{"id":567,"date":"2023-07-29T11:50:27","date_gmt":"2023-07-29T11:50:27","guid":{"rendered":"https:\/\/statorials.org\/tr\/ceyrekler-arasi-aykiri-degerler\/"},"modified":"2023-07-29T11:50:27","modified_gmt":"2023-07-29T11:50:27","slug":"ceyrekler-arasi-aykiri-degerler","status":"publish","type":"post","link":"https:\/\/statorials.org\/tr\/ceyrekler-arasi-aykiri-degerler\/","title":{"rendered":"\u00c7eyrekler aras\u0131 aral\u0131k (iqr) ayk\u0131r\u0131 de\u011ferlerden etkileniyor mu?"},"content":{"rendered":"<p><\/p>\n<hr>\n<p><span style=\"color: #000000;\">\u0130statistikte genellikle de\u011ferlerin bir da\u011f\u0131l\u0131mda ne kadar geni\u015f bir alana yay\u0131ld\u0131\u011f\u0131n\u0131 bilmek isteriz.<\/span><\/p>\n<p> <span style=\"color: #000000;\">Yay\u0131l\u0131m\u0131 \u00f6l\u00e7menin pop\u00fcler bir yolu, bir veri k\u00fcmesinin ilk d\u00f6rtte biri ile \u00fc\u00e7\u00fcnc\u00fc d\u00f6rtte biri aras\u0131ndaki fark olarak hesaplanan <strong>\u00e7eyrekler aras\u0131 aral\u0131kt\u0131r<\/strong> . \u00c7eyrekler basit\u00e7e bir veri k\u00fcmesini d\u00f6rt e\u015fit par\u00e7aya b\u00f6len de\u011ferlerdir.<\/span><\/p>\n<h2> <span style=\"color: #000000;\"><strong>\u00d6rnek: \u00c7eyrekler aras\u0131 aral\u0131\u011f\u0131n hesaplanmas\u0131<\/strong><\/span><\/h2>\n<p> <span style=\"color: #000000;\">A\u015fa\u011f\u0131daki \u00f6rnek, belirli bir veri k\u00fcmesi i\u00e7in \u00e7eyrekler aras\u0131 aral\u0131\u011f\u0131n nas\u0131l hesaplanaca\u011f\u0131n\u0131 g\u00f6sterir:<\/span> <\/p>\n<p><img decoding=\"async\" loading=\"lazy\" class=\"aligncenter wp-image-534 size-full\" src=\"https:\/\/statorials.org\/wp-content\/uploads\/2023\/08\/examen_scores1.jpg\" sizes=\"auto, \" srcset=\"\" alt=\"Bir veri setinin varyans\u0131 ve standart sapmas\u0131\" width=\"148\" height=\"450\"><\/p>\n<p> <span style=\"color: #000000;\"><strong>Ad\u0131m 1: De\u011ferleri en k\u00fc\u00e7\u00fckten en b\u00fcy\u00fc\u011fe do\u011fru s\u0131ralay\u0131n.<\/strong><\/span><\/p>\n<p> <span style=\"color: #000000;\">58, 66, 71, 73, 74, 77, 78, 82, 84, 85, 88, 88, 88, 90, 90, 92, 92, 94, 96, 98<\/span><\/p>\n<p> <span style=\"color: #000000;\"><strong>2. Ortancay\u0131 bulun.<\/strong><\/span><\/p>\n<p> <span style=\"color: #000000;\">58, 66, 71, 73, 74, <strong>77<\/strong> <strong>,<\/strong> 78, 82, 84, 85, 88, 88, 88, 90, 90, 92, 92, 94, 96, 98<\/span><\/p>\n<p> <span style=\"color: #000000;\">Bu durumda medyan 85 ile 88 aras\u0131ndad\u0131r.