{"id":1652,"date":"2023-07-25T12:33:47","date_gmt":"2023-07-25T12:33:47","guid":{"rendered":"https:\/\/statorials.org\/tr\/normal-dagilim-ve-standart-normal-dagilim\/"},"modified":"2023-07-25T12:33:47","modified_gmt":"2023-07-25T12:33:47","slug":"normal-dagilim-ve-standart-normal-dagilim","status":"publish","type":"post","link":"https:\/\/statorials.org\/tr\/normal-dagilim-ve-standart-normal-dagilim\/","title":{"rendered":"Normal da\u011f\u0131l\u0131m ve standart normal da\u011f\u0131l\u0131m: fark"},"content":{"rendered":"<p><\/p>\n<hr>\n<p><span style=\"color: #000000;\">Normal da\u011f\u0131l\u0131m istatistikte en s\u0131k kullan\u0131lan olas\u0131l\u0131k da\u011f\u0131l\u0131m\u0131d\u0131r.<\/span><\/p>\n<p> <span style=\"color: #000000;\">A\u015fa\u011f\u0131daki \u00f6zelliklere sahiptir:<\/span><\/p>\n<ul>\n<li> <span style=\"color: #000000;\"><a href=\"https:\/\/statorials.org\/tr\/simetrik-dagilim-1\/\" target=\"_blank\" rel=\"noopener\">Simetrik<\/a><\/span><\/li>\n<li> <span style=\"color: #000000;\">\u00c7an \u015feklinde<\/span><\/li>\n<li> <span style=\"color: #000000;\">Ortalama ve medyan e\u015fittir; her ikisi de da\u011f\u0131t\u0131m\u0131n merkezinde yer al\u0131r<\/span><\/li>\n<\/ul>\n<p> <span style=\"color: #000000;\">Normal da\u011f\u0131l\u0131m\u0131n ortalamas\u0131 yerini, standart sapmas\u0131 ise yay\u0131lmas\u0131n\u0131 belirler.<\/span><\/p>\n<p> <span style=\"color: #000000;\">\u00d6rne\u011fin, a\u015fa\u011f\u0131daki grafik farkl\u0131 ortalamalara ve standart sapmalara sahip \u00fc\u00e7 normal da\u011f\u0131l\u0131m\u0131 g\u00f6stermektedir:<\/span> <\/p>\n<p><img decoding=\"async\" loading=\"lazy\" class=\" wp-image-16281 aligncenter\" src=\"https:\/\/statorials.org\/wp-content\/uploads\/2023\/08\/standardnorme2-1.png\" alt=\"\" width=\"518\" height=\"394\" srcset=\"\" sizes=\"auto, \"><\/p>\n<p> <span style=\"color: #000000;\"><strong>Standart normal da\u011f\u0131l\u0131m, ortalaman\u0131n 0 ve standart sapman\u0131n 1 oldu\u011fu \u00f6zel bir normal da\u011f\u0131l\u0131m t\u00fcr\u00fcd\u00fcr.<\/strong><\/span><\/p>\n<p> <span style=\"color: #000000;\">A\u015fa\u011f\u0131daki grafik standart normal da\u011f\u0131l\u0131m\u0131 g\u00f6stermektedir:<\/span> <\/p>\n<p><img decoding=\"async\" loading=\"lazy\" class=\"aligncenter wp-image-16282\" src=\"https:\/\/statorials.org\/wp-content\/uploads\/2023\/08\/standardnorme3.png\" alt=\"Standart Normal Da\u011f\u0131l\u0131m \u00d6rne\u011fi\" width=\"505\" height=\"375\" srcset=\"\" sizes=\"auto, \"><\/p>\n<h3> <span style=\"color: #000000;\"><strong>Normal da\u011f\u0131l\u0131m standart normal da\u011f\u0131l\u0131ma nas\u0131l d\u00f6n\u00fc\u015ft\u00fcr\u00fcl\u00fcr?