{"id":244,"date":"2023-08-03T17:24:22","date_gmt":"2023-08-03T17:24:22","guid":{"rendered":"https:\/\/statorials.org\/tr\/varyans-icin-guven-araligi\/"},"modified":"2023-08-03T17:24:22","modified_gmt":"2023-08-03T17:24:22","slug":"varyans-icin-guven-araligi","status":"publish","type":"post","link":"https:\/\/statorials.org\/tr\/varyans-icin-guven-araligi\/","title":{"rendered":"Varyans i\u00e7in g\u00fcven aral\u0131\u011f\u0131"},"content":{"rendered":"<p>Bu makalede, varyans i\u00e7in g\u00fcven aral\u0131\u011f\u0131n\u0131n ne oldu\u011fu ve istatistikte ne i\u00e7in kullan\u0131ld\u0131\u011f\u0131 a\u00e7\u0131klanmaktad\u0131r. Benzer \u015fekilde, varyans g\u00fcven aral\u0131\u011f\u0131n\u0131 nas\u0131l hesaplayaca\u011f\u0131n\u0131z\u0131 ve ad\u0131m ad\u0131m bir al\u0131\u015ft\u0131rma yapmay\u0131 \u00f6\u011freneceksiniz. <\/p>\n<h2 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"%c2%bfque-es-el-intervalo-de-confianza-para-la-varianza\"><\/span> Varyans\u0131n g\u00fcven aral\u0131\u011f\u0131 nedir?<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p> <strong>Varyans i\u00e7in g\u00fcven aral\u0131\u011f\u0131,<\/strong> bir pop\u00fclasyonun varyans\u0131n\u0131n bulundu\u011fu de\u011ferlere yakla\u015fan bir aral\u0131kt\u0131r. Yani, varyansa ili\u015fkin g\u00fcven aral\u0131\u011f\u0131, bir g\u00fcven d\u00fczeyi i\u00e7in pop\u00fclasyon varyans\u0131n\u0131n maksimum de\u011ferini ve minimum de\u011ferini g\u00f6sterir.<\/p>\n<p> \u00d6rne\u011fin bir pop\u00fclasyon varyans\u0131 i\u00e7in %95 g\u00fcven aral\u0131\u011f\u0131 (55,75) ise bu, pop\u00fclasyon varyans\u0131n\u0131n %95 olas\u0131l\u0131kla 55 ile 75 aras\u0131nda olaca\u011f\u0131 anlam\u0131na gelir.<\/p>\n<p> Bu nedenle varyansa ili\u015fkin g\u00fcven aral\u0131\u011f\u0131, pop\u00fclasyon varyans\u0131n\u0131n aralar\u0131nda yer ald\u0131\u011f\u0131 iki de\u011feri tahmin etmek i\u00e7in kullan\u0131l\u0131r. \u00d6rnek varyans\u0131 hesaplanabilir, ancak pop\u00fclasyon varyans\u0131 genellikle bilinmez, bu nedenle varyans\u0131n g\u00fcven aral\u0131\u011f\u0131, de\u011ferine yakla\u015f\u0131k olarak yakla\u015fmam\u0131z\u0131 sa\u011flar. <\/p>\n<h2 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"formula-del-intervalo-de-confianza-para-la-varianza\"><\/span> Varyans i\u00e7in g\u00fcven aral\u0131\u011f\u0131 form\u00fcl\u00fc<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p> Bir pop\u00fclasyonun varyans\u0131n\u0131n g\u00fcven aral\u0131\u011f\u0131n\u0131 hesaplamak i\u00e7in <a href=\"https:\/\/statorials.org\/tr\/ki-kare-dagilimi\/\">ki-kare da\u011f\u0131l\u0131m\u0131<\/a> kullan\u0131l\u0131r. Daha spesifik olarak <strong>varyans\u0131n g\u00fcven aral\u0131\u011f\u0131n\u0131 hesaplama 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-c81b971afee9691573e8400dc0945c37_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle \\left( (n-1)\\frac{s^2}{\\chi_{n-1;\\alpha\/2}} \\ , \\ (n-1)\\frac{s^2}{\\chi_{n-1;1-\\alpha\/2}}\\right)\" title=\"Rendered by QuickLaTeX.com\" height=\"47\" width=\"304\" style=\"vertical-align: -20px;\"><\/p>\n<\/p>\n<p style=\"margin-bottom:5px\"> Alt\u0131n:<\/p>\n<ul style=\"color:#FF8A05; font-weight: bold;\">\n<li style=\"margin-bottom:5px\">\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/statorials.org\/wp-content\/ql-cache\/quicklatex.com-ec4217f4fa5fcd92a9edceba0e708cf7_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"n\" title=\"Rendered by QuickLaTeX.com\" height=\"8\" width=\"11\" style=\"vertical-align: 0px;\"><\/p>\n<p> \u00f6rneklem b\u00fcy\u00fckl\u00fc\u011f\u00fcd\u00fcr.<\/li>\n<li style=\"margin-bottom:5px\">\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/statorials.org\/wp-content\/ql-cache\/quicklatex.com-1edc883862ceed1a21913f60358e31d8_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"s\" title=\"Rendered by QuickLaTeX.com\" height=\"8\" width=\"8\" style=\"vertical-align: 0px;\"><\/p>\n<p> \u00f6rnek standart sapmas\u0131d\u0131r.