Bir bara on ki\u015fi oturmu\u015f, hepsinin ayl\u0131k geliri 20 bin lira. Ortalama gelir: 20 bin. Sonra i\u00e7eri bir milyarder giriyor. \u015eimdi \u201cortalama gelir\u201d aniden milyonlara f\u0131rl\u0131yor \u2014 ama masadaki kimsenin hayat\u0131 de\u011fi\u015fmedi. \u0130\u015fte \u201cortalama\u201d dedi\u011fimiz say\u0131 tek ba\u015f\u0131na b\u00f6yle yan\u0131lt\u0131r. Bu yaz\u0131da, bir veriyi d\u00fcr\u00fcst\u00e7e \u00f6zetlemek i\u00e7in ortalaman\u0131n yan\u0131na neden mutlaka medyan ve standart sapmay\u0131 koymam\u0131z gerekti\u011fini anlat\u0131yoruz.<\/p>
Ortalama (aritmetik ortalama), t\u00fcm de\u011ferleri toplay\u0131p say\u0131ya b\u00f6lmektir. Sorun \u015fu: a\u015f\u0131r\u0131 u\u00e7 de\u011ferler (outlier\u2019lar) ortalamay\u0131 kendine do\u011fru \u00e7eker. Birka\u00e7 dev de\u011fer, kalabal\u0131k bir grubun ger\u00e7e\u011fini g\u00f6lgeleyebilir. Bu y\u00fczden \u201cortalama maa\u015f\u201d, \u201cortalama ev fiyat\u0131\u201d gibi ba\u015fl\u0131klar \u00e7o\u011fu zaman tipik durumu de\u011fil, \u00e7arp\u0131k bir resmi anlat\u0131r.<\/p>
Medyan, verileri k\u00fc\u00e7\u00fckten b\u00fcy\u00fc\u011fe s\u0131ralad\u0131\u011f\u0131n\u0131zda tam ortada kalan de\u011ferdir. Bardaki \u00f6rnekte medyan h\u00e2l\u00e2 20 bin lirad\u0131r, \u00e7\u00fcnk\u00fc ortadaki ki\u015finin geliri de\u011fi\u015fmedi. Medyan, u\u00e7 de\u011ferlerden etkilenmedi\u011fi i\u00e7in \u201ctipik\u201d de\u011feri ortalamaya g\u00f6re \u00e7ok daha d\u00fcr\u00fcst yans\u0131t\u0131r. Gelir, fiyat gibi \u00e7arp\u0131k da\u011f\u0131l\u0131mlarda medyan ortalamadan daha bilgilendiricidir.<\/p>
Ortalama ve medyan \u201cmerkez\u201d hakk\u0131nda konu\u015fur ama veriler ne kadar da\u011f\u0131n\u0131k, onu s\u00f6ylemez. \u0130\u015fte standart sapma burada devreye girer: de\u011ferlerin ortalamadan ne kadar uza\u011fa yay\u0131ld\u0131\u011f\u0131n\u0131 \u00f6l\u00e7er. K\u00fc\u00e7\u00fck standart sapma \u201cherkes birbirine yak\u0131n\u201d; b\u00fcy\u00fck standart sapma \u201cu\u00e7lar aras\u0131nda b\u00fcy\u00fck fark var\u201d demektir. \u0130ki s\u0131n\u0131f\u0131n not ortalamas\u0131 ayn\u0131 olabilir ama biri herkesin orta seviyede, di\u011feri yar\u0131s\u0131 \u00e7ok iyi yar\u0131s\u0131 \u00e7ok k\u00f6t\u00fc olabilir \u2014 fark\u0131 ancak standart sapma g\u00f6sterir. Tan\u0131m\u0131n matematiksel detay\u0131 i\u00e7in standart sapman\u0131n tan\u0131m\u0131<\/a> iyi bir kaynakt\u0131r.<\/p> D\u00fcr\u00fcst bir \u00f6zet \u00fc\u00e7 soruyu birden yan\u0131tlar: Merkez nerede (ortalama\/medyan)? Veri ne kadar yay\u0131lm\u0131\u015f (standart sapma)? Ve da\u011f\u0131l\u0131m \u00e7arp\u0131k m\u0131 (ortalama ile medyan birbirinden \u00e7ok mu uzak)? Tek bir say\u0131ya \u201cortalama \u015fu\u201d deyip ge\u00e7mek, ger\u00e7e\u011fin yar\u0131s\u0131n\u0131 saklamakt\u0131r. Bu, olas\u0131l\u0131kta s\u0131k\u00e7a d\u00fc\u015f\u00fclen sezgisel tuzaklar\u0131n<\/a> bir akrabas\u0131d\u0131r. \u0130\u015fin hocas\u0131, bir say\u0131y\u0131 g\u00f6r\u00fcnce \u201cpeki ya yay\u0131l\u0131m?\u201d diye sorand\u0131r.<\/p>","protected":false},"excerpt":{"rendered":" Bir bara on ki\u015fi oturmu\u015f, hepsinin ayl\u0131k geliri 20 bin lira. Ortalama gelir: 20 bin. Sonra i\u00e7eri bir milyarder giriyor. \u015eimdi \u201cortalama gelir\u201d aniden milyonlara f\u0131rl\u0131yor \u2014 ama masadaki kimsenin hayat\u0131 de\u011fi\u015fmedi. \u0130\u015fte \u201cortalama\u201d dedi\u011fimiz say\u0131 tek ba\u015f\u0131na b\u00f6yle yan\u0131lt\u0131r. Bu yaz\u0131da, bir veriyi d\u00fcr\u00fcst\u00e7e \u00f6zetlemek i\u00e7in ortalaman\u0131n yan\u0131na neden mutlaka medyan ve standart sapmay\u0131 … Read more<\/a><\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[2],"tags":[],"class_list":["post-31","post","type-post","status-publish","format-standard","hentry","category-istatistik-olasilik"],"_links":{"self":[{"href":"https:\/\/hocabul.net\/index.php?rest_route=\/wp\/v2\/posts\/31","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/hocabul.net\/index.php?rest_route=\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/hocabul.net\/index.php?rest_route=\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/hocabul.net\/index.php?rest_route=\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/hocabul.net\/index.php?rest_route=%2Fwp%2Fv2%2Fcomments&post=31"}],"version-history":[{"count":1,"href":"https:\/\/hocabul.net\/index.php?rest_route=\/wp\/v2\/posts\/31\/revisions"}],"predecessor-version":[{"id":32,"href":"https:\/\/hocabul.net\/index.php?rest_route=\/wp\/v2\/posts\/31\/revisions\/32"}],"wp:attachment":[{"href":"https:\/\/hocabul.net\/index.php?rest_route=%2Fwp%2Fv2%2Fmedia&parent=31"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/hocabul.net\/index.php?rest_route=%2Fwp%2Fv2%2Fcategories&post=31"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/hocabul.net\/index.php?rest_route=%2Fwp%2Fv2%2Ftags&post=31"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}\u00dc\u00e7\u00fcn\u00fc birlikte okumak<\/h2>