<\/strong><\/span><\/h3>\n<p> <span style=\"color: #000000;\">Herhangi bir normal da\u011f\u0131l\u0131m, a\u015fa\u011f\u0131daki form\u00fcl kullan\u0131larak veri de\u011ferleri z-puanlar\u0131na d\u00f6n\u00fc\u015ft\u00fcr\u00fclerek standart normal da\u011f\u0131l\u0131ma d\u00f6n\u00fc\u015ft\u00fcr\u00fclebilir:<\/span><\/p>\n<p> <span style=\"color: #000000;\"><strong>z = (x \u2013 \u03bc) \/ \u03c3<\/strong><\/span><\/p>\n<p> <span style=\"color: #000000;\">Alt\u0131n:<\/span><\/p>\n<ul>\n<li> <span style=\"color: #000000;\"><strong>x:<\/strong> bireysel verilerin de\u011feri<\/span><\/li>\n<li> <span style=\"color: #000000;\"><strong>\u03bc:<\/strong> Da\u011f\u0131l\u0131m\u0131n ortalamas\u0131<\/span><\/li>\n<li> <span style=\"color: #000000;\"><strong>\u03c3:<\/strong> Da\u011f\u0131l\u0131m\u0131n standart sapmas\u0131<\/span><\/li>\n<\/ul>\n<p> <span style=\"color: #000000;\">\u00d6rne\u011fin, ortalamas\u0131 6 ve standart sapmas\u0131 2,152 olan a\u015fa\u011f\u0131daki veri setine sahip oldu\u011fumuzu varsayal\u0131m:<\/span> <\/p>\n<p><img decoding=\"async\" loading=\"lazy\" class=\" wp-image-16284 aligncenter\" src=\"https:\/\/statorials.org\/wp-content\/uploads\/2023\/08\/standardnorme4.png\" alt=\"\" width=\"96\" height=\"438\" srcset=\"\" sizes=\"auto, \"><\/p>\n<p> <span style=\"color: #000000;\">Her bir veri de\u011ferini, her de\u011ferden 6 \u00e7\u0131kar\u0131p 2,152&#8217;ye b\u00f6lerek z puan\u0131na d\u00f6n\u00fc\u015ft\u00fcrebiliriz:<\/span> <\/p>\n<p><img decoding=\"async\" loading=\"lazy\" class=\"aligncenter wp-image-16283\" src=\"https:\/\/statorials.org\/wp-content\/uploads\/2023\/08\/standardnorme5.png\" alt=\"Normal da\u011f\u0131l\u0131m\u0131 standart normal da\u011f\u0131l\u0131ma d\u00f6n\u00fc\u015ft\u00fcrme\" width=\"184\" height=\"454\" srcset=\"\" sizes=\"auto, \"><\/p>\n<p> <span style=\"color: #000000;\"><strong>Z-puan\u0131<\/strong> bize her veri noktas\u0131n\u0131n ortalamadan ka\u00e7 standart sapma oldu\u011funu s\u00f6yler. \u00d6rne\u011fin ilk veri de\u011feri &#8220;3&#8221; ortalaman\u0131n 1,39 standart sapma alt\u0131ndad\u0131r.<\/span><\/p>\n<p> <span style=\"color: #000000;\">Bu puan da\u011f\u0131l\u0131m\u0131n\u0131n ortalamas\u0131n\u0131n ortalamas\u0131 s\u0131f\u0131r, standart sapmas\u0131 ise birdir.<\/span><\/p>\n<h3> <span style=\"color: #000000;\"><strong>Standart normal da\u011f\u0131l\u0131m nas\u0131l kullan\u0131l\u0131r?<\/strong><\/span><\/h3>\n<p> <span style=\"color: #000000;\">Standart bir normal da\u011f\u0131l\u0131m a\u015fa\u011f\u0131daki \u00f6zelliklere sahiptir:<\/span><\/p>\n<ul>\n<li> <span style=\"color: #000000;\">Verilerin yakla\u015f\u0131k %68&#8217;i ortalaman\u0131n bir standart sapmas\u0131 dahilindedir<\/span><\/li>\n<li> <span style=\"color: #000000;\">Verilerin yakla\u015f\u0131k %95&#8217;i ortalaman\u0131n iki standart sapmas\u0131 dahilindedir.<\/span><\/li>\n<li> <span style=\"color: #000000;\">Verilerin yakla\u015f\u0131k %99,7&#8217;si ortalaman\u0131n \u00fc\u00e7 standart sapmas\u0131 dahilindedir.<\/span> <\/li>\n<\/ul>\n<p><img decoding=\"async\" loading=\"lazy\" class=\" wp-image-952 aligncenter\" src=\"https:\/\/statorials.org\/wp-content\/uploads\/2023\/08\/liste_normale.png\" alt=\"\" width=\"651\" height=\"275\" srcset=\"\" sizes=\"auto, \"><\/p>\n<p> <span style=\"color: #000000;\">Bu, <strong>genel kural<\/strong> olarak bilinir ve bir veri k\u00fcmesindeki de\u011ferlerin da\u011f\u0131l\u0131m\u0131n\u0131 anlamak i\u00e7in kullan\u0131l\u0131r.