{"id":136,"date":"2023-08-05T02:21:20","date_gmt":"2023-08-05T02:21:20","guid":{"rendered":"https:\/\/statorials.org\/tr\/chebyshevin-teoremi\/"},"modified":"2023-08-05T02:21:20","modified_gmt":"2023-08-05T02:21:20","slug":"chebyshevin-teoremi","status":"publish","type":"post","link":"https:\/\/statorials.org\/tr\/chebyshevin-teoremi\/","title":{"rendered":"Chebyshev&#39;in teoremi"},"content":{"rendered":"<p>Bu makale Chebyshev teoreminin ne oldu\u011funu a\u00e7\u0131klamaktad\u0131r. Burada Chebyshev teoremi form\u00fcl\u00fcn\u00fc, \u00e7\u00f6z\u00fclm\u00fc\u015f bir al\u0131\u015ft\u0131rmay\u0131 ve ayr\u0131ca \u00e7evrimi\u00e7i bir Chebyshev teoremi hesaplay\u0131c\u0131s\u0131n\u0131 bulacaks\u0131n\u0131z. Son olarak Chebyshev teoremi ile ampirik kural aras\u0131ndaki fark\u0131 g\u00f6sterir. <\/p>\n<h2 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"%c2%bfque-es-el-teorema-de-chebyshev\"><\/span> Chebyshev teoremi nedir?<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p> <strong>Chebyshev<\/strong> <strong>e\u015fitsizli\u011fi<\/strong> olarak da bilinen Chebyshev teoremi, rastgele bir de\u011fi\u015fkenin de\u011ferinin ortalamas\u0131ndan belirli bir mesafede bulunma olas\u0131l\u0131\u011f\u0131n\u0131 hesaplamak i\u00e7in kullan\u0131lan istatistiksel bir kurald\u0131r.<\/p>\n<p> Ba\u015fka bir deyi\u015fle istatistikte Chebyshev teoremi, bir de\u011ferin g\u00fcven aral\u0131\u011f\u0131 dahilinde olma olas\u0131l\u0131\u011f\u0131n\u0131 belirlemek i\u00e7in kullan\u0131l\u0131r.<\/p>\n<p> Ek olarak Chebyshev teoremi, b\u00fcy\u00fck say\u0131lar kanunu gibi di\u011fer istatistiksel teoremleri kan\u0131tlamak i\u00e7in de kullan\u0131l\u0131r.<\/p>\n<p> Chebyshev teoremi ilk olarak Frans\u0131z Ir\u00e9n\u00e9e-Jules Bienaym\u00e9 taraf\u0131ndan form\u00fcle edilmi\u015f olmas\u0131na ra\u011fmen, teorem 1867&#8217;de Rus Pafnuty Chebushev taraf\u0131ndan ortaya at\u0131ld\u0131\u011f\u0131 i\u00e7in bu \u015fekilde adland\u0131r\u0131lm\u0131\u015ft\u0131r.<\/p>\n<h2 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"formula-del-teorema-de-chebyshev\"><\/span> Chebyshev teoreminin form\u00fcl\u00fc<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p> Chebyshev teoremi, bir de\u011ferin ortalamadan <em>k<\/em> standart sapmaya e\u015fit olma olas\u0131l\u0131\u011f\u0131n\u0131n, bir eksi birin <em>k<\/em> kareye oran\u0131 kadar b\u00fcy\u00fck veya ona e\u015fit oldu\u011funu s\u00f6yl\u00fcyor.<\/p>\n<p> Bu nedenle <strong>Chebyshev teoreminin form\u00fcl\u00fc<\/strong> a\u015fa\u011f\u0131daki gibidir:<\/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-f13ff7c0d76ea2442ecd978dbfc457a4_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle P(\\mu-k\\sigma\\leq X \\leq \\mu+k\\sigma)\\geq 1 -\\frac{1}{k^2}\" title=\"Rendered by QuickLaTeX.com\" height=\"36\" width=\"271\" style=\"vertical-align: -12px;\"><\/p>\n<\/p>\n<p> Alt\u0131n<\/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-996ff7036e644e89f8ac379fa58d0cf7_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"X\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"16\" style=\"vertical-align: 0px;\"><\/p>\n<p> rastgele