ortalama<\/strong> = (g\u00f6zlemlerin toplam\u0131) \/ (g\u00f6zlem say\u0131s\u0131)<\/span><\/p>\n \u00d6rne\u011fin a\u015fa\u011f\u0131daki veri setine sahip oldu\u011fumuzu varsayal\u0131m:<\/span><\/p>\n [1, 4, 5, 6, 7]<\/span><\/p>\n Veri k\u00fcmesinin ortalamas\u0131 (1+4+5+6+7) \/ (5) = 4,6<\/strong><\/span><\/p>\n Ancak ortalama yararl\u0131 ve hesaplanmas\u0131 kolay olmas\u0131na ra\u011fmen bir dezavantaj\u0131 vard\u0131r: Ayk\u0131r\u0131 de\u011ferlerden etkilenebilir<\/strong> . \u00d6zellikle, veri seti ne kadar k\u00fc\u00e7\u00fck olursa, ayk\u0131r\u0131 de\u011fer ortalamay\u0131 o kadar fazla etkileyebilir.<\/span><\/p>\n Bunu a\u00e7\u0131klamak i\u00e7in a\u015fa\u011f\u0131daki klasik \u00f6rne\u011fi d\u00fc\u015f\u00fcn\u00fcn:<\/span><\/p>\n On adam bir barda oturuyor. On erke\u011fin ortalama geliri 50.000 dolard\u0131r. Aniden bir adam d\u0131\u015far\u0131 \u00e7\u0131k\u0131yor ve Bill Gates i\u00e7eri giriyor. Bug\u00fcn bardaki on adam\u0131n ortalama geliri 40 milyon dolar.<\/span><\/p>\n<\/blockquote>\n Bu \u00f6rnek, bir ayk\u0131r\u0131 de\u011ferin (Bill Gates) ortalamay\u0131 nas\u0131l \u00f6nemli \u00f6l\u00e7\u00fcde etkileyebilece\u011fini g\u00f6stermektedir.<\/span><\/p>\n Bir ayk\u0131r\u0131 de\u011fer, al\u0131\u015f\u0131lmad\u0131k derecede k\u00fc\u00e7\u00fck veya al\u0131\u015f\u0131lmad\u0131k derecede b\u00fcy\u00fck olarak ortalamay\u0131 etkileyebilir. \u00d6nceki \u00f6rnekte Bill Gates’in al\u0131\u015f\u0131lmad\u0131k derecede y\u00fcksek bir geliri vard\u0131 ve bu da ortalamay\u0131 yan\u0131lt\u0131c\u0131 hale getiriyordu.<\/span><\/p>\n Ancak al\u0131\u015f\u0131lmad\u0131k derecede d\u00fc\u015f\u00fck bir de\u011fer de ortalamay\u0131 etkileyebilir. Bunu a\u00e7\u0131klamak i\u00e7in a\u015fa\u011f\u0131daki \u00f6rne\u011fi g\u00f6z \u00f6n\u00fcnde bulundurun:<\/span><\/p>\n On \u00f6\u011frenci s\u0131nava girer ve a\u015fa\u011f\u0131daki notlar\u0131 al\u0131r:<\/span><\/p>\n [0, 88, 90, 92, 94, 95, 95, 96, 97, 99]<\/span><\/p>\n Ortalama puan 84,6’d\u0131r<\/strong> .<\/span><\/p>\n Ancak veri setinden \u201c0\u201d puan\u0131n\u0131 \u00e7\u0131kar\u0131rsak ortalama puan 94<\/strong> olur.<\/span><\/p>\n<\/blockquote>\n Bir \u00f6\u011frencinin al\u0131\u015f\u0131lmad\u0131k derecede d\u00fc\u015f\u00fck puan\u0131, t\u00fcm veri setinin ortalamas\u0131n\u0131 d\u00fc\u015f\u00fcr\u00fcr.<\/span><\/p>\n Veri setinin \u00f6rneklem boyutu ne kadar k\u00fc\u00e7\u00fckse, ayk\u0131r\u0131 de\u011ferin ortalamay\u0131 etkileme olas\u0131l\u0131\u011f\u0131 da o kadar y\u00fcksektir.<\/span><\/p>\n \u00d6rne\u011fin, s\u0131f\u0131r puan alan bir \u00f6\u011frenci d\u0131\u015f\u0131nda t\u00fcm \u00f6\u011frencilerin en az 90 veya daha y\u00fcksek puan ald\u0131\u011f\u0131 100 s\u0131nav puan\u0131 i\u00e7eren bir veri k\u00fcmemiz oldu\u011funu varsayal\u0131m:<\/span><\/p>\n [ 0<\/strong> , 90, 90, 92, 94, 95, 95, 96, 97, 99, 94, 90, 90, 92, 94, 95, 95, 96, 97, 99, 93, 90, 90, 92, 94 , 95, 95, 96, 97, 99, 93, 90, 90, 92, 94, 95, 95, 96, 97, 99, 93, 90, 90, 92, 94, 95, 95, 96, 97, 99 , 93, 90, 90, 92, 94, 95, 95, 96, 97, 99, 93, 90, 90, 92, 94, 95, 95, 96, 97, 99, 93, 90, 90, 92, 94 , 95, 95, 96, 97, 99, 93, 90, 90, 92, 94, 95, 95, 96, 97, 99, 93, 90, 90, 92, 94, 95, 95, 96, 97, 99 ]<\/span><\/p>\n Ortalama 93,18<\/strong> \u00e7\u0131k\u0131yor. Veri setinden \u201c0\u201d\u0131 \u00e7\u0131kar\u0131rsak ortalama 94,12<\/strong> olacakt\u0131r. Bu nispeten k\u00fc\u00e7\u00fck bir farkt\u0131r. Bu, e\u011fer veri seti yeterince b\u00fcy\u00fckse, u\u00e7 noktadaki bir ayk\u0131r\u0131 de\u011ferin bile yaln\u0131zca minimal bir etkiye sahip oldu\u011funu g\u00f6stermektedir.<\/span><\/p>\n Veri k\u00fcmenizde ayk\u0131r\u0131 bir de\u011fer olabilece\u011finden endi\u015feleniyorsan\u0131z birka\u00e7 se\u00e7ene\u011finiz vard\u0131r:<\/span><\/p>\n Bir veri k\u00fcmesinin “merkezini” bulman\u0131n bir ba\u015fka yolu, bir veri k\u00fcmesindeki t\u00fcm bireysel de\u011ferlerin en k\u00fc\u00e7\u00fckten en b\u00fcy\u00fc\u011fe s\u0131ralanmas\u0131 ve ortanca de\u011ferinin bulunmas\u0131yla elde edilen medyan\u0131<\/strong> kullanmakt\u0131r.<\/span><\/p>\n Hesaplanma \u015fekli nedeniyle medyan ayk\u0131r\u0131 de\u011ferlerden daha az etkilenir ve ayk\u0131r\u0131 de\u011ferler oldu\u011funda da\u011f\u0131l\u0131m\u0131n merkezi konumunu daha iyi yakalar.<\/span><\/p>\n \u00d6rne\u011fin, belirli bir mahalledeki evlerin metrekaresini g\u00f6steren a\u015fa\u011f\u0131daki grafi\u011fi d\u00fc\u015f\u00fcn\u00fcn:<\/span> <\/p>\n Ortalama, birka\u00e7 a\u015f\u0131r\u0131 b\u00fcy\u00fck evden b\u00fcy\u00fck \u00f6l\u00e7\u00fcde etkilenirken, medyan etkilenmemektedir. Dolay\u0131s\u0131yla medyan, o mahalledeki bir evin “tipik” metrekaresini ortalamadan daha iyi yakal\u0131yor.<\/span><\/p>\n Daha fazla okuma:<\/strong><\/span><\/p>\n Merkezi e\u011filim \u00f6l\u00e7\u00fcleri \u2013 ortalama, medyan ve mod<\/a> \u0130statistikte bir veri k\u00fcmesinin ortalamas\u0131 ortalama de\u011ferdir. Bunu bilmek faydal\u0131d\u0131r \u00e7\u00fcnk\u00fc bize veri k\u00fcmesinin “merkezinin” nerede oldu\u011funa dair bir fikir verir. Basit form\u00fcl kullan\u0131larak hesaplan\u0131r: ortalama = (g\u00f6zlemlerin toplam\u0131) \/ (g\u00f6zlem say\u0131s\u0131) \u00d6rne\u011fin a\u015fa\u011f\u0131daki veri setine sahip oldu\u011fumuzu varsayal\u0131m: [1, 4, 5, 6, 7] Veri k\u00fcmesinin ortalamas\u0131 (1+4+5+6+7) \/ (5) = 4,6 Ancak ortalama yararl\u0131 […]<\/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-566","post","type-post","status-publish","format-standard","hentry","category-rehber"],"yoast_head":"\n\n
K\u00fc\u00e7\u00fck ve b\u00fcy\u00fck ayk\u0131r\u0131 de\u011ferler<\/strong><\/span><\/h2>\n
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\u00d6rneklem b\u00fcy\u00fckl\u00fc\u011f\u00fc ve ayk\u0131r\u0131 de\u011ferler<\/strong><\/span><\/h2>\n
Ayk\u0131r\u0131 de\u011ferler nas\u0131l ele al\u0131n\u0131r?<\/strong><\/span><\/h2>\n
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Medyan\u0131 kullan<\/strong><\/span><\/h2>\n
![](\"https:\/\/statorials.org\/wp-content\/uploads\/2023\/08\/moyenne_dist3.jpg\")
<\/p>\n
Ayk\u0131r\u0131 de\u011ferleri tespit etmek i\u00e7in Dixon’\u0131n Q testi
Ayk\u0131r\u0131 De\u011fer Hesaplay\u0131c\u0131<\/a><\/strong><\/p>\n","protected":false},"excerpt":{"rendered":"