<\/span><\/p>\n<p> <span style=\"color: #000000;\"><strong>3. Medyan veri setini ikiye b\u00f6ler. Alt yar\u0131n\u0131n medyan\u0131 alt \u00e7eyrektir ve \u00fcst yar\u0131n\u0131n medyan\u0131 \u00fcst \u00e7eyrektir:<\/strong><\/span><\/p>\n<p> <span style=\"color: #ff0000;\">58, 66, 71, 73, <strong>74<\/strong> , 77, 78, 82, 84, 85, 88, 88, 88, 90, 90, 92, 92, 94, 96,<\/span> <span style=\"color: #000080;\"><strong>98<\/strong><\/span><\/p>\n<p> <span style=\"color: #000000;\"><strong>4. \u00c7eyrekler aras\u0131 aral\u0131\u011f\u0131 hesaplay\u0131n.<\/strong><\/span><\/p>\n<p> <span style=\"color: #000000;\">Bu durumda ilk \u00e7eyrek, veri setinin alt yar\u0131s\u0131ndaki ortadaki iki de\u011ferin ortalamas\u0131d\u0131r (75,5), \u00fc\u00e7\u00fcnc\u00fc \u00e7eyrek ise set verilerinin \u00fcst yar\u0131s\u0131ndaki orta iki de\u011ferin ortalamas\u0131d\u0131r (91).<\/span><\/p>\n<p> <span style=\"color: #000000;\">Yani \u00e7eyrekler aras\u0131 aral\u0131k 91 \u2013 75,5 = <strong>15,5<\/strong><\/span><\/p>\n<h2> <span style=\"color: #000000;\"><strong>\u00c7eyrekler aras\u0131 aral\u0131k ayk\u0131r\u0131 de\u011ferlerden etkilenmez<\/strong><\/span><\/h2>\n<p> <span style=\"color: #000000;\">\u0130nsanlar\u0131n bir veri k\u00fcmesinin &#8220;yay\u0131l\u0131m\u0131n\u0131&#8221; hesaplarken \u00e7eyrekler aras\u0131 aral\u0131\u011f\u0131 (IQR) kullanmay\u0131 tercih etmelerinin nedenlerinden biri, bunun ayk\u0131r\u0131 de\u011ferlere kar\u015f\u0131 dayan\u0131kl\u0131 olmas\u0131d\u0131r. IQR, veri de\u011ferlerinin ortadaki %50&#8217;lik aral\u0131\u011f\u0131 oldu\u011fundan <a href=\"https:\/\/statorials.org\/tr\/aykiri-degerler-ortalamayi-nasil-etkiler\/\" target=\"_blank\" rel=\"noopener\">a\u015f\u0131r\u0131 u\u00e7<\/a> de\u011ferlerden etkilenmez.<\/span><\/p>\n<p> <span style=\"color: #000000;\">Bunu g\u00f6stermek i\u00e7in a\u015fa\u011f\u0131daki veri k\u00fcmesini g\u00f6z \u00f6n\u00fcnde bulundurun:<\/span><\/p>\n<p style=\"text-align: center;\"> <span style=\"color: #000000;\">[1, 4, 8, 11, 13, 17, 17, 20]<\/span><\/p>\n<p> <span style=\"color: #000000;\">Bu veri k\u00fcmesi i\u00e7in farkl\u0131 yay\u0131lma \u00f6l\u00e7\u00fcmleri \u015funlard\u0131r:<\/span><\/p>\n<ul>\n<li> <span style=\"color: #000000;\">\u00c7eyrekler aras\u0131 aral\u0131k: 11<\/span><\/li>\n<li> <span style=\"color: #000000;\">Aral\u0131k: 19<\/span><\/li>\n<li> <span style=\"color: #000000;\">Standart sapma: 6,26<\/span><\/li>\n<li> <span style=\"color: #000000;\">Fark: 39.23<\/span><\/li>\n<\/ul>\n<p> <span style=\"color: #000000;\">\u015eimdi ayn\u0131 veri setini d\u00fc\u015f\u00fcn\u00fcn, ancak a\u015f\u0131r\u0131 u\u00e7 