de\u011fi\u015fkenin de\u011feridir,<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/statorials.org\/wp-content\/ql-cache\/quicklatex.com-05d9eae892416bd34247a25207f8b718_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\mu\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"11\" style=\"vertical-align: -4px;\"><\/p>\n<p> de\u011fi\u015fkenin <a href=\"https:\/\/statorials.org\/tr\/aritmetik-ortalama\/\">aritmetik ortalamas\u0131<\/a> ,<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/statorials.org\/wp-content\/ql-cache\/quicklatex.com-eaaf379fee5e67946f3fedf5631047b1_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\sigma\" title=\"Rendered by QuickLaTeX.com\" height=\"8\" width=\"11\" style=\"vertical-align: 0px;\"><\/p>\n<p> <a href=\"https:\/\/statorials.org\/tr\/standart-sapma-veya-standart-sapma\/\">standart sapmas\u0131<\/a> ve<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/statorials.org\/wp-content\/ql-cache\/quicklatex.com-d42bc2203d6f76ad01b27ac9acc0bee1_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"k\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"9\" style=\"vertical-align: 0px;\"><\/p>\n<p> olas\u0131l\u0131\u011f\u0131n hesaplanaca\u011f\u0131 ortalamadan standart sapmalar\u0131n say\u0131s\u0131.<\/p>\n<p> Bu form\u00fcl\u00fcn yaln\u0131zca hesaplaman\u0131n yap\u0131ld\u0131\u011f\u0131 standart sapma say\u0131s\u0131 1&#8217;den b\u00fcy\u00fckse veya ba\u015fka bir deyi\u015fle <em>k<\/em> 1&#8217;den b\u00fcy\u00fckse kullan\u0131labilece\u011fini unutmay\u0131n.<\/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-76b1d6dbe5ee35b66ff33156e238ad73_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"k>1&#8243; title=&#8221;Rendered by QuickLaTeX.com&#8221; height=&#8221;14&#8243; width=&#8221;41&#8243; style=&#8221;vertical-align: -2px;&#8221;><\/p>\n<\/p>\n<p> \ud83d\udc49 <u style=\"text-decoration-color:#FF8A05;\">Olas\u0131l\u0131\u011f\u0131 hesaplamak i\u00e7in a\u015fa\u011f\u0131daki \u00e7evrimi\u00e7i Chebyshev Teoremi hesaplay\u0131c\u0131s\u0131n\u0131 kullanabilirsiniz.<\/u><\/p>\n<h2 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"ejemplo-del-teorema-de-chebyshev\"><\/span> Chebyshev teoreminin \u00f6rne\u011fi<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p> Chebyshev teoreminin tan\u0131m\u0131n\u0131 ve form\u00fcl\u00fcn\u00fcn ne oldu\u011funu g\u00f6rd\u00fckten sonra, kavram\u0131 daha iyi anlamak i\u00e7in bu istatistiksel teoremin \u00e7\u00f6z\u00fclm\u00fc\u015f bir \u00f6rne\u011fini burada bulabilirsiniz.<\/p>\n<ul>\n<li> Bir \u00fcniversitenin ders istatistiklerinde al\u0131nan notlar ortalamas\u0131 65, standart sapmas\u0131 10 olan bir da\u011f\u0131l\u0131mla tan\u0131mlan\u0131yorsa, \u00f6\u011frencilerin y\u00fczde ka\u00e7\u0131 50 ile 80 aras\u0131nda not alm\u0131\u015ft\u0131r?