{"id":267,"date":"2023-08-03T09:33:05","date_gmt":"2023-08-03T09:33:05","guid":{"rendered":"https:\/\/statorials.org\/tr\/numune-sapmasi\/"},"modified":"2023-08-03T09:33:05","modified_gmt":"2023-08-03T09:33:05","slug":"numune-sapmasi","status":"publish","type":"post","link":"https:\/\/statorials.org\/tr\/numune-sapmasi\/","title":{"rendered":"\u00d6rnek varyans"},"content":{"rendered":"<p>Bu makalede istatistiklerde \u00f6rneklem varyans\u0131n\u0131n ne oldu\u011fu ve \u00f6rneklem varyans\u0131 ile pop\u00fclasyon varyans\u0131 aras\u0131ndaki fark\u0131n ne oldu\u011fu a\u00e7\u0131klanmaktad\u0131r. B\u00f6ylece bir numunenin varyans\u0131n\u0131 nas\u0131l hesaplayaca\u011f\u0131n\u0131z\u0131, \u00e7\u00f6z\u00fclm\u00fc\u015f bir al\u0131\u015ft\u0131rmay\u0131 ve ayr\u0131ca herhangi bir numunenin varyans\u0131n\u0131 bulmak i\u00e7in \u00e7evrimi\u00e7i bir hesap makinesini bulacaks\u0131n\u0131z. <\/p>\n<h2 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"%c2%bfque-es-la-varianza-muestral\"><\/span> \u00d6rnek varyans\u0131 nedir?<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p> <strong>\u00d6rnek varyans\u0131,<\/strong> istatistiksel bir \u00f6rne\u011fin de\u011fi\u015fkenli\u011fini g\u00f6steren bir da\u011f\u0131l\u0131m \u00f6l\u00e7\u00fcs\u00fcd\u00fcr. Numune varyans\u0131n\u0131 hesaplamak i\u00e7in, t\u00fcm numune art\u0131klar\u0131n\u0131n karelerini ekleyin ve ard\u0131ndan numune boyutunun bir eksi\u011fine b\u00f6l\u00fcn.<\/p>\n<p> \u00d6rnek varyans\u0131n sembol\u00fc s <sup>2&#8217;dir<\/sup> .<\/p>\n<p> \u00d6rnek varyans de\u011ferinin yorumlanmas\u0131 basittir: \u00f6rnek varyans de\u011feri ne kadar b\u00fcy\u00fck olursa, \u00f6rnek veriler o kadar da\u011f\u0131n\u0131k olur. Yani \u00f6rneklem varyans\u0131n\u0131n b\u00fcy\u00fck de\u011feri verilerin birbirinden uzak oldu\u011fu anlam\u0131na gelirken, \u00f6rneklem varyans\u0131n\u0131n k\u00fc\u00e7\u00fck de\u011feri verilerin birbirine \u00e7ok yak\u0131n oldu\u011funu g\u00f6sterir. Ancak \u00f6rnek varyans\u0131n\u0131 yorumlarken, \u00f6rnek varyans de\u011ferini bozabilece\u011finden ayk\u0131r\u0131 <a href=\"https:\/\/statorials.org\/tr\/aykiri-degerler\/\">de\u011ferlere<\/a> dikkat edilmelidir. <\/p>\n<h2 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"formula-de-la-varianza-muestral\"><\/span> Varyans Form\u00fcl\u00fc \u00d6rne\u011fi<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p> \u00d6rnek varyans\u0131, \u00f6rnek art\u0131klar\u0131n\u0131n karelerinin toplam\u0131n\u0131n, toplam g\u00f6zlem say\u0131s\u0131na b\u00f6l\u00fcnerek bir eksi\u011fine e\u015fittir.<\/p>\n<p> Bu nedenle <strong>\u00f6rneklem varyans\u0131n\u0131 hesaplama form\u00fcl\u00fc<\/strong> \u015fu \u015fekildedir: <\/p>\n<figure class=\"wp-block-image aligncenter size-full is-resized\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/statorials.org\/wp-content\/uploads\/2023\/08\/formule-de-variance-de-lechantillon.png\" alt=\"\u00f6rnek varyans form\u00fcl\u00fc\" class=\"wp-image-5705\" width=\"330\" height=\"276\" srcset=\"\" sizes=\"auto, \"><\/figure>\n<p style=\"margin-bottom:5px\"> Alt\u0131n:<\/p>\n<ul style=\"color:#FF8A05; font-weight: bold;\">\n<li style=\"margin-bottom:3px\">\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/statorials.org\/wp-content\/ql-cache\/quicklatex.com-3ab572e85f9cb7cb6f495387f2a6ab0b_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"s^2\" title=\"Rendered by QuickLaTeX.com\" height=\"15\" width=\"15\" style=\"vertical-align: 0px;\"><\/p>\n<p> \u00f6rnek varyans\u0131d\u0131r.