u0131kta olacakt\u0131r.<\/p>\n<p> Ve ondal\u0131k dilimin ait oldu\u011fu aral\u0131\u011f\u0131 zaten bildi\u011fimizde, ondal\u0131k dilimin 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-a1d3bc81e73284fb06ed26d26e993256_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"D_k=L_i+\\cfrac{\\displaystyle\\frac{k\\cdot (n+1)}{10}-F_{i-1}}{f_i}\\cdot I_i \\qquad k=1,2,3,4,5,6,7,8,9\" title=\"Rendered by QuickLaTeX.com\" height=\"61\" width=\"463\" style=\"vertical-align: -16px;\"><\/p>\n<\/p>\n<p> Alt\u0131n:<\/p>\n<ul>\n<li> <em>L <sub>i,<\/sub><\/em> ondal\u0131k dilimin bulundu\u011fu aral\u0131\u011f\u0131n alt s\u0131n\u0131r\u0131d\u0131r.<\/li>\n<li> <em>n<\/em> , istatistiksel verilerin toplam 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> ondal\u0131k dilimin bulundu\u011fu aral\u0131\u011f\u0131n mutlak frekans\u0131d\u0131r.<\/li>\n<li> <em>ben <sub>i<\/sub><\/em> ondal\u0131k aral\u0131\u011f\u0131n geni\u015fli\u011fidir.<\/li>\n<\/ul>\n<p> Bunun nas\u0131l yap\u0131ld\u0131\u011f\u0131n\u0131 g\u00f6rebilmeniz i\u00e7in a\u015fa\u011f\u0131da, aral\u0131klara g\u00f6re grupland\u0131r\u0131lm\u0131\u015f a\u015fa\u011f\u0131daki verilerin 3, 5 ve 8&#8217;inci ondal\u0131klar\u0131n\u0131n hesapland\u0131\u011f\u0131 tamamlanm\u0131\u015f bir al\u0131\u015ft\u0131rman\u0131z var. <\/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\/donnees-groupees-en-intervalles-1.png\" alt=\"aral\u0131klar halinde grupland\u0131r\u0131lm\u0131\u015f veriler\" class=\"wp-image-1401\" width=\"236\" height=\"256\" srcset=\"\" sizes=\"auto, \"><\/figure>\n<\/div>\n<p> Veriler grupland\u0131r\u0131ld\u0131\u011f\u0131 i\u00e7in her ondal\u0131k dilimin hesaplanmas\u0131 iki ad\u0131mdan olu\u015fur: \u00f6nce ondal\u0131k dilimin d\u00fc\u015ft\u00fc\u011f\u00fc aral\u0131\u011f\u0131 bulun, ard\u0131ndan ondal\u0131k dilimin tam de\u011ferini hesaplay\u0131n. Bu nedenle \u00fc\u00e7\u00fcnc\u00fc ondal\u0131k dilimin 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-a73819ded2771d2c1e148aed6c357f55_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\cfrac{k\\cdot (n+1)}{10}\" 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-d253d8f8e82eeb915a51e39b5e90f5cc_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\cfrac{3\\cdot (70+1)}{10} =21,3 \\quad \\color{orange}\\bm{\\longrightarrow}\\color{black}\\quad [30,35)\" title=\"Rendered by QuickLaTeX.com\" height=\"40\" width=\"355\" style=\"vertical-align: -12px;\"><\/p>\n<\/p>\n<p> Ondal\u0131k aral\u0131k, mutlak k\u00fcm\u00fclatif frekans\u0131 21,3&#8217;ten hemen b\u00fcy\u00fck olan aral\u0131k olacakt\u0131r ve bu durumda mutlak k\u00fcm\u00fclatif frekans\u0131 31 olan aral\u0131kt\u0131r [30,35). Art\u0131k ondal\u0131k aral\u0131\u011f\u0131n\u0131 bildi\u011fimize g\u00f6re, bulmak i\u00e7in a\u015fa\u011f\u0131daki form\u00fcl\u00fc uygular\u0131z. ondal\u0131k dilimin tam de\u011feri:<\/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-e44ab71e13a408406f6896c04bcf0c04_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"D_k=L_i+\\cfrac{\\displaystyle\\frac{k\\cdot (n+1)}{10}-F_{i-1}}{f_i}\\cdot I_i \" title=\"Rendered by QuickLaTeX.com\" height=\"61\" width=\"251\" 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-1b56e9d16a9dec5f1c478a0a463efd57_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"D_3=30+ \\cfrac{\\displaystyle\\frac{3\\cdot (70+1)}{10}-17}{14}\\cdot 5=31,54\" title=\"Rendered by QuickLaTeX.com\" height=\"57\" width=\"303\" style=\"vertical-align: -12px;\"><\/p>\n<\/p>\n<p> \u015eimdi be\u015finci ondal\u0131k dilimi elde etmek i\u00e7in y\u00f6ntemi yeniden uygulamam\u0131z gerekiyor. \u0130lk \u00f6nce bulundu\u011fu aral\u0131\u011f\u0131 