de\u011ferler eklenmi\u015f olarak:<\/span><\/p>\n<p style=\"text-align: center;\"> <span style=\"color: #000000;\">[1, 4, 8, 11, 13, 17, 17, 20, <strong>150<\/strong> ]<\/span><\/p>\n<p> <span style=\"color: #000000;\">Bu veri k\u00fcmesi i\u00e7in farkl\u0131 yay\u0131lma \u00f6l\u00e7\u00fcmleri \u015funlard\u0131r:<\/span><\/p>\n<ul>\n<li> <span style=\"color: #000000;\">\u00c7eyrekler aras\u0131 aral\u0131k: 12,5<\/span><\/li>\n<li> <span style=\"color: #000000;\">Aral\u0131k: 149<\/span><\/li>\n<li> <span style=\"color: #000000;\">Standart sapma: 43,96<\/span><\/li>\n<li> <span style=\"color: #000000;\">Fark: 1.932,84<\/span><\/li>\n<\/ul>\n<p> <span style=\"color: #000000;\">\u00c7eyrekler aras\u0131 aral\u0131\u011f\u0131n 11&#8217;den 12,5&#8217;e kadar \u00e7ok az de\u011fi\u015fti\u011fine dikkat edin. Bununla birlikte, di\u011fer t\u00fcm da\u011f\u0131l\u0131m \u00f6l\u00e7\u00fcleri \u00f6nemli \u00f6l\u00e7\u00fcde de\u011fi\u015fir.<\/span><\/p>\n<p> <span style=\"color: #000000;\">Bu, \u00e7eyrekler aras\u0131 aral\u0131\u011f\u0131n di\u011fer da\u011f\u0131l\u0131m \u00f6l\u00e7\u00fcleri gibi ayk\u0131r\u0131 de\u011ferlerden etkilenmedi\u011fini g\u00f6stermektedir. Bu nedenle herhangi bir da\u011f\u0131l\u0131mda de\u011ferlerin ortadaki %50&#8217;lik da\u011f\u0131l\u0131m\u0131n\u0131 \u00f6l\u00e7menin g\u00fcvenilir bir yoludur.<\/span><\/p>\n<p> <span style=\"color: #000000;\"><strong>Daha fazla okuma:<\/strong><\/span><\/p>\n<p> <span style=\"color: #000000;\">Da\u011f\u0131l\u0131m \u00f6l\u00e7\u00fcmleri<br \/> \u00c7eyrekler Aras\u0131 Aral\u0131k Hesaplay\u0131c\u0131<br \/><\/span><\/p>\n","protected":false},"excerpt":{"rendered":"<p>\u0130statistikte genellikle de\u011ferlerin bir da\u011f\u0131l\u0131mda ne kadar geni\u015f bir alana yay\u0131ld\u0131\u011f\u0131n\u0131 bilmek isteriz. Yay\u0131l\u0131m\u0131 \u00f6l\u00e7menin pop\u00fcler bir yolu, bir veri k\u00fcmesinin ilk d\u00f6rtte biri ile \u00fc\u00e7\u00fcnc\u00fc d\u00f6rtte biri aras\u0131ndaki fark olarak hesaplanan \u00e7eyrekler aras\u0131 aral\u0131kt\u0131r . \u00c7eyrekler basit\u00e7e bir veri k\u00fcmesini d\u00f6rt e\u015fit par\u00e7aya b\u00f6len de\u011ferlerdir. \u00d6rnek: \u00c7eyrekler aras\u0131 aral\u0131\u011f\u0131n hesaplanmas\u0131 A\u015fa\u011f\u0131daki \u00f6rnek, belirli bir [&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-567","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>\u00c7eyrekler aras\u0131 aral\u0131k (IQR) ayk\u0131r\u0131 de\u011ferlerden etkileniyor mu? 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