{"id":1697,"date":"2023-07-25T08:30:35","date_gmt":"2023-07-25T08:30:35","guid":{"rendered":"https:\/\/statorials.org\/tr\/medyan-icin-guven-araligi\/"},"modified":"2023-07-25T08:30:35","modified_gmt":"2023-07-25T08:30:35","slug":"medyan-icin-guven-araligi","status":"publish","type":"post","link":"https:\/\/statorials.org\/tr\/medyan-icin-guven-araligi\/","title":{"rendered":"Medyan i\u0307\u00e7in g\u00fcven aral\u0131\u011f\u0131 nas\u0131l bulunur (ad\u0131m ad\u0131m)"},"content":{"rendered":"<p><\/p>\n<hr>\n<p><span style=\"color: #000000;\">N\u00fcfus medyan\u0131 i\u00e7in <a href=\"https:\/\/statorials.org\/tr\/guvenilirlik-araligi\/\" target=\"_blank\" rel=\"noopener\">g\u00fcven aral\u0131\u011f\u0131n\u0131n<\/a> \u00fcst ve alt s\u0131n\u0131rlar\u0131n\u0131 hesaplamak i\u00e7in a\u015fa\u011f\u0131daki form\u00fcl\u00fc kullanabiliriz:<\/span><\/p>\n<p> <strong>j:<\/strong> <span style=\"color: #000000;\">nq \u2013 z\u221a <span style=\"border-top: 1px solid black;\">nq(1-q)<\/span><\/span><\/p>\n<p> <strong>k:<\/strong> <span style=\"color: #000000;\">nq + z\u221a <span style=\"border-top: 1px solid black;\">nq(1-q)<\/span><\/span><\/p>\n<p> <span style=\"color: #000000;\">Alt\u0131n:<\/span><\/p>\n<ul>\n<li> <span style=\"color: #000000;\"><strong>n:<\/strong> \u00d6rneklem b\u00fcy\u00fckl\u00fc\u011f\u00fc<\/span><\/li>\n<li> <span style=\"color: #000000;\"><strong>q:<\/strong> \u0130lginin niceli\u011fi. Medyan i\u00e7in q = 0,5&#8217;i kullanaca\u011f\u0131z.<\/span><\/li>\n<li> <span style=\"color: #000000;\"><strong>z:<\/strong> z-kritik de\u011feri<\/span><\/li>\n<\/ul>\n<p> <span style=\"color: #000000;\">j ve k&#8217;yi bir sonraki tamsay\u0131ya yuvarl\u0131yoruz. Ortaya \u00e7\u0131kan g\u00fcven aral\u0131\u011f\u0131, s\u0131ral\u0131 \u00f6rnek verilerdeki <sup>j&#8217;inci<\/sup> ve <sup>k&#8217;inci<\/sup> g\u00f6zlemler aras\u0131nda yer al\u0131r.<\/span><\/p>\n<p> <span style=\"color: #000000;\">Kulland\u0131\u011f\u0131n\u0131z z de\u011ferinin se\u00e7ti\u011finiz g\u00fcven d\u00fczeyine ba\u011fl\u0131 oldu\u011funu unutmay\u0131n. A\u015fa\u011f\u0131daki tabloda en yayg\u0131n g\u00fcven d\u00fczeyi se\u00e7eneklerine kar\u015f\u0131l\u0131k gelen z de\u011feri g\u00f6sterilmektedir:<\/span><\/p>\n<table>\n<tbody>\n<tr>\n<th style=\"text-align: center;\"> <span style=\"color: #000000;\"><strong>Bir g\u00fcven d\u00fczeyi<\/strong><\/span><\/th>\n<th style=\"text-align: center;\"> <span style=\"color: #000000;\"><strong>z de\u011feri<\/strong><\/span><\/th>\n<\/tr>\n<tr>\n<td style=\"text-align: center;\"> <span style=\"color: #000000;\">0,90<\/span><\/td>\n<td style=\"text-align: center;\"> <span style=\"color: #000000;\">1.645<\/span><\/td>\n<\/tr>\n<tr>\n<td style=\"text-align: center;\"> <span style=\"color: #000000;\">0,95<\/span><\/td>\n<td style=\"text-align: center;\"> <span