{"id":2776,"date":"2023-07-20T18:20:24","date_gmt":"2023-07-20T18:20:24","guid":{"rendered":"https:\/\/statorials.org\/tr\/gruplandirilmis-verilerin-medyani\/"},"modified":"2023-07-20T18:20:24","modified_gmt":"2023-07-20T18:20:24","slug":"gruplandirilmis-verilerin-medyani","status":"publish","type":"post","link":"https:\/\/statorials.org\/tr\/gruplandirilmis-verilerin-medyani\/","title":{"rendered":"Grupland\u0131r\u0131lm\u0131\u015f verilerin medyan\u0131 nas\u0131l bulunur: \u00f6rneklerle"},"content":{"rendered":"<p><\/p>\n<hr>\n<p><span style=\"color: #000000;\">\u00c7o\u011fu zaman bir \u015fekilde bir arada gruplanan verilerin medyan\u0131n\u0131 hesaplamak isteriz.<\/span><\/p>\n<p> <span style=\"color: #000000;\">T\u00fcm de\u011ferler en k\u00fc\u00e7\u00fckten en b\u00fcy\u00fc\u011fe s\u0131raland\u0131\u011f\u0131nda <a href=\"https:\/\/statorials.org\/tr\/medyanin-onemi\/\" target=\"_blank\" rel=\"noopener\">medyan\u0131n<\/a> , bir veri k\u00fcmesinin do\u011frudan ortas\u0131nda yer alan de\u011feri temsil etti\u011fini hat\u0131rlay\u0131n.<\/span><\/p>\n<p> <span style=\"color: #000000;\">\u00d6rne\u011fin, a\u015fa\u011f\u0131daki grupland\u0131r\u0131lm\u0131\u015f verilere sahip oldu\u011fumuzu varsayal\u0131m:<\/span> <\/p>\n<p><img decoding=\"async\" loading=\"lazy\" class=\"aligncenter wp-image-14462 \" src=\"https:\/\/statorials.org\/wp-content\/uploads\/2023\/08\/mean_sd_grouped1.png\" alt=\"\" width=\"211\" height=\"223\" srcset=\"\" sizes=\"auto, \"><\/p>\n<p> <span style=\"color: #000000;\">Ham <a href=\"https:\/\/statorials.org\/tr\/islenmemis-veri\/\" target=\"_blank\" rel=\"noopener\">veri de\u011ferlerini<\/a> bilmedi\u011fimiz i\u00e7in tam medyan\u0131 hesaplamak m\u00fcmk\u00fcn olmasa da a\u015fa\u011f\u0131daki form\u00fcl\u00fc kullanarak medyan\u0131 tahmin etmek m\u00fcmk\u00fcnd\u00fcr:<\/span><\/p>\n<p> <span style=\"color: #000000;\"><strong>Grupland\u0131r\u0131lm\u0131\u015f verilerin medyan\u0131 = L + W[(N\/2 \u2013 C) \/ F]<\/strong><\/span><\/p>\n<p> <span style=\"color: #000000;\">Alt\u0131n:<\/span><\/p>\n<ul>\n<li> <span style=\"color: #000000;\"><strong>L<\/strong> : Medyan s\u0131n\u0131f\u0131n alt s\u0131n\u0131r\u0131<\/span><\/li>\n<li> <span style=\"color: #000000;\"><strong>W<\/strong> : Medyan s\u0131n\u0131f geni\u015fli\u011fi<\/span><\/li>\n<li> <span style=\"color: #000000;\"><strong>N<\/strong> : Toplam frekans<\/span><\/li>\n<li> <span style=\"color: #000000;\"><b>C<\/b> : Medyan s\u0131n\u0131f\u0131na kadar k\u00fcm\u00fclatif frekans<\/span><\/li>\n<li> <span style=\"color: #000000;\"><strong>F<\/strong> : Medyan s\u0131n\u0131f frekans\u0131<\/span><\/li>\n<\/ul>\n<p> <span style=\"color: #000000;\"><strong>Not<\/strong> : <strong>Orta s\u0131n\u0131f,<\/strong> N\/2&#8217;de yer alan de\u011feri i\u00e7eren s\u0131n\u0131ft\u0131r. Yukar\u0131daki \u00f6rnekte N = 23 toplam de\u011fer vard\u0131r. Dolay\u0131s\u0131yla medyan de\u011feri 23\/2 = 11,5 konumunda olup 21-30 s\u0131n\u0131f\u0131ndad\u0131r.<\/span><\/p>\n<p> <span style=\"color: #000000;\">A\u015fa\u011f\u0131daki \u00f6rnekler, farkl\u0131 senaryolarda grupland\u0131r\u0131lm\u0131\u015f verilerin medyan\u0131n\u0131n nas\u0131l hesaplanaca\u011f\u0131n\u0131 g\u00f6sterir.