{"id":76,"date":"2023-08-05T18:14:48","date_gmt":"2023-08-05T18:14:48","guid":{"rendered":"https:\/\/statorials.org\/tr\/orta-fark\/"},"modified":"2023-08-05T18:14:48","modified_gmt":"2023-08-05T18:14:48","slug":"orta-fark","status":"publish","type":"post","link":"https:\/\/statorials.org\/tr\/orta-fark\/","title":{"rendered":"Orta fark"},"content":{"rendered":"

Bu makalede ortalama sapman\u0131n ne oldu\u011fu ve nas\u0131l hesapland\u0131\u011f\u0131 a\u00e7\u0131klanmaktad\u0131r. Ayr\u0131ca ortalama sapman\u0131n hesaplanmas\u0131na ili\u015fkin somut \u00f6rnekler de bulacaks\u0131n\u0131z. \u00dcstelik \u00e7evrimi\u00e7i bir hesap makinesi kullanarak herhangi bir istatistiksel veri setinin ortalama sapmas\u0131n\u0131 hesaplayabileceksiniz.<\/p>\n

<\/span> Ortalama sapma nedir?<\/span><\/h2>\n

Ortalama mutlak sapma<\/strong> olarak da adland\u0131r\u0131lan ortalama sapma<\/strong> , istatistiksel da\u011f\u0131l\u0131m\u0131n bir \u00f6l\u00e7\u00fcs\u00fcd\u00fcr.<\/p>\n

Bir veri setinin ortalama sapmas\u0131 mutlak sapmalar\u0131n ortalamas\u0131d\u0131r<\/strong> . Bu nedenle ortalama sapma, her veri \u00f6\u011fesinin aritmetik ortalamadan sapmalar\u0131n\u0131n toplam\u0131n\u0131n toplam veri \u00f6\u011fesi say\u0131s\u0131na b\u00f6l\u00fcnmesine e\u015fittir.<\/p>\n

Ba\u015fka bir deyi\u015fle ortalama sapman\u0131n form\u00fcl\u00fc<\/strong> a\u015fa\u011f\u0131daki gibidir: <\/p>\n

\"orta<\/figure>\n

\ud83d\udc49Herhangi bir veri setinin ortalama sapmas\u0131n\u0131 hesaplamak i\u00e7in a\u015fa\u011f\u0131daki hesaplay\u0131c\u0131y\u0131 kullanabilirsiniz.<\/u><\/p>\n

\u0130statistikte ortalama sapmaya ortalama mutlak sapma<\/strong> da denir.<\/p>\n

Ortalama sapman\u0131n yorumlanmas\u0131 \u015fu \u015fekilde yap\u0131l\u0131r: ortalama sapman\u0131n de\u011feri ne kadar b\u00fcy\u00fck olursa, bu, verilerin ortalama olarak aritmetik ortalamadan daha uzakta oldu\u011fu anlam\u0131na gelir; tersine, ortalama sapma ne kadar d\u00fc\u015f\u00fck olursa de\u011fer o kadar yak\u0131n olur. veriler \u015f\u00f6yle. Ortalama sapma bu nedenle bir veri serisinin da\u011f\u0131l\u0131m\u0131n\u0131 g\u00f6sterir.<\/p>\n

Da\u011f\u0131t\u0131ld\u0131\u011f\u0131 d\u00fc\u015f\u00fcn\u00fclen di\u011fer \u00f6nlemler aral\u0131k, \u00e7eyrekler aras\u0131 aral\u0131k, standart sapma (veya standart sapma), varyans ve varyasyon katsay\u0131s\u0131d\u0131r. <\/p>\n

<\/span> Ortalama sapma nas\u0131l hesaplan\u0131r<\/span><\/h2>\n

Bir veri serisinin ortalama sapmas\u0131n\u0131 hesaplamak i\u00e7in a\u015fa\u011f\u0131daki ad\u0131mlar\u0131n izlenmesi gerekir:<\/p>\n

    \n
  1. \u0130statistiksel veri setinin aritmetik ortalamas\u0131n\u0131 hesaplay\u0131n<\/a> .<\/span><\/li>\n
  2. Her veri noktas\u0131n\u0131n, veriler ile ortalama aras\u0131ndaki fark\u0131n mutlak de\u011feri olarak tan\u0131mlanan ortalamadan sapmas\u0131n\u0131 hesaplay\u0131n.<\/span><\/li>\n
  3. \u00d6nceki ad\u0131mda hesaplanan t\u00fcm farklar\u0131 toplay\u0131n.<\/span><\/li>\n
  4. Toplam veri say\u0131s\u0131na b\u00f6l\u00fcn. Elde edilen sonu\u00e7, veri serisinin ortalama sapmas\u0131d\u0131r.<\/span><\/li>\n<\/ol>\n

