{"id":89,"date":"2023-08-05T14:45:56","date_gmt":"2023-08-05T14:45:56","guid":{"rendered":"https:\/\/statorials.org\/tr\/varyasyon-katsayisi\/"},"modified":"2023-08-05T14:45:56","modified_gmt":"2023-08-05T14:45:56","slug":"varyasyon-katsayisi","status":"publish","type":"post","link":"https:\/\/statorials.org\/tr\/varyasyon-katsayisi\/","title":{"rendered":"De\u011fi\u015fim katsay\u0131s\u0131"},"content":{"rendered":"

Bu makalede varyasyon katsay\u0131s\u0131n\u0131n ne oldu\u011fu ve ne i\u00e7in kullan\u0131ld\u0131\u011f\u0131 a\u00e7\u0131klanmaktad\u0131r. De\u011fi\u015fim katsay\u0131s\u0131n\u0131n nas\u0131l hesapland\u0131\u011f\u0131n\u0131 ve ad\u0131m ad\u0131m \u00e7\u00f6z\u00fclen bir al\u0131\u015ft\u0131rmay\u0131 ke\u015ffedeceksiniz. \u00dcstelik herhangi bir veri setinin varyasyon katsay\u0131s\u0131n\u0131 \u00e7evrimi\u00e7i bir hesap makinesi kullanarak hesaplayabilirsiniz. <\/p>\n

<\/span> De\u011fi\u015fim katsay\u0131s\u0131 nedir?<\/span><\/h2>\n

De\u011fi\u015fim katsay\u0131s\u0131,<\/strong> bir veri k\u00fcmesinin ortalamas\u0131na g\u00f6re da\u011f\u0131l\u0131m\u0131n\u0131 belirlemek i\u00e7in kullan\u0131lan istatistiksel bir \u00f6l\u00e7\u00fcd\u00fcr. De\u011fi\u015fim katsay\u0131s\u0131, verinin standart sapmas\u0131n\u0131n ortalamas\u0131na b\u00f6l\u00fcnmesiyle hesaplan\u0131r.<\/p>\n

De\u011fi\u015fim katsay\u0131s\u0131 y\u00fczde olarak ifade edilir ve CV k\u0131saltmas\u0131 s\u0131kl\u0131kla bu istatistiksel \u00f6l\u00e7\u00fcm i\u00e7in bir sembol olarak kullan\u0131l\u0131r.<\/p>\n

De\u011fi\u015fim katsay\u0131s\u0131 ayn\u0131 zamanda Pearson de\u011fi\u015fim katsay\u0131s\u0131<\/strong> olarak da bilinir. <\/p>\n

<\/span> Varyasyon katsay\u0131s\u0131 form\u00fcl\u00fc<\/span><\/h2>\n

De\u011fi\u015fim katsay\u0131s\u0131, standart sapman\u0131n (veya standart sapman\u0131n) ortalamaya b\u00f6l\u00fcnmesiyle elde edilen de\u011ferin 100 ile \u00e7arp\u0131m\u0131na e\u015fittir.<\/strong> Bu nedenle, de\u011fi\u015fim katsay\u0131s\u0131n\u0131 hesaplamak i\u00e7in \u00f6nce verilerin standart sapmas\u0131 ve aritmetik ortalamas\u0131 belirlenmeli, ard\u0131ndan veriler b\u00f6l\u00fcnmelidir. iki istatistiksel \u00f6l\u00e7\u00fcm ve son olarak 100 ile \u00e7arp\u0131n.<\/p>\n

Dolay\u0131s\u0131yla varyasyon katsay\u0131s\u0131n\u0131n form\u00fcl\u00fc<\/strong> a\u015fa\u011f\u0131daki gibidir: <\/p>\n

\n
\"varyasyon<\/figure>\n<\/div>\n

\ud83d\udc49Herhangi bir veri seti i\u00e7in varyasyon katsay\u0131s\u0131n\u0131 hesaplamak i\u00e7in a\u015fa\u011f\u0131daki hesaplay\u0131c\u0131y\u0131 kullanabilirsiniz.<\/u><\/p>\n

De\u011fi\u015fim katsay\u0131s\u0131 hesaplan\u0131rken istatistiksel de\u011ferin y\u00fczde olarak ifade edilmesi i\u00e7in y\u00fcz ile \u00e7arp\u0131l\u0131r.<\/p>\n