<\/span><\/p>\n<p> <span style=\"color: #000000;\">\u00d6rne\u011fin, belirli bir bah\u00e7edeki bitkilerin y\u00fcksekli\u011finin ortalama 47,4 in\u00e7 ve standart sapman\u0131n 2,4 in\u00e7 olacak \u015fekilde normal da\u011f\u0131ld\u0131\u011f\u0131n\u0131 varsayal\u0131m.<\/span><\/p>\n<p> <span style=\"color: #000000;\"><em>Temel kurala g\u00f6re bitkilerin y\u00fczde ka\u00e7\u0131 54,6 in\u00e7ten k\u0131sad\u0131r?<\/em><\/span><\/p>\n<p> <span style=\"color: #000000;\">Temel kural, normal da\u011f\u0131l\u0131ma sahip belirli bir veri seti i\u00e7in veri de\u011ferlerinin %99,7&#8217;sinin ortalaman\u0131n \u00fc\u00e7 standart sapmas\u0131 dahilinde oldu\u011funu belirtir. Bu, de\u011ferlerin %49,85&#8217;inin ortalama ile ortalaman\u0131n \u00fczerindeki \u00fc\u00e7 standart sapma aras\u0131nda oldu\u011fu anlam\u0131na gelir.<\/span><\/p>\n<p> <span style=\"color: #000000;\">Bu \u00f6rnekte 54,6, ortalaman\u0131n \u00fc\u00e7 standart sapma \u00fczerindedir. Normal da\u011f\u0131l\u0131mda veri de\u011ferlerinin %50&#8217;sinin ortalamadan k\u00fc\u00e7\u00fck oldu\u011funu bildi\u011fimiz i\u00e7in %50 + %49,85 = %99,85 de\u011ferlerinin toplam\u0131 54,6&#8217;dan k\u00fc\u00e7\u00fckt\u00fcr.<\/span><\/p>\n<p> <span style=\"color: #000000;\">Yani bitkilerin <strong>%99,85&#8217;inin<\/strong> boyu 54,6 in\u00e7ten k\u0131sad\u0131r.<\/span><\/p>\n<h3> <span style=\"color: #000000;\"><strong>Ek kaynaklar<\/strong><\/span><\/h3>\n<p><a href=\"https:\/\/statorials.org\/tr\/pratik-kural-ampirik-problemler\/\" target=\"_blank\" rel=\"noopener\">Temel kurallar\u0131 uygulamada sorunlar<\/a><br \/> <a href=\"https:\/\/statorials.org\/tr\/basparmak-kurallari-hesaplayicisi\/\" target=\"_blank\" rel=\"noopener\">Ba\u015fparmak Hesaplay\u0131c\u0131 Kurallar\u0131<\/a><br \/> <a href=\"https:\/\/statorials.org\/tr\/excelin-temel-kurali\/\" target=\"_blank\" rel=\"noopener\">Excel&#8217;de temel kural nas\u0131l uygulan\u0131r?<\/a><\/p>\n","protected":false},"excerpt":{"rendered":"<p>Normal da\u011f\u0131l\u0131m istatistikte en s\u0131k kullan\u0131lan olas\u0131l\u0131k da\u011f\u0131l\u0131m\u0131d\u0131r. A\u015fa\u011f\u0131daki \u00f6zelliklere sahiptir: Simetrik \u00c7an \u015feklinde Ortalama ve medyan e\u015fittir; her ikisi de da\u011f\u0131t\u0131m\u0131n merkezinde yer al\u0131r Normal da\u011f\u0131l\u0131m\u0131n ortalamas\u0131 yerini, standart sapmas\u0131 ise yay\u0131lmas\u0131n\u0131 belirler. \u00d6rne\u011fin, a\u015fa\u011f\u0131daki grafik farkl\u0131 ortalamalara ve standart sapmalara sahip \u00fc\u00e7 normal da\u011f\u0131l\u0131m\u0131 g\u00f6stermektedir: Standart normal da\u011f\u0131l\u0131m, ortalaman\u0131n 0 ve standart sapman\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":[11],"tags":[],"class_list":["post-1652","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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