<\/li>\n<li style=\"margin-bottom:3px\">\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/statorials.org\/wp-content\/ql-cache\/quicklatex.com-a39858a792fb4fe9a3173e004701f2a7_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\overline{x}\" title=\"Rendered by QuickLaTeX.com\" height=\"11\" width=\"11\" style=\"vertical-align: 0px;\"><\/p>\n<p> \u00f6rnek anlam\u0131na gelir.<\/li>\n<li style=\"margin-bottom:3px\">\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/statorials.org\/wp-content\/ql-cache\/quicklatex.com-dad27a9703483183e1afd245f5232b83_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"x_i\" title=\"Rendered by QuickLaTeX.com\" height=\"11\" width=\"15\" style=\"vertical-align: -3px;\"><\/p>\n<p> veri de\u011feri<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/statorials.org\/wp-content\/ql-cache\/quicklatex.com-31318c5dcb226c69e0818e5f7d2422b5_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"i\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"6\" style=\"vertical-align: 0px;\"><\/p>\n<p> .<\/li>\n<li style=\"margin-bottom:3px\">\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/statorials.org\/wp-content\/ql-cache\/quicklatex.com-ec4217f4fa5fcd92a9edceba0e708cf7_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"n\" title=\"Rendered by QuickLaTeX.com\" height=\"8\" width=\"11\" style=\"vertical-align: 0px;\"><\/p>\n<p> \u00f6rnekteki veri \u00f6\u011felerinin toplam say\u0131s\u0131d\u0131r.<\/li>\n<\/ul>\n<p> \ud83d\udc49Herhangi <u style=\"text-decoration-color:#FF8A05;\">bir \u00f6rnek verinin varyans\u0131n\u0131 hesaplamak i\u00e7in a\u015fa\u011f\u0131daki hesaplay\u0131c\u0131y\u0131 kullanabilirsiniz.<\/u> <\/p>\n<h2 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"ejemplo-del-calculo-de-la-varianza-muestral\"><\/span> Sapma hesaplama \u00f6rne\u011fi<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p> \u00d6rnek varyans\u0131n tan\u0131m\u0131n\u0131 ve form\u00fcl\u00fcn\u00fc g\u00f6rd\u00fckten sonra nas\u0131l hesapland\u0131\u011f\u0131n\u0131 anlamak i\u00e7in basit bir \u00f6rnek \u00e7\u00f6zece\u011fiz:<\/p>\n<ul>\n<li> Bir ayakkab\u0131 \u015firketi yeni bir ayakkab\u0131 modeli piyasaya s\u00fcr\u00fcp s\u00fcrmemeye karar vermek i\u00e7in pazar ara\u015ft\u0131rmas\u0131 yap\u0131yor. Pek \u00e7ok farkl\u0131 model oldu\u011fu ve h\u0131zl\u0131 bir \u00f6n analiz yapmak istedi\u011finiz i\u00e7in, en iyi be\u015f rakip ayakkab\u0131 markas\u0131n\u0131n fiyatlar\u0131na bakmaya karar veriyorsunuz (fiyatlar a\u015fa\u011f\u0131da g\u00f6sterilmi\u015ftir). Bu veri setinin \u00f6rneklem varyans\u0131 nedir?<\/li>\n<\/ul>\n<p class=\"has-text-align-center\"> \u20ac98 \u20ac70 \u20ac125 \u20ac89 \u20ac75<\/p>\n<p> \u00d6ncelikle <a href=\"https:\/\/statorials.org\/tr\/ornek-ortalama\/\">\u00f6rnek ortalamas\u0131n\u0131<\/a> hesaplamam\u0131z gerekiyor:<\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/statorials.org\/wp-content\/ql-cache\/quicklatex.com-129bc4568ffeb630fec0f50f68232d78_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\overline{x}=\\cfrac{98+70+125+89+75}{5}=91,4\" title=\"Rendered by QuickLaTeX.com\" height=\"39\" width=\"278\" style=\"vertical-align: -12px;\"><\/p>\n<\/p>\n<p> Art\u0131k \u00f6rnek ortalama de\u011ferini bildi\u011fimize g\u00f6re \u00f6rnek varyans form\u00fcl\u00fcn\u00fc uyguluyoruz:<\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/statorials.org\/wp-content\/ql-cache\/quicklatex.com-4d44545d85232885fa19f4c074ee8cfd_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"s^2=\\cfrac{\\displaystyle\\sum_{i=1}^n\\left(x_i-\\overline{x}\\right)^2}{n-1}\" title=\"Rendered by QuickLaTeX.com\" height=\"70\" width=\"143\" style=\"vertical-align: -12px;\"><\/p>\n<\/p>\n<p> \u00d6rnek verileri form\u00fclde de\u011fi\u015ftiririz:<\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/statorials.org\/wp-content\/ql-cache\/quicklatex.com-09aa21cb5332280eece6ee18282beaf7_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"s^2=\\cfrac{\\displaystyle (98-91,4)^2+(70-91,4)^2+(125-91,4)^2+(89-91,4)^2+(75-91,4)^2}{5-1}\" title=\"Rendered by QuickLaTeX.com\" height=\"42\" width=\"615\" style=\"vertical-align: -12px;\"><\/p>\n<\/p>\n<p> Geriye kalan tek \u015fey \u00f6rneklem varyans\u0131n\u0131 hesaplamak i\u00e7in gerekli i\u015flemleri \u00e7\u00f6zmektir:<\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/statorials.org\/wp-content\/ql-cache\/quicklatex.com-452d40b912c0189b2fda06f894e2b0da_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\begin{aligned}s^2&amp;=\\cfrac{6,6^2+(-21,4)^2+33,6^2+(-2,4)^2+(-16,4)^2}{4}\\\\[2ex]s^2&amp;=\\cfrac{43,56+457,96+1128,96+5,76+268,96}{4}\\\\[2ex]s^2&amp;= \\cfrac{1905,2}{4} \\\\[2ex]s^2&amp;=476,3 \\end{aligned}\" title=\"Rendered by QuickLaTeX.com\" height=\"208\" width=\"405\" style=\"vertical-align: 0px;\"><\/p>\n<\/p>\n<p> Bu nedenle analiz edilen numunenin varyans\u0131 476,3 \u20ac <sup>2&#8217;dir<\/sup> . \u00d6rnek varyans\u0131n birimlerinin istatistiksel verilerle ayn\u0131 birimler oldu\u011funu ancak kareleri oldu\u011funu unutmay\u0131n. <\/p>\n<h2 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"varianza-muestral-y-varianza-poblacional\"><\/span> \u00d6rnek varyans\u0131 ve pop\u00fclasyon varyans\u0131<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p> Bu b\u00f6l\u00fcmde \u00f6rnek varyans\u0131 ile pop\u00fclasyon varyans\u0131 aras\u0131ndaki fark\u0131 g\u00f6rece\u011fiz, \u00e7\u00fcnk\u00fc bunlar nas\u0131l ay\u0131rt edilece\u011fini bilmek \u00f6nemli olan iki istatistiksel kavramd\u0131r.<\/p>\n<p> \u0130statistikte <strong>pop\u00fclasyon varyans\u0131<\/strong> , hesaplaman\u0131n pop\u00fclasyonun t\u00fcm unsurlar\u0131 ile yap\u0131lmas\u0131yla elde edilen varyans iken, <strong>\u00f6rneklem varyans\u0131,<\/strong> hesaplaman\u0131n pop\u00fclasyondan yaln\u0131zca bir \u00f6rnek veri ile yap\u0131lmas\u0131yla elde edilen varyanst\u0131r.<\/p>\n<p> Matematiksel olarak <strong>\u00f6rneklem varyans\u0131 ile pop\u00fclasyon varyans\u0131 aras\u0131ndaki fark,<\/strong> onu hesaplamak i\u00e7in kullan\u0131lan form\u00fcl\u00fcn paydas\u0131d\u0131r. \u00d6rnek varyans\u0131n\u0131 hesaplamak i\u00e7in n-1&#8217;e b\u00f6l\u00fcnmesi gerekir. Ancak pop\u00fclasyon varyans\u0131 n&#8217;ye b\u00f6l\u00fcnerek hesaplan\u0131r.<\/p>\n<p> \u00d6rneklem varyans\u0131n\u0131 pop\u00fclasyon varyans\u0131ndan ay\u0131rmak i\u00e7in farkl\u0131 semboller kullan\u0131l\u0131r. \u00d6rneklem varyans\u0131n\u0131n sembol\u00fc <sup>s2&#8217;dir<\/sup> , pop\u00fclasyon varyans\u0131n\u0131n sembol\u00fc ise <sup>\u03c32&#8217;dir<\/sup> .