<\/li>\n<\/ul>\n<p> Bu sorunu \u00e7\u00f6zmek i\u00e7in Chebyshev teoreminin form\u00fcl\u00fcn\u00fc uygulamam\u0131z gerekiyor. Ancak \u00f6ncelikle 50 ve 80 de\u011ferlerinin de\u011fi\u015fkenin ortalamas\u0131ndan ka\u00e7 standart sapma oldu\u011funu belirlememiz gerekiyor, bunun i\u00e7in a\u015fa\u011f\u0131daki hesaplamay\u0131 yapmam\u0131z yeterli: <\/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-23a555d6493c0a0be742097fe319932d_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"k=\\cfrac{\\text{valor}-\\text{media}}{\\text{desviaci\\'on t\\'ipica}}\" title=\"Rendered by QuickLaTeX.com\" height=\"42\" width=\"165\" style=\"vertical-align: -16px;\"><\/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-edee4613c11e3eebd7e1158ad7f7b5c4_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"k=\\cfrac{50-65}{10}=-1,5\" title=\"Rendered by QuickLaTeX.com\" height=\"39\" width=\"155\" style=\"vertical-align: -12px;\"><\/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-7668ffc75752b84a5fdfe4de807efe0d_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"k=\\cfrac{80-65}{10}=1,5\" title=\"Rendered by QuickLaTeX.com\" height=\"39\" width=\"141\" style=\"vertical-align: -12px;\"><\/p>\n<\/p>\n<p> Dolay\u0131s\u0131yla 50 ve 80 de\u011ferleri s\u0131ras\u0131yla alt ve \u00fcst ortalamadan 1,5 standart sapmaya kar\u015f\u0131l\u0131k gelir. Bu nedenle Chebysheva teoreminin form\u00fcl\u00fcn\u00fc k=1,5 olarak kullan\u0131yoruz: <\/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-6dede501857215fec033905b64a01431_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle P(\\mu-k\\sigma\\leq X \\leq \\mu+k\\sigma)\\leq 1 -\\frac{1}{k^2}\" title=\"Rendered by QuickLaTeX.com\" height=\"36\" width=\"271\" style=\"vertical-align: -12px;\"><\/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-ace95ab1310d82dc6a6275b123556c07_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle P(\\mu-1,5\\sigma\\leq X \\leq \\mu+1,5\\sigma)\\leq 1 -\\frac{1}{1,5^2}\" title=\"Rendered by QuickLaTeX.com\" height=\"40\" width=\"319\" style=\"vertical-align: -16px;\"><\/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-aa011250591257ffebf651292398d016_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle P(50\\leq X \\leq 80)\\leq 0,5556\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"203\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<p> B\u00f6ylece \u00f6\u011frencilerin en az %55,56&#8217;s\u0131 50 ile 80 aras\u0131nda not ald\u0131. <\/p>\n<h2 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"calculadora-del-teorema-de-chebyshev\"><\/span> Chebyshev Teoremi Hesaplay\u0131c\u0131s\u0131<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p> S\u00f6z konusu de\u011ferler ile ortalama <em>(k)<\/em> aras\u0131ndaki standart sapma say\u0131s\u0131n\u0131 girin ve ard\u0131ndan \u201cHesapla\u201dya t\u0131klay\u0131n. Hesap makinesi daha sonra g\u00fcven aral\u0131\u011f\u0131n\u0131n minimum olas\u0131l\u0131\u011f\u0131n\u0131 d\u00f6nd\u00fcrecektir.