Bu nedenle bir veri setinin de\u011fi\u015fim katsay\u0131s\u0131n\u0131 elde edebilmek i\u00e7in \u00f6ncelikle standart sapman\u0131n ve aritmetik ortalaman\u0131n nas\u0131l hesapland\u0131\u011f\u0131n\u0131 bilmeniz gerekir. E\u011fer bunu nas\u0131l yapaca\u011f\u0131n\u0131z\u0131 hat\u0131rlam\u0131yorsan\u0131z a\u00e7\u0131klamaya devam etmeden \u00f6nce a\u015fa\u011f\u0131daki ba\u011flant\u0131lar\u0131 ziyaret etmeniz \u00f6nerilir: <\/p>\n

\u27a4<\/span> Bak\u0131n\u0131z:<\/strong> standart sapma nas\u0131l hesaplan\u0131r<\/a>
\u27a4<\/span> Bak\u0131n\u0131z:<\/strong> aritmetik ortalama nas\u0131l hesaplan\u0131r<\/a> <\/div>\n

<\/span> De\u011fi\u015fim katsay\u0131s\u0131n\u0131n hesaplanmas\u0131na \u00f6rnek<\/span><\/h2>\n

De\u011fi\u015fim katsay\u0131s\u0131n\u0131n tan\u0131m\u0131 ve form\u00fcl\u00fc dikkate al\u0131nd\u0131\u011f\u0131nda, a\u015fa\u011f\u0131da bu ba\u011f\u0131l da\u011f\u0131l\u0131m \u00f6l\u00e7\u00fcs\u00fcn\u00fcn nas\u0131l elde edildi\u011fine dair somut bir \u00f6rnek g\u00f6rebilirsiniz.<\/p>\n

    \n
  • A\u015fa\u011f\u0131daki istatistiksel veri setinin varyasyon katsay\u0131s\u0131n\u0131 hesaplay\u0131n:
    4, 1, 3, 9, 12, 2, 5, 8, 3, 6<\/li>\n<\/ul>\n

    \u00d6ncelikle veri serisinin standart sapmas\u0131n\u0131 hesaplamam\u0131z gerekiyor:<\/p>\n<\/p>\n

    \"\\sigma=<\/p>\n<\/p>\n

    \u27a4<\/span> Not:<\/strong> Standart sapman\u0131n nas\u0131l belirlenece\u011fini bilmiyorsan\u0131z yukar\u0131daki ba\u011flant\u0131dan a\u00e7\u0131klamay\u0131 g\u00f6rebilirsiniz.<\/p>\n

    Daha sonra t\u00fcm veri k\u00fcmesinin aritmetik ortalamas\u0131n\u0131 hesapl\u0131yoruz:<\/p>\n<\/p>\n

    \"\\overline{x}=5,3\"<\/p>\n<\/p>\n

    \u27a4<\/span> Not:<\/strong> Aritmetik ortalaman\u0131n nas\u0131l hesaplanaca\u011f\u0131n\u0131 bilmiyorsan\u0131z yukar\u0131daki ba\u011flant\u0131dan a\u00e7\u0131klamay\u0131 g\u00f6rebilirsiniz.<\/p>\n

    Verilerin standart sapmas\u0131n\u0131 ve ortalamas\u0131n\u0131 \u00f6\u011frendikten sonra de\u011ferini bulmak i\u00e7in varyasyon katsay\u0131s\u0131 form\u00fcl\u00fcn\u00fc kullanman\u0131z yeterlidir:<\/p>\n<\/p>\n

    \"CV=\\cfrac{\\sigma}{\\overline{x}}\\cdot<\/p>\n<\/p>\n

    Bu nedenle hesaplanan de\u011ferleri form\u00fclde yerine koyar\u0131z ve varyasyon katsay\u0131s\u0131n\u0131 hesaplar\u0131z: <\/p>\n<\/p>\n

    \"CV=\\cfrac{3,29}{5,3}\\cdot<\/p>\n<\/p>\n

    <\/span> De\u011fi\u015fim katsay\u0131s\u0131 hesaplay\u0131c\u0131s\u0131<\/span><\/h2>\n

    De\u011fi\u015fim katsay\u0131s\u0131n\u0131 hesaplamak i\u00e7in a\u015fa\u011f\u0131daki \u00e7evrimi\u00e7i 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