style=\"color: #000000;\">1.96<\/span><\/td>\n<\/tr>\n<tr>\n<td style=\"text-align: center;\"> <span style=\"color: #000000;\">0,99<\/span><\/td>\n<td style=\"text-align: center;\"> <span style=\"color: #000000;\">2.58<\/span><\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<p> <span style=\"color: #000000;\"><strong>Kaynak:<\/strong> Bu form\u00fcl <em><a href=\"https:\/\/www.wiley.com\/en-us\/Practical+Nonparametric+Statistics%2C+3rd+Edition-p-9780471160687\" target=\"_blank\" rel=\"noopener\">, WJ Conover&#8217;\u0131n Practical Nonparametrik \u0130statistikleri&#8217;nin 3. bask\u0131s\u0131ndan<\/a> al\u0131nm\u0131\u015ft\u0131r.<\/em><\/span><\/p>\n<p> <span style=\"color: #000000;\">A\u015fa\u011f\u0131daki ad\u0131m ad\u0131m \u00f6rnek, a\u015fa\u011f\u0131daki 15 de\u011ferli \u00f6rnek verileri kullanarak bir pop\u00fclasyon medyan\u0131 i\u00e7in g\u00fcven aral\u0131\u011f\u0131n\u0131n nas\u0131l hesaplanaca\u011f\u0131n\u0131 g\u00f6sterir:<\/span><\/p>\n<p> <span style=\"color: #000000;\"><strong>\u00d6rnek veriler:<\/strong> 8, 11, 12, 13, 15, 17, 19, 20, 21, 21, 22, 23, 25, 26, 28<\/span><\/p>\n<h3> <span style=\"color: #000000;\"><strong>Ad\u0131m 1: Medyan\u0131 Bulun<\/strong><\/span><\/h3>\n<p> <span style=\"color: #000000;\">\u00d6ncelikle \u00f6rnek verilerin medyan\u0131n\u0131 bulmam\u0131z gerekiyor. Bu, <strong>20&#8217;nin<\/strong> ortalama de\u011feri olarak ortaya \u00e7\u0131k\u0131yor:<\/span><\/p>\n<p style=\"text-align: center;\"> <span style=\"color: #000000;\">8, 11, 12, 13, 15, 17, 19, 20, 21, <span style=\"color: #ff0000;\"><strong>21<\/strong><\/span> , 22, 23, 25, 26, 28<\/span><\/p>\n<h3> <span style=\"color: #000000;\"><strong>Ad\u0131m 2: <em>j<\/em> ve <em>k&#8217;yi<\/em> bulun<\/strong><\/span><\/h3>\n<p> <span style=\"color: #000000;\">Medyan pop\u00fclasyon i\u00e7in %95&#8217;lik bir g\u00fcven aral\u0131\u011f\u0131 bulmak istedi\u011fimizi varsayal\u0131m. Bunu yapmak i\u00e7in \u00f6nce <em>j<\/em> ve <em>k&#8217;yi<\/em> bulmam\u0131z gerekiyor:<\/span><\/p>\n<ul>\n<li> <span style=\"color: #000000;\"><strong>j:<\/strong> nq \u2013 z\u221a <span style=\"border-top: 1px solid black;\">nq(1-q)<\/span> = (15)(.5) \u2013 1.96\u221a <span style=\"border-top: 1px solid black;\">(15)(.5)(1-.5)<\/span> = 3.7<\/span><\/li>\n<li> <span style=\"color: #000000;\"><strong>k:<\/strong> nq + z\u221a <span style=\"border-top: 1px solid black;\">nq(1-q)<\/span> = (15)(.5) + 1.96\u221a <span style=\"border-top: 1px solid black;\">(15)(.5)(1-.5)<\/span> = 11.3<\/span><\/li>\n<\/ul>\n<p> <span style=\"color: #000000;\"><em>j<\/em> ve <em>k&#8217;yi<\/em> en yak\u0131n tam say\u0131ya yuvarlayaca\u011f\u0131z:<\/span><\/p>\n<ul>\n<li> <span style=\"color: #000000;\"><strong>g\u00fcn:<\/strong> 4<\/span><\/li>\n<li> <span style=\"color: #000000;\"><strong>k:<\/strong> 12<\/span><\/li>\n<\/ul>\n<h3> <span style=\"color: #000000;\"><strong>Ad\u0131m 3: G\u00fcven Aral\u0131\u011f\u0131n\u0131 Bulun<\/strong><\/span><\/h3>\n<p> <span style=\"color: #000000;\">Medyan i\u00e7in %95 g\u00fcven aral\u0131\u011f\u0131, veri \u00f6rne\u011findeki j = <sup>4.