<\/p>\n<p> Bu nedenle, \u00f6rneklem varyans\u0131 t\u00fcm pop\u00fclasyonun varyans\u0131n\u0131n ger\u00e7ek de\u011ferini tahmin etmek i\u00e7in kullan\u0131l\u0131r, \u00e7\u00fcnk\u00fc normalde bir pop\u00fclasyonun t\u00fcm de\u011ferlerini bilmek m\u00fcmk\u00fcn de\u011fildir ve bu nedenle istatistiksel parametrelerinin bir tahmininin yap\u0131lmas\u0131 gerekir. . <\/p>\n<div style=\"background-color:#FFFDE7; padding-top: 10px; padding-bottom: 10px; padding-right: 20px; padding-left: 30px; border: 2.5px dashed #FFB74D; border-radius:20px;\"> <span style=\"color:#ff951b\">\u27a4<\/span> <strong>Bak\u0131n\u0131z:<\/strong> <a href=\"https:\/\/statorials.org\/tr\/varyans\/\">N\u00fcfus farkl\u0131l\u0131\u011f\u0131<\/a> <\/div>\n<h2 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"calculadora-de-la-varianza-muestral\"><\/span> Bo\u015fluk Hesaplay\u0131c\u0131 \u00d6rne\u011fi<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p> \u00d6rnek varyans\u0131n\u0131 hesaplamak i\u00e7in bir \u00f6rne\u011fin verilerini a\u015fa\u011f\u0131daki hesaplay\u0131c\u0131ya girin. Veriler bir bo\u015flukla ayr\u0131lmal\u0131 ve ondal\u0131k ay\u0131r\u0131c\u0131 olarak nokta kullan\u0131larak girilmelidir. <\/p>\n<form action=\"\" method=\"post\"><textarea name=\"datos\" style=\"border:1.5px solid #4FC3F7; border-radius:15px;\" placeholder=\"8 2 1 5.7 6 ...\" required=\"\" oninvalid=\"this.setCustomValidity('Introduce los datos aqu\u00ed')\" oninput=\"this.setCustomValidity('')\"><\/textarea><\/p>\n<div style=\"text-align:center\"><input align=\"center\" style=\"border-radius:30px; margin: 20px\" type=\"submit\" name=\"submit\" value=\"\u00d6rnek varyans\u0131n\u0131 hesaplay\u0131n\"><\/div>\n<\/form>\n","protected":false},"excerpt":{"rendered":"<p>Bu makalede istatistiklerde \u00f6rneklem varyans\u0131n\u0131n ne oldu\u011fu ve \u00f6rneklem varyans\u0131 ile pop\u00fclasyon varyans\u0131 aras\u0131ndaki fark\u0131n ne oldu\u011fu a\u00e7\u0131klanmaktad\u0131r. B\u00f6ylece bir numunenin varyans\u0131n\u0131 nas\u0131l hesaplayaca\u011f\u0131n\u0131z\u0131, \u00e7\u00f6z\u00fclm\u00fc\u015f bir al\u0131\u015ft\u0131rmay\u0131 ve ayr\u0131ca herhangi bir numunenin varyans\u0131n\u0131 bulmak i\u00e7in \u00e7evrimi\u00e7i bir hesap makinesini bulacaks\u0131n\u0131z. \u00d6rnek varyans\u0131 nedir? \u00d6rnek varyans\u0131, istatistiksel bir \u00f6rne\u011fin de\u011fi\u015fkenli\u011fini g\u00f6steren bir da\u011f\u0131l\u0131m \u00f6l\u00e7\u00fcs\u00fcd\u00fcr. Numune varyans\u0131n\u0131 [&hellip;]<\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[14],"tags":[],"class_list":["post-267","post","type-post","status-publish","format-standard","hentry","category-istatistik"],"yoast_head":"<!-- This site is optimized with the Yoast SEO plugin v21.3 - https:\/\/yoast.com\/wordpress\/plugins\/seo\/ -->\n<title>\u25b7 \u00d6rnek varyans: nedir, form\u00fcl, \u00f6rnek ve hesap makinesi<\/title>\n<meta name=\"description\" content=\"Burada \u00f6rnek varyans\u0131n\u0131n ne oldu\u011funu, nas\u0131l hesapland\u0131\u011f\u0131n\u0131 (form\u00fcl), \u00e7al\u0131\u015f\u0131lm\u0131\u015f bir \u00f6rne\u011fi ve \u00e7evrimi\u00e7i \u00f6rnek varyans hesaplay\u0131c\u0131s\u0131n\u0131 bulacaks\u0131n\u0131z.\" \/>\n<meta name=\"robots\" content=\"index, follow, max-snippet:-1, max-image-preview:large, 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