<\/li>\n<li style=\"margin-bottom:5px\">\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/statorials.org\/wp-content\/ql-cache\/quicklatex.com-a1f2f5b5bd065f40d0b8c175d6d48950_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\chi_{n-1;\\alpha\/2}\" title=\"Rendered by QuickLaTeX.com\" height=\"16\" width=\"64\" style=\"vertical-align: -8px;\"><\/p>\n<p> \u03b1\/2&#8217;den k\u00fc\u00e7\u00fck bir olas\u0131l\u0131k i\u00e7in n-1 serbestlik derecesine sahip Ki-kare da\u011f\u0131l\u0131m\u0131n\u0131n de\u011feridir.<\/li>\n<li style=\"margin-bottom:5px\">\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/statorials.org\/wp-content\/ql-cache\/quicklatex.com-f1726e9973441084f7ac98c5550f1b23_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\chi_{n-1;1-\\alpha\/2}\" title=\"Rendered by QuickLaTeX.com\" height=\"16\" width=\"82\" style=\"vertical-align: -8px;\"><\/p>\n<p> 1-\u03b1\/2&#8217;den b\u00fcy\u00fck bir olas\u0131l\u0131k i\u00e7in n-1 serbestlik derecesine sahip Ki-kare da\u011f\u0131l\u0131m\u0131n\u0131n de\u011feridir. <\/li>\n<\/ul>\n<h2 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"ejemplo-del-calculo-del-intervalo-de-confianza-para-la-varianza\"><\/span> Varyans i\u00e7in g\u00fcven aral\u0131\u011f\u0131n\u0131 hesaplama \u00f6rne\u011fi<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p> Kavram\u0131 daha iyi anlayabilmeniz i\u00e7in, bu b\u00f6l\u00fcmde size varyans i\u00e7in g\u00fcven aral\u0131\u011f\u0131n\u0131n nas\u0131l hesapland\u0131\u011f\u0131na dair \u00e7\u00f6z\u00fclm\u00fc\u015f bir \u00f6rnek b\u0131rak\u0131yoruz.<\/p>\n<ul>\n<li> A\u015fa\u011f\u0131da g\u00f6sterilen de\u011ferlere sahip 8 g\u00f6zlemlik bir \u00f6rne\u011fimiz var. 1-\u03b1=%95 g\u00fcven d\u00fczeyine sahip pop\u00fclasyon varyans\u0131n\u0131n g\u00fcven aral\u0131\u011f\u0131 nedir?<\/li>\n<\/ul>\n<p class=\"has-text-align-center\"> 206 203 201 212<br \/> 194 176 208 201<\/p>\n<p> Yukar\u0131da a\u00e7\u0131kland\u0131\u011f\u0131 gibi pop\u00fclasyon varyans\u0131n\u0131n g\u00fcven aral\u0131\u011f\u0131n\u0131 belirleme form\u00fcl\u00fc 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-c81b971afee9691573e8400dc0945c37_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle \\left( (n-1)\\frac{s^2}{\\chi_{n-1;\\alpha\/2}} \\ , \\ (n-1)\\frac{s^2}{\\chi_{n-1;1-\\alpha\/2}}\\right)\" title=\"Rendered by QuickLaTeX.com\" height=\"47\" width=\"304\" style=\"vertical-align: -20px;\"><\/p>\n<\/p>\n<p> Bu nedenle g\u00fcven aral\u0131\u011f\u0131n\u0131 bulmak i\u00e7in \u00f6ncelikle \u00f6rneklem standart sapmas\u0131n\u0131 hesaplamam\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-0710aa65b2fb918489f96dbe762b9478_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"s=11,13\" title=\"Rendered by QuickLaTeX.com\" height=\"16\" width=\"76\" style=\"vertical-align: -4px;\"><\/p>\n<\/p>\n<div style=\"background-color:#FFFDE7; padding-top: 10px; padding-bottom: 10px; padding-right: 20px; padding-left: 30px; border: 2.5px dashed #FFB74D; border-radius:20px;\"> <span style=\"color:#ff951b\">\u27a4<\/span> <strong>Bak\u0131n\u0131z:<\/strong> <a href=\"https:\/\/statorials.org\/tr\/standart-sapma-veya-standart-sapma\/\">Standart sapma nas\u0131l hesaplan\u0131r<\/a><\/div>\n<p> \u0130kinci olarak, ihtiyac\u0131m\u0131z olan kar\u015f\u0131l\u0131k gelen de\u011ferlerin ne oldu\u011funu g\u00f6rmek i\u00e7in ki-kare da\u011f\u0131l\u0131m tablosuna bak\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-b68ae2b68b8c4caabf162f13aa199c5a_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\begin{array}{c}\\chi_{n-1;\\alpha\/2}= \\ \\color{orange}\\bm{?