<\/p>\n<p> Ondal\u0131k ay\u0131r\u0131c\u0131 olarak noktay\u0131 kullanarak standart sapma say\u0131s\u0131n\u0131 girmelisiniz. <\/p>\n<form action=\"\" method=\"post\">\n<ul style=\"color:#1C2C92;\">\n<li style=\"margin-bottom:15px\"><span style=\"color:#101010;font-weight: normal;\">\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/statorials.org\/wp-content\/ql-cache\/quicklatex.com-f4c08f6419fa469da3aa1c832f5c6b2b_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"k = \" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"28\" style=\"vertical-align: 0px;\"><\/p>\n<p><input name=\"datos\" style=\"border:1.5px solid #1C2C92; border-radius:5px;  padding:7px; color:#000000; background-color:#EBF5FB; width:60px\" placeholder=\"1.5\" required=\"\" oninvalid=\"this.setCustomValidity('Introduce el n\u00famero total de datos aqu\u00ed')\" oninput=\"this.setCustomValidity('')\"><\/span><\/li>\n<\/ul>\n<div style=\"text-align:center\"><input align=\"center\" style=\"font-size:105%; border-radius:30px; margin: 20px\" type=\"submit\" name=\"submit\" value=\"Hesaplamak\"><\/div>\n<\/form>\n<h2 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"el-teorema-de-chebyshev-y-la-regla-empirica\"><\/span> Chebyshev teoremi ve temel kural<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p> \u0130statistikte birbiriyle yak\u0131ndan ili\u015fkili iki kavram Chebyshev teoremi ve ampirik kurald\u0131r, \u00e7\u00fcnk\u00fc her ikisi de g\u00fcven aral\u0131klar\u0131n\u0131n olas\u0131l\u0131\u011f\u0131n\u0131 hesaplamak i\u00e7in kullan\u0131l\u0131r.<\/p>\n<p> <strong>Chebyshev teoremi ile ampirik kural aras\u0131ndaki fark<\/strong> , Chebyshev teoreminin her t\u00fcrl\u00fc da\u011f\u0131l\u0131mda kullan\u0131labilmesi, ampirik kural\u0131n ise yaln\u0131zca normal da\u011f\u0131l\u0131m i\u00e7in ge\u00e7erli olmas\u0131d\u0131r.<\/p>\n<p> Bu nedenle Chebyshev teoreminin kullan\u0131m\u0131 daha geni\u015ftir, ancak ampirik kural normal da\u011f\u0131l\u0131m i\u00e7in daha kesin sonu\u00e7lar sa\u011flar.<\/p>\n<p> Temel kural\u0131n tam olarak ne oldu\u011funu g\u00f6rmek i\u00e7in buray\u0131 t\u0131klay\u0131n: <\/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\/temel-kural\/\">genel kural<\/a><\/div>\n","protected":false},"excerpt":{"rendered":"<p>Bu makale Chebyshev teoreminin ne oldu\u011funu a\u00e7\u0131klamaktad\u0131r. Burada Chebyshev teoremi form\u00fcl\u00fcn\u00fc, \u00e7\u00f6z\u00fclm\u00fc\u015f bir al\u0131\u015ft\u0131rmay\u0131 ve ayr\u0131ca \u00e7evrimi\u00e7i bir Chebyshev teoremi hesaplay\u0131c\u0131s\u0131n\u0131 bulacaks\u0131n\u0131z. Son olarak Chebyshev teoremi ile ampirik kural aras\u0131ndaki fark\u0131 g\u00f6sterir. Chebyshev teoremi nedir? Chebyshev e\u015fitsizli\u011fi olarak da bilinen Chebyshev teoremi, rastgele bir de\u011fi\u015fkenin de\u011ferinin ortalamas\u0131ndan belirli bir mesafede bulunma olas\u0131l\u0131\u011f\u0131n\u0131 hesaplamak i\u00e7in kullan\u0131lan [&hellip;]<\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[12],"tags":[],"class_list":["post-136","post","type-post","status-publish","format-standard","hentry","category-olasilik"],"yoast_head":"<!-- This site is optimized with the Yoast SEO plugin v21.3 - https:\/\/yoast.com\/wordpress\/plugins\/seo\/ -->\n<title>\u25b7 Chebyshev teoremi: form\u00fcl, \u00f6rnek ve hesap makinesi<\/title>\n<meta name=\"description\" content=\"Burada Chebyshev teoreminin (veya Chebyshev e\u015fitsizli\u011finin), form\u00fcl\u00fcn\u00fcn, somut bir \u00f6rne\u011finin ve Chebyshev teoremi hesaplay\u0131c\u0131s\u0131n\u0131n 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