<\/span><\/p>\n<h3> <span style=\"color: #000000;\"><strong>\u00d6rnek 1: Grupland\u0131r\u0131lm\u0131\u015f Verilerin Medyan\u0131n\u0131 Hesaplama<\/strong><\/span><\/h3>\n<p> <span style=\"color: #000000;\">Belirli bir s\u0131n\u0131ftaki 40 \u00f6\u011frencinin not verdi\u011fi s\u0131nav\u0131 g\u00f6steren a\u015fa\u011f\u0131daki frekans da\u011f\u0131l\u0131m\u0131na sahip oldu\u011fumuzu varsayal\u0131m:<\/span> <\/p>\n<p><img decoding=\"async\" loading=\"lazy\" class=\" wp-image-24369 aligncenter\" src=\"https:\/\/statorials.org\/wp-content\/uploads\/2023\/08\/modefreq1.jpg\" alt=\"\" width=\"247\" height=\"223\" srcset=\"\" sizes=\"auto, \"><\/p>\n<p> <span style=\"color: #000000;\">Bu \u00f6rnekte N = 40 toplam de\u011fer vard\u0131r. Yani medyan de\u011feri 40\/2=20\u2019nin bulundu\u011fu s\u0131n\u0131ftad\u0131r. 20. en b\u00fcy\u00fck de\u011fer <strong>71-80<\/strong> s\u0131n\u0131f\u0131nda olacakt\u0131r.<\/span><\/p>\n<p> <span style=\"color: #000000;\">Bunu bilerek a\u015fa\u011f\u0131daki de\u011ferleri hesaplayabiliriz:<\/span><\/p>\n<ul>\n<li> <span style=\"color: #000000;\"><strong>L<\/strong> : Alt orta s\u0131n\u0131f s\u0131n\u0131r\u0131: <strong>71<\/strong><\/span><\/li>\n<li> <span style=\"color: #000000;\"><strong>W<\/strong> : Medyan s\u0131n\u0131f geni\u015fli\u011fi: <strong>9<\/strong><\/span><\/li>\n<li> <span style=\"color: #000000;\"><strong>N<\/strong> : Toplam frekans: <strong>40<\/strong><\/span><\/li>\n<li> <span style=\"color: #000000;\"><b>C<\/b> : Medyan s\u0131n\u0131fa kadar k\u00fcm\u00fclatif frekans: <strong>12<\/strong><\/span><\/li>\n<li> <span style=\"color: #000000;\"><strong>F<\/strong> : Medyan s\u0131n\u0131f frekans\u0131: <strong>15<\/strong><\/span><\/li>\n<\/ul>\n<p> <span style=\"color: #000000;\">Da\u011f\u0131l\u0131m\u0131n medyan\u0131n\u0131 hesaplamak i\u00e7in bu de\u011ferleri form\u00fcle ekleyebiliriz:<\/span><\/p>\n<ul>\n<li> <span style=\"color: #000000;\">Medyan = L + W[(N\/2 \u2013 C) \/ F]<\/span><\/li>\n<li> <span style=\"color: #000000;\">Medyan = 71 + 9[(40\/2 \u2013 12) \/ 15]<\/span><\/li>\n<li> <span style=\"color: #000000;\">Medyan = <strong>75,8<\/strong><\/span><\/li>\n<\/ul>\n<p> <span style=\"color: #000000;\">Ortalama s\u0131nav puan\u0131n\u0131n <strong>75,8<\/strong> oldu\u011funu tahmin ediyoruz.<\/span><\/p>\n<h3> <span style=\"color: #000000;\"><strong>\u00d6rnek 2: Grupland\u0131r\u0131lm\u0131\u015f Verilerin Medyan\u0131n\u0131 Hesaplama<\/strong><\/span><\/h3>\n<p> <span style=\"color: #000000;\">60 basketbolcunun ma\u00e7 ba\u015f\u0131na att\u0131\u011f\u0131 say\u0131y\u0131 g\u00f6steren a\u015fa\u011f\u0131daki frekans da\u011f\u0131l\u0131m\u0131na sahip oldu\u011fumuzu varsayal\u0131m:<\/span> <\/p>\n<p><img decoding=\"async\" loading=\"lazy\" class=\" wp-image-24370 aligncenter\" src=\"https:\/\/statorials.org\/wp-content\/uploads\/2023\/08\/modefreq2.jpg\" alt=\"\" width=\"248\" height=\"219\" srcset=\"\" sizes=\"auto, \"><\/p>\n<p> <span style=\"color: #000000;\">Bu \u00f6rnekte N = 60 toplam de\u011fer vard\u0131r. Yani medyan de\u011feri 60\/2=30\u2019un yer ald\u0131\u011f\u0131 s\u0131n\u0131fta yer almaktad\u0131r. 30&#8217;uncu en b\u00fcy\u00fck de\u011fer <strong>11-20<\/strong> s\u0131n\u0131f\u0131nda olacakt\u0131r.