    \u00d6zetle ortalama sapmay\u0131 bulmak i\u00e7in uygulanmas\u0131 gereken form\u00fcl \u015fudur: <\/p>\n<\/p>\n

    \"D_{\\overline{x}}=\\cfrac{\\sum_{i=1}^N|x_i-\\overline{x}|}{N}\"<\/p>\n<\/p>\n

    <\/span> Ortalama sapmay\u0131 hesaplama \u00f6rne\u011fi<\/span><\/h2>\n

    Ortalama sapman\u0131n tan\u0131m\u0131 g\u00f6z \u00f6n\u00fcne al\u0131nd\u0131\u011f\u0131nda, a\u015fa\u011f\u0131da bir istatistiksel \u00f6rne\u011fin ortalama sapmas\u0131n\u0131 hesaplaman\u0131n ad\u0131m ad\u0131m \u00e7\u00f6z\u00fclm\u00fc\u015f bir \u00f6rne\u011fi bulunmaktad\u0131r. Bu \u015fekilde ortalama sapman\u0131n nas\u0131l elde edilece\u011fini daha iyi anlayacaks\u0131n\u0131z.<\/p>\n

      \n
    • Bir analist, bir \u015firketin ge\u00e7ti\u011fimiz y\u0131ldaki ekonomik sonu\u00e7lar\u0131n\u0131 inceliyor ve \u015firketin s\u00f6z konusu y\u0131l\u0131n her \u00e7eyre\u011finde elde etti\u011fi k\u00e2r hakk\u0131nda bilgi sahibi oluyor: 2, 3, 7 ve 5 milyon dolar. Verilerin ortalama sapmas\u0131 nedir?<\/li>\n<\/ul>\n

      \u00d6ncelikle verilerin ortalamas\u0131n\u0131 almam\u0131z gerekiyor, bu nedenle toplay\u0131p toplam g\u00f6zlem say\u0131s\u0131na b\u00f6l\u00fcyoruz (4):<\/p>\n<\/p>\n

      \"\\overline{x}=\\cfrac{2+3+7+5}{4}=4,25\"<\/p>\n<\/p>\n

      Aritmetik ortalamay\u0131 hesaplad\u0131ktan sonra ortalama sapma form\u00fcl\u00fcn\u00fc kullan\u0131r\u0131z:<\/p>\n<\/p>\n

      \"D_{\\overline{x}}=\\cfrac{\\sum_{i=1}^N|x_i-\\overline{x}|}{N}\"<\/p>\n<\/p>\n

      Verileri form\u00fclde de\u011fi\u015ftiririz:<\/p>\n<\/p>\n

      \"D_{\\overline{x}}=\\cfrac{|2-4,25|+|3-4,25|+|7-4,25|+|5-4,25|}{4}\"<\/p>\n<\/p>\n

      Hesaplamalar\u0131 payda yap\u0131yoruz: <\/p>\n<\/p>\n

      \"D_{\\overline{x}}=\\cfrac{|-2,25|+|-1,25|+|2,75|+|0,75|}{4}\"<\/p>\n<\/p>\n

      \"D_{\\overline{x}}=\\cfrac{2,25+1,25+2,75+0,75}{4}\"<\/p>\n<\/p>\n

      \"D_{\\overline{x}}=\\cfrac{7}{4}\"<\/p>\n<\/p>\n

      Son olarak, numunenin ortalama sapmas\u0131n\u0131 elde etmek i\u00e7in toplam veri say\u0131s\u0131na b\u00f6l\u00fcyoruz: <\/p>\n<\/p>\n

      \"D_{\\overline{x}}=1,75\"<\/p>\n<\/p>\n

      <\/span> Ortalama Sapma Hesaplay\u0131c\u0131<\/span><\/h2>\n

      Ortalama sapmas\u0131n\u0131 hesaplamak i\u00e7in a\u015fa\u011f\u0131daki hesap makinesine bir dizi istatistiksel veri girin. Veriler bir bo\u015flukla ayr\u0131lmal\u0131 ve ondal\u0131k ay\u0131r\u0131c\u0131 olarak nokta kullan\u0131larak girilmelidir. <\/p>\n