\u0130statistikte yar\u0131 de\u011fi\u015fkenlik<\/strong> , bir numunenin de\u011fi\u015fkenli\u011fini g\u00f6steren bir da\u011f\u0131l\u0131m \u00f6l\u00e7\u00fcs\u00fcd\u00fcr. Daha kesin olarak yar\u0131 de\u011fi\u015fkenlik, sapmalar\u0131n karelerinin toplam\u0131n\u0131n toplam g\u00f6zlem say\u0131s\u0131na b\u00f6l\u00fcnerek bir eksi\u011fine e\u015fittir.<\/p>\n Yar\u0131-de\u011fi\u015fkenlik sembol\u00fc<\/p>\n<\/p>\n herhangi biri<\/p>\n . Bazen sembol de kullan\u0131lsa da<\/p>\n yar\u0131-varyans\u0131 temsil etmek i\u00e7in.<\/p>\n Yar\u0131 de\u011fi\u015fkenlik, \u00f6nyarg\u0131dan ka\u00e7\u0131narak bir numunenin da\u011f\u0131l\u0131m\u0131n\u0131 belirlemek i\u00e7in kullan\u0131l\u0131r; bu nedenle buna genellikle tarafs\u0131z varyans denir. Dolay\u0131s\u0131yla quasivariance pop\u00fclasyon varyans\u0131n\u0131n iyi bir tahmincisidir. Asl\u0131nda \u00f6rneklem varyans\u0131n\u0131 hesaplarken varyans form\u00fcl\u00fc yerine s\u0131kl\u0131kla yar\u0131 varyans form\u00fcl\u00fc kullan\u0131l\u0131r. A\u015fa\u011f\u0131da bu iki istatistiksel \u00f6l\u00e7\u00fcm aras\u0131ndaki fark hakk\u0131nda ayr\u0131nt\u0131l\u0131 bilgi verece\u011fiz. <\/p>\n Yar\u0131-varyans\u0131 hesaplamak i\u00e7in, de\u011ferler ile veri k\u00fcmesinin ortalamas\u0131 aras\u0131ndaki farklar\u0131n karelerinin toplam\u0131n\u0131 bulmak ve daha sonra bunu toplam veri say\u0131s\u0131ndan bir eksi\u011fine b\u00f6lmek gerekir.<\/p>\n Dolay\u0131s\u0131yla yar\u0131-varyans\u0131 hesaplamak i\u00e7in kullan\u0131lan form\u00fcl<\/strong> a\u015fa\u011f\u0131daki gibidir: <\/p>\n Alt\u0131n:<\/p>\n yar\u0131-varyanst\u0131r.<\/li>\n veri de\u011feri<\/p>\n .<\/li>\n toplam veri say\u0131s\u0131d\u0131r.<\/li>\n veri setinin ortalamas\u0131d\u0131r.<\/li>\n<\/ul>\n \ud83d\udc49 Herhangi bir veri setinin yar\u0131 varyans\u0131n\u0131 hesaplamak i\u00e7in a\u015fa\u011f\u0131daki hesaplay\u0131c\u0131y\u0131 kullanabilirsiniz.<\/u><\/p>\n Neden n’ye de\u011fil de n-1’e b\u00f6l\u00fcnd\u00fc\u011f\u00fcn\u00fc merak ediyor olabilirsiniz? Bu \u00f6nyarg\u0131y\u0131 ortadan kald\u0131rmakla ilgili, bu \u015fekilde tarafs\u0131z bir tahminci elde ediyoruz. Yar\u0131-de\u011fi\u015fkenli\u011fin pop\u00fclasyon varyans\u0131n\u0131n iyi bir tahmincisi olmas\u0131n\u0131n nedeni tam olarak budur. <\/p>\n Art\u0131k yar\u0131 de\u011fi\u015fkenli\u011fin tan\u0131m\u0131n\u0131 bildi\u011fimize g\u00f6re, bir veri serisinin yar\u0131 de\u011fi\u015fkenli\u011finin nas\u0131l hesapland\u0131\u011f\u0131n\u0131 g\u00f6rebilmeniz i\u00e7in basit bir \u00f6rnek \u00e7\u00f6zece\u011fiz.