belirleriz:<\/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-0539500e31bfdcca0446784ea448fc6f_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\cfrac{5\\cdot (70+1)}{10} =35,5 \\quad \\color{orange}\\bm{\\longrightarrow}\\color{black}\\quad [35,40)\" title=\"Rendered by QuickLaTeX.com\" height=\"40\" width=\"355\" style=\"vertical-align: -12px;\"><\/p>\n<\/p>\n<p> Sonu\u00e7 35, [35,40) aral\u0131\u011f\u0131nda oldu\u011fu anlam\u0131na gelir, ancak aral\u0131k ifadesinde 35 oldu\u011fu i\u00e7in de\u011fil, birikmi\u015f mutlak frekans\u0131n\u0131n (42) en do\u011frudan y\u00fcksek olmas\u0131 nedeniyle. Aral\u0131k belirlendikten sonra s\u00fcrecin ikinci form\u00fcl\u00fcn\u00fc uygular\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-27fa5a7c469a7dee527ebca2ad180bd3_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"D_5=35+ \\cfrac{\\displaystyle\\frac{5\\cdot (70+1)}{10}-31}{11}\\cdot 5=37,05\" title=\"Rendered by QuickLaTeX.com\" height=\"57\" width=\"302\" style=\"vertical-align: -12px;\"><\/p>\n<\/p>\n<p> Son olarak sekizinci ondal\u0131k dilimi buluyoruz. Bunu yapmak i\u00e7in \u00f6nce aral\u0131\u011f\u0131n\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-ebbe344cb24b1da267340523c208d76d_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\cfrac{8\\cdot (70+1)}{10} =56,8 \\quad \\color{orange}\\bm{\\longrightarrow}\\color{black}\\quad [40,45)\" title=\"Rendered by QuickLaTeX.com\" height=\"40\" width=\"355\" style=\"vertical-align: -12px;\"><\/p>\n<\/p>\n<p> 56,8&#8217;in hemen \u00fczerindeki k\u00fcm\u00fclatif mutlak frekans 58&#8217;dir, yani sekizinci ondal\u0131k aral\u0131k [40,45&#8217;tir. Bu nedenle ondal\u0131k dilimin tam de\u011ferini belirlemek yeterlidir:<\/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-2df59239d6c2ddad6636a60fa7791b87_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"D_8=40+ \\cfrac{\\displaystyle\\frac{8\\cdot (70+1)}{10}-42}{16}\\cdot 5=44,63\" title=\"Rendered by QuickLaTeX.com\" height=\"57\" width=\"303\" style=\"vertical-align: -12px;\"><\/p><\/p>\n","protected":false},"excerpt":{"rendered":"<p>Bu yaz\u0131da ondal\u0131k say\u0131lar\u0131n ne oldu\u011funu ve nas\u0131l hesapland\u0131klar\u0131n\u0131 a\u00e7\u0131kl\u0131yoruz. Ayr\u0131ca, ondal\u0131k hesaplamalar\u0131n birka\u00e7 ad\u0131m ad\u0131m \u00e7\u00f6z\u00fclm\u00fc\u015f \u00f6rne\u011fini bulacaks\u0131n\u0131z ve buna ek olarak, \u00e7evrimi\u00e7i bir hesap makinesiyle herhangi bir istatistiksel \u00f6rne\u011fin ondal\u0131klar\u0131n\u0131 hesaplayabileceksiniz. Ondal\u0131k dilimler nedir? \u0130statistikte ondal\u0131k say\u0131lar, s\u0131ral\u0131 bir veri k\u00fcmesini on e\u015fit par\u00e7aya b\u00f6len dokuz de\u011ferdir. B\u00f6ylece birinci, ikinci, \u00fc\u00e7\u00fcnc\u00fc,\u2026 ondal\u0131k dilim [&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-71","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 Ondal\u0131k say\u0131lar: nedir, form\u00fcl, \u00f6rnekler, hesap makinesi,...<\/title>\n<meta name=\"description\" content=\"Ondal\u0131k say\u0131 nedir - Ondal\u0131k say\u0131 nas\u0131l hesaplan\u0131r - Grupland\u0131r\u0131lm\u0131\u015f verilerdeki ondal\u0131k say\u0131 - \u00c7\u00f6z\u00fclm\u00fc\u015f \u00f6rnekler - Ondal\u0131k 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\/ondalik-dilimler\/\" \/>\n<meta property=\"og:locale\" content=\"tr_TR\" \/>\n<meta property=\"og:type\" content=\"article\" \/>\n<meta property=\"og:title\" content=\"\u25b7 Ondal\u0131k say\u0131lar: nedir, form\u00fcl, \u00f6rnekler, hesap makinesi,...\" \/>\n<meta property=\"og:description\" content=\"Ondal\u0131k say\u0131 nedir - 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