<\/sup> ve k = <sup>12.<\/sup> g\u00f6zlemler aras\u0131nda olacakt\u0131r.<\/span><\/p>\n<p> <span style=\"color: #000000;\"><sup>4.<\/sup> g\u00f6zlem 13&#8217;e, <sup>12.<\/sup> g\u00f6zlem ise 23&#8217;e e\u015fittir:<\/span><\/p>\n<p style=\"text-align: center;\"> <span style=\"color: #000000;\">8, 11, 12, <span style=\"color: #ff0000;\"><strong>13<\/strong><\/span> , 15, 17, 19, 20, 21, 21, 22, <span style=\"color: #ff0000;\"><strong>23<\/strong><\/span> , 25, 26, 28<\/span><\/p>\n<p> <span style=\"color: #000000;\">B\u00f6ylece medyan i\u00e7in %95 g\u00fcven aral\u0131\u011f\u0131 \u015fu \u015fekilde ortaya \u00e7\u0131kar <strong>: [13, 23]<\/strong> .<\/span><\/p>\n<h3> <span style=\"color: #000000;\"><strong>Ek kaynaklar<\/strong><\/span><\/h3>\n<p> <a href=\"https:\/\/statorials.org\/tr\/guven-araligi-orani\/\" target=\"_blank\" rel=\"noopener\">Bir orant\u0131 i\u00e7in g\u00fcven aral\u0131\u011f\u0131 nas\u0131l bulunur?<\/a><br \/> <a href=\"https:\/\/statorials.org\/tr\/ortalama-guven-araligi\/\" target=\"_blank\" rel=\"noopener\">Bir ortalama i\u00e7in g\u00fcven aral\u0131\u011f\u0131 nas\u0131l bulunur?<\/a><br \/> <a href=\"https:\/\/statorials.org\/tr\/guven-araligi-standart-sapmasi\/\" target=\"_blank\" rel=\"noopener\">Standart sapma i\u00e7in g\u00fcven aral\u0131\u011f\u0131 nas\u0131l bulunur?<\/a><\/p>\n","protected":false},"excerpt":{"rendered":"<p>N\u00fcfus medyan\u0131 i\u00e7in g\u00fcven aral\u0131\u011f\u0131n\u0131n \u00fcst ve alt s\u0131n\u0131rlar\u0131n\u0131 hesaplamak i\u00e7in a\u015fa\u011f\u0131daki form\u00fcl\u00fc kullanabiliriz: j: nq \u2013 z\u221a nq(1-q) k: nq + z\u221a nq(1-q) Alt\u0131n: n: \u00d6rneklem b\u00fcy\u00fckl\u00fc\u011f\u00fc q: \u0130lginin niceli\u011fi. Medyan i\u00e7in q = 0,5&#8217;i kullanaca\u011f\u0131z. z: z-kritik de\u011feri j ve k&#8217;yi bir sonraki tamsay\u0131ya yuvarl\u0131yoruz. Ortaya \u00e7\u0131kan g\u00fcven aral\u0131\u011f\u0131, s\u0131ral\u0131 \u00f6rnek verilerdeki j&#8217;inci [&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-1697","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>Medyan \u0130\u00e7in G\u00fcven Aral\u0131\u011f\u0131 Nas\u0131l Bulunur (Ad\u0131m Ad\u0131m)<\/title>\n<meta name=\"description\" content=\"Bu e\u011fitimde, ad\u0131m ad\u0131m bir \u00f6rnekle bir medyan i\u00e7in g\u00fcven aral\u0131\u011f\u0131n\u0131n nas\u0131l bulunaca\u011f\u0131 a\u00e7\u0131klanmaktad\u0131r.\" \/>\n<meta name=\"robots\" content=\"index, follow, max-snippet:-1, max-image-preview:large, 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