<\/span><\/p>\n<p> <span style=\"color: #000000;\">Bunu bilerek a\u015fa\u011f\u0131daki de\u011ferleri hesaplayabiliriz:<\/span><\/p>\n<ul>\n<li> <span style=\"color: #000000;\"><strong>L<\/strong> : Alt orta s\u0131n\u0131f s\u0131n\u0131r\u0131: <strong>11<\/strong><\/span><\/li>\n<li> <span style=\"color: #000000;\"><strong>W<\/strong> : Medyan s\u0131n\u0131f geni\u015fli\u011fi: <strong>9<\/strong><\/span><\/li>\n<li> <span style=\"color: #000000;\"><strong>N<\/strong> : Toplam frekans: <strong>60<\/strong><\/span><\/li>\n<li> <span style=\"color: #000000;\"><b>C<\/b> : Medyan s\u0131n\u0131fa kadar k\u00fcm\u00fclatif frekans: <strong>8<\/strong><\/span><\/li>\n<li> <span style=\"color: #000000;\"><strong>F<\/strong> : Medyan s\u0131n\u0131f frekans\u0131: <strong>25<\/strong><\/span><\/li>\n<\/ul>\n<p> <span style=\"color: #000000;\">Da\u011f\u0131l\u0131m\u0131n medyan\u0131n\u0131 hesaplamak i\u00e7in bu de\u011ferleri form\u00fcle ekleyebiliriz:<\/span><\/p>\n<ul>\n<li> <span style=\"color: #000000;\">Medyan = L + W[(N\/2 \u2013 C) \/ F]<\/span><\/li>\n<li> <span style=\"color: #000000;\">Medyan = 11 + 9[(60\/2 \u2013 8) \/ 25]<\/span><\/li>\n<li> <span style=\"color: #000000;\">Medyan = <strong>18,92<\/strong><\/span><\/li>\n<\/ul>\n<p> <span style=\"color: #000000;\">Ortalama s\u0131nav puan\u0131n\u0131n <strong>18,92<\/strong> olaca\u011f\u0131n\u0131 tahmin ediyoruz.<\/span><\/p>\n<h3> <span style=\"color: #000000;\"><strong>Ek kaynaklar<\/strong><\/span><\/h3>\n<p> <span style=\"color: #000000;\">A\u015fa\u011f\u0131daki e\u011fitimlerde grupland\u0131r\u0131lm\u0131\u015f verilerle di\u011fer ortak i\u015flemlerin nas\u0131l ger\u00e7ekle\u015ftirilece\u011fi a\u00e7\u0131klanmaktad\u0131r:<\/span><\/p>\n<p> <a href=\"https:\/\/statorials.org\/tr\/ortalama-standart-sapma-havuzlanmis-veriler\/\" target=\"_blank\" rel=\"noopener\">Grupland\u0131r\u0131lm\u0131\u015f verilerin ortalamas\u0131n\u0131 ve standart sapmas\u0131n\u0131 bulma<\/a><br \/> <a href=\"https:\/\/statorials.org\/tr\/gruplandirilmis-veri-modu\/\" target=\"_blank\" rel=\"noopener\">Grupland\u0131r\u0131lm\u0131\u015f veri modunu bulma<\/a><br \/> <a href=\"https:\/\/statorials.org\/tr\/gruplandirilmis-veriler-icin-yuzdelik-siralama\/\" target=\"_blank\" rel=\"noopener\">Grupland\u0131r\u0131lm\u0131\u015f veriler i\u00e7in y\u00fczdelik s\u0131ralama nas\u0131l hesaplan\u0131r?<\/a><\/p>\n","protected":false},"excerpt":{"rendered":"<p>\u00c7o\u011fu zaman bir \u015fekilde bir arada gruplanan verilerin medyan\u0131n\u0131 hesaplamak isteriz. T\u00fcm de\u011ferler en k\u00fc\u00e7\u00fckten en b\u00fcy\u00fc\u011fe s\u0131raland\u0131\u011f\u0131nda medyan\u0131n , bir veri k\u00fcmesinin do\u011frudan ortas\u0131nda yer alan de\u011feri temsil etti\u011fini hat\u0131rlay\u0131n. \u00d6rne\u011fin, a\u015fa\u011f\u0131daki grupland\u0131r\u0131lm\u0131\u015f verilere sahip oldu\u011fumuzu varsayal\u0131m: Ham veri de\u011ferlerini bilmedi\u011fimiz i\u00e7in tam medyan\u0131 hesaplamak m\u00fcmk\u00fcn olmasa da a\u015fa\u011f\u0131daki form\u00fcl\u00fc kullanarak medyan\u0131 tahmin etmek [&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-2776","post","type-post","status-publish","format-standard","hentry","category-rehber"],"yoast_head":"<!-- This site is optimized with the Yoast SEO plugin v21.3 - 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