}\\\\[2ex]\\chi_{_{7;0,025}}=16,013\\end{array}\" title=\"Rendered by QuickLaTeX.com\" height=\"56\" width=\"156\" style=\"vertical-align: 0px;\"><\/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-07baae9e30db85030d566f59b660a7f7_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\begin{array}{c}\\chi_{n-1;1-\\alpha\/2}= \\ \\color{orange}\\bm{?}\\\\[2ex]\\chi_{_{7;0,975}}=1,690\\end{array}\" title=\"Rendered by QuickLaTeX.com\" height=\"56\" width=\"174\" style=\"vertical-align: 0px;\"><\/p>\n<\/p>\n<div style=\"background-color:#FFFDE7; padding-top: 10px; padding-bottom: 10px; padding-right: 20px; padding-left: 30px; border: 2.5px dashed #FFB74D; border-radius:20px;\"> <span style=\"color:#ff951b\">\u27a4<\/span> <strong>Bak\u0131n\u0131z:<\/strong> Ki-kare da\u011f\u0131l\u0131m tablosu de\u011ferleri<\/div>\n<p> B\u00f6ylece de\u011ferleri varyans\u0131n g\u00fcven aral\u0131\u011f\u0131 form\u00fcl\u00fcne yerle\u015ftirip hesaplamay\u0131 yap\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-c81b971afee9691573e8400dc0945c37_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle \\left( (n-1)\\frac{s^2}{\\chi_{n-1;\\alpha\/2}} \\ , \\ (n-1)\\frac{s^2}{\\chi_{n-1;1-\\alpha\/2}}\\right)\" title=\"Rendered by QuickLaTeX.com\" height=\"47\" width=\"304\" style=\"vertical-align: -20px;\"><\/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-d9c72782ebf40d0fb3d0f63bd052c68b_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle \\left( (8-1)\\frac{11,13^2}{16,013} \\ , \\ (8-1)\\frac{11,13^2}{1,690}\\right)\" title=\"Rendered by QuickLaTeX.com\" height=\"44\" width=\"257\" style=\"vertical-align: -17px;\"><\/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-6878d54e28345cc23afa271c4441948a_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle \\left( 54,15 \\ , \\ 513,10\\right)\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"127\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<p> Sonu\u00e7 olarak, \u00e7al\u0131\u015fma evreninin varyans\u0131n\u0131n %95 g\u00fcven d\u00fczeyi ile 54,15 ile 513,10 aras\u0131nda oldu\u011fu g\u00f6r\u00fclmektedir. <\/p>\n<div style=\"background-color:#FFFDE7; padding-top: 10px; padding-bottom: 10px; padding-right: 20px; padding-left: 30px; border: 2.5px dashed #FFB74D; border-radius:20px;\"> <span style=\"color:#ff951b\">\u27a4<\/span> <strong>Bak\u0131n\u0131z:<\/strong> <a href=\"https:\/\/statorials.org\/tr\/ortalama-icin-guven-araligi\/\">Ortalama i\u00e7in g\u00fcven aral\u0131\u011f\u0131<\/a><\/div>\n","protected":false},"excerpt":{"rendered":"<p>Bu makalede, varyans i\u00e7in g\u00fcven aral\u0131\u011f\u0131n\u0131n ne oldu\u011fu ve istatistikte ne i\u00e7in kullan\u0131ld\u0131\u011f\u0131 a\u00e7\u0131klanmaktad\u0131r. Benzer \u015fekilde, varyans g\u00fcven aral\u0131\u011f\u0131n\u0131 nas\u0131l hesaplayaca\u011f\u0131n\u0131z\u0131 ve ad\u0131m ad\u0131m bir al\u0131\u015ft\u0131rma yapmay\u0131 \u00f6\u011freneceksiniz. Varyans\u0131n g\u00fcven aral\u0131\u011f\u0131 nedir? Varyans i\u00e7in g\u00fcven aral\u0131\u011f\u0131, bir pop\u00fclasyonun varyans\u0131n\u0131n bulundu\u011fu de\u011ferlere yakla\u015fan bir aral\u0131kt\u0131r. Yani, varyansa ili\u015fkin g\u00fcven aral\u0131\u011f\u0131, bir g\u00fcven d\u00fczeyi i\u00e7in pop\u00fclasyon varyans\u0131n\u0131n [&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-244","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>\u25b7Varyans i\u00e7in g\u00fcven aral\u0131\u011f\u0131<\/title>\n<meta name=\"description\" content=\"Burada varyans\u0131n g\u00fcven aral\u0131\u011f\u0131n\u0131n ne oldu\u011funu, nas\u0131l hesapland\u0131\u011f\u0131n\u0131 (form\u00fcl) ve ad\u0131m ad\u0131m \u00e7\u00f6z\u00fclm\u00fc\u015f bir al\u0131\u015ft\u0131rmay\u0131 bulacaks\u0131n\u0131z.\" \/>\n<meta name=\"robots\" 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