<\/p>\n Bir veri setinin yar\u0131-varyans\u0131n\u0131 elde etmek i\u00e7in yapmam\u0131z gereken ilk \u015fey aritmetik ortalamas\u0131n\u0131 hesaplamakt\u0131r:<\/p>\n<\/p>\n Verilerin ortalama de\u011ferini bildi\u011fimizde yar\u0131-varyans form\u00fcl\u00fcn\u00fc uygular\u0131z:<\/p>\n<\/p>\n Bu nedenle, egzersiz talimat\u0131n\u0131n sa\u011flad\u0131\u011f\u0131 verileri form\u00fclde de\u011fi\u015ftiriyoruz:<\/p>\n<\/p>\n Son olarak, yar\u0131-varyans\u0131 hesaplamak i\u00e7in i\u015flemleri \u00e7\u00f6zmek yeterlidir:<\/p>\n<\/p>\n Yar\u0131-de\u011fi\u015fkenlik birimlerinin istatistiksel veri birimleriyle ayn\u0131 birimler oldu\u011funu ancak kareleri oldu\u011funu unutmay\u0131n; dolay\u0131s\u0131yla bu veri k\u00fcmesinin yar\u0131-de\u011fi\u015fkenli\u011fi 57,2 milyon 2’dir<\/sup> . <\/p>\n Yar\u0131 de\u011fi\u015fkenli\u011fini hesaplamak i\u00e7in a\u015fa\u011f\u0131daki hesap makinesine bir istatistiksel veri seti girin. Veriler bir bo\u015flukla ayr\u0131lmal\u0131 ve ondal\u0131k ay\u0131r\u0131c\u0131 olarak nokta kullan\u0131larak girilmelidir. <\/p>\n![\"\\sigma_{n-1}^2\"](\"https:\/\/statorials.org\/wp-content\/ql-cache\/quicklatex.com-0b549724a0e683e8a610c965ab71bd60_l3.png\" "\\"Rendered")
<\/p>\n![\"s_{n-1}^2\"](\"https:\/\/statorials.org\/wp-content\/ql-cache\/quicklatex.com-c524e2c99de0d0c00774c93d2ef52b0d_l3.png\" "\\"Rendered")
<\/p>\n![\"\\widehat{s}^2\"](\"https:\/\/statorials.org\/wp-content\/ql-cache\/quicklatex.com-32b7e0177b393245eab2613fbda7ec59_l3.png\" "\\"Rendered")
<\/p>\n<\/span> Yar\u0131 varyans form\u00fcl\u00fc<\/span><\/h2>\n
![\"yar\u0131-varyans](\"https:\/\/statorials.org\/wp-content\/uploads\/2023\/08\/quasivariance.png\")
<\/figure>\n\n
<\/p>\n![\"x_i\"](\"https:\/\/statorials.org\/wp-content\/ql-cache\/quicklatex.com-dad27a9703483183e1afd245f5232b83_l3.png\" "\\"Rendered")
<\/p>\n![\"i\"](\"https:\/\/statorials.org\/wp-content\/ql-cache\/quicklatex.com-31318c5dcb226c69e0818e5f7d2422b5_l3.png\" "\\"Rendered")
<\/p>\n![\"n\"](\"https:\/\/statorials.org\/wp-content\/ql-cache\/quicklatex.com-ec4217f4fa5fcd92a9edceba0e708cf7_l3.png\" "\\"Rendered")
<\/p>\n![\"\\overline{X}\"](\"https:\/\/statorials.org\/wp-content\/ql-cache\/quicklatex.com-5b485d4231dfeb4b50ddf271c3abb0b3_l3.png\" "\\"Rendered")
<\/p>\n<\/span> Yar\u0131 de\u011fi\u015fkenlik hesaplama \u00f6rne\u011fi<\/span><\/h2>\n
\n
![\"\\overline{X}=\\cfrac{11+5+2+(-9)+7}{5}=3,2\"](\"https:\/\/statorials.org\/wp-content\/ql-cache\/quicklatex.com-0a2fc458e6a80794b9b8fdc1120ddedb_l3.png\" "\\"Rendered")
<\/p>\n<\/p>\n![\"\\sigma_{n-1}^2=\\cfrac{\\displaystyle\\sum_{i=1}^n\\left(x_i-\\overline{X}\\right)^2}{n-1}\"](\"https:\/\/statorials.org\/wp-content\/ql-cache\/quicklatex.com-757173b2ef76e4e1e3cd9f5302609c0c_l3.png\" "\\"Rendered")
<\/p>\n<\/p>\n![\"\\sigma_{n-1}^2=\\cfrac{\\displaystyle](\"https:\/\/statorials.org\/wp-content\/ql-cache\/quicklatex.com-f911e419af54c571c2144aff70f2eee6_l3.png\" "\\"Rendered")
<\/p>\n<\/p>\n![\"\\begin{aligned}\\sigma_{n-1}^2&=\\cfrac{7,8^2+1,8^2+(-1,2)^2+(-12,2)^2+3,8^2}{5}\\\\[2ex]&=\\cfrac{60,84+3,24+1,44+148,84+14,44}{5-1}\\\\[2ex]&=](\"https:\/\/statorials.org\/wp-content\/ql-cache\/quicklatex.com-5d64d58e69b766d9075ec1220386d8c0_l3.png\" "\\"Rendered")
<\/p>\n<\/p>\n<\/span> Yar\u0131-varyans hesaplay\u0131c\u0131s\u0131<\/span><\/h2>\n