{"id":265,"date":"2023-08-03T10:12:31","date_gmt":"2023-08-03T10:12:31","guid":{"rendered":"https:\/\/statorials.org\/tr\/nufus-anlamina-gelir\/"},"modified":"2023-08-03T10:12:31","modified_gmt":"2023-08-03T10:12:31","slug":"nufus-anlamina-gelir","status":"publish","type":"post","link":"https:\/\/statorials.org\/tr\/nufus-anlamina-gelir\/","title":{"rendered":"N\u00fcfus anlam\u0131na gelir"},"content":{"rendered":"<p>Bu makale istatistikte n\u00fcfusun ne anlama geldi\u011fini a\u00e7\u0131klamaktad\u0131r. Ayn\u0131 \u015fekilde pop\u00fclasyon ortalamas\u0131 form\u00fcl\u00fcn\u00fcn ne oldu\u011funu, pop\u00fclasyon ortalamas\u0131n\u0131n g\u00fcven aral\u0131\u011f\u0131n\u0131n nas\u0131l hesapland\u0131\u011f\u0131n\u0131 ve ayr\u0131ca pop\u00fclasyon ortalamas\u0131 ile &#8216;\u00f6rneklem&#8217; ortalamas\u0131 aras\u0131ndaki fark\u0131n ne oldu\u011funu \u00f6\u011freneceksiniz. <\/p>\n<h2 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"%c2%bfque-es-la-media-poblacional\"><\/span> N\u00fcfus ortalamas\u0131 nedir?<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p> <strong>N\u00fcfus ortalamas\u0131,<\/strong> istatistiksel pop\u00fclasyonun t\u00fcm \u00f6\u011felerinin aritmetik ortalamas\u0131d\u0131r. Bu nedenle pop\u00fclasyon ortalamas\u0131n\u0131 hesaplamak i\u00e7in t\u00fcm pop\u00fclasyon de\u011ferlerinin toplanmas\u0131 ve ard\u0131ndan pop\u00fclasyondaki toplam element say\u0131s\u0131na b\u00f6l\u00fcnmesi gerekir.<\/p>\n<p> Pop\u00fclasyon ortalamas\u0131n\u0131n sembol\u00fc Yunanca \u03bc harfidir.<\/p>\n<p> Benzer \u015fekilde pop\u00fclasyon ortalamas\u0131 da bir pop\u00fclasyonu temsil eden de\u011fi\u015fkenin <a href=\"https:\/\/statorials.org\/tr\/matematiksel-beklenti-veya-beklenen-deger\/\">beklenen de\u011feri<\/a> olarak tan\u0131mlanabilir. <\/p>\n<h2 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"como-calcular-la-media-poblacional\"><\/span> N\u00fcfus ortalamas\u0131 nas\u0131l hesaplan\u0131r<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p> N\u00fcfus ortalamas\u0131n\u0131n tan\u0131m\u0131n\u0131 g\u00f6rd\u00fckten sonra, anlam\u0131n\u0131 daha iyi anlamak i\u00e7in n\u00fcfus ortalamas\u0131n\u0131n nas\u0131l hesapland\u0131\u011f\u0131na bakal\u0131m.<\/p>\n<p> \u0130statistiksel pop\u00fclasyondaki t\u00fcm de\u011ferler biliniyorsa, pop\u00fclasyon ortalamas\u0131n\u0131 hesaplamak i\u00e7in aritmetik ortalama form\u00fcl\u00fc basit\u00e7e uygulanmal\u0131d\u0131r. Yani bu durumda n\u00fcfus ortalamas\u0131n\u0131 hesaplamak i\u00e7in t\u00fcm n\u00fcfus de\u011ferlerini toplay\u0131p ard\u0131ndan toplam veri say\u0131s\u0131na b\u00f6lmemiz gerekiyor.<\/p>\n<p> Dolay\u0131s\u0131yla, pop\u00fclasyonun t\u00fcm unsurlar\u0131n\u0131n de\u011ferini biliyorsak, <strong>pop\u00fclasyon ortalamas\u0131n\u0131 hesaplama 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-0a76fc9639a07bbae5a5f269110f9d7b_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle\\mu=\\frac{\\displaystyle \\sum_{i=1}^N x_i}{N}=\\frac{x_1+x_2+\\dots +x_N}{N}\" title=\"Rendered by QuickLaTeX.com\" height=\"73\" width=\"253\" style=\"vertical-align: -12px;\"><\/p>\n<\/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\/aritmetik-ortalama\/\">Aritmetik ortalamay\u0131 hesaplama \u00f6rne\u011fi<\/a><\/div>\n<p> Ancak genel olarak t\u00fcm pop\u00fclasyon de\u011ferleri bilinmedi\u011finden, normalde pop\u00fclasyon ortalamas\u0131n\u0131n de\u011feri <a href=\"https:\/\/statorials.org\/tr\/aralik-tahmini\/\">aral\u0131klarla tahmin edilir<\/a> . <\/p>\n<h2 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"intervalo-de-confianza-para-la-media-poblacional\"><\/span> N\u00fcfus ortalamas\u0131 i\u00e7in g\u00fcven aral\u0131\u011f\u0131<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p> Uygulamada, bir pop\u00fclasyondaki t\u00fcm bireyleri incelemek imkans\u0131zd\u0131r, bu nedenle normal olarak pop\u00fclasyonun rastgele bir \u00f6rne\u011fi se\u00e7ilir ve bu \u00f6rneklemin de\u011ferlerine dayal\u0131 olarak pop\u00fclasyon ortalamas\u0131n\u0131n de\u011ferinin bir tahmini yap\u0131l\u0131r. Daha kesin olarak, t\u00fcm pop\u00fclasyonun ortalamas\u0131n\u0131n b\u00fcy\u00fck olas\u0131l\u0131kla bulunaca\u011f\u0131 bir aral\u0131k hesapl\u0131yoruz; bu aral\u0131\u011fa pop\u00fclasyon ortalamas\u0131n\u0131n g\u00fcven aral\u0131\u011f\u0131 denir.<\/p>\n<p> Pop\u00fclasyon ortalamas\u0131 i\u00e7in <a href=\"https:\/\/statorials.org\/tr\/guven-araligi\/\">g\u00fcven aral\u0131\u011f\u0131,<\/a> Z <sub>\u03b1\/2<\/sub> de\u011ferinin standart sapma (\u03c3) ile \u00e7arp\u0131lmas\u0131 ve numune y\u00fcksekli\u011finin (n) karek\u00f6k\u00fcne b\u00f6l\u00fcnmesiyle numune ortalamas\u0131ndan toplan\u0131p \u00e7\u0131kar\u0131larak hesaplan\u0131r. Bu nedenle pop\u00fclasyon ortalamas\u0131 i\u00e7in g\u00fcven aral\u0131\u011f\u0131n\u0131 hesaplama form\u00fcl\u00fc \u015f\u00f6yledir:<\/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-985a374c69b468deb3d6d159fcbe6de5_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle \\left(\\overline{x}-z_{\\alpha\/2}\\cdot \\frac{\\sigma}{\\sqrt{n}} \\ , \\ \\overline{x}+z_{\\alpha\/2}\\cdot \\frac{\\sigma}{\\sqrt{n}} \\right)\" title=\"Rendered by QuickLaTeX.com\" height=\"43\" width=\"251\" style=\"vertical-align: -17px;\"><\/p>\n<\/p>\n<p> Pop\u00fclasyon varyans\u0131 bilindi\u011finde yukar\u0131daki form\u00fcl kullan\u0131l\u0131r. Bununla birlikte, en yayg\u0131n durum olan pop\u00fclasyon varyans\u0131 bilinmiyorsa, <strong>ortalaman\u0131n g\u00fcven aral\u0131\u011f\u0131 a\u015fa\u011f\u0131daki form\u00fcl kullan\u0131larak hesaplan\u0131r:<\/strong><\/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-e40e2c40fbfe4f5aa96c21ff979aae5a_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle \\left(\\overline{x}-t_{\\alpha\/2}\\cdot \\frac{s}{\\sqrt{n}} \\ , \\ \\overline{x}+t_{\\alpha\/2}\\cdot \\frac{s}{\\sqrt{n}} \\right)\" title=\"Rendered by QuickLaTeX.com\" height=\"43\" width=\"247\" style=\"vertical-align: -17px;\"><\/p>\n<\/p>\n<p style=\"margin-bottom:5px\"> Alt\u0131n:<\/p>\n<ul style=\"color:#FF8A05; font-weight: bold;\">\n<li style=\"margin-bottom:5px\">\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:5px\">\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/statorials.org\/wp-content\/ql-cache\/quicklatex.com-33bd5d525ddf37600aef97b0c8c08f94_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"t_{\\alpha\/2}\" title=\"Rendered by QuickLaTeX.com\" height=\"20\" width=\"29\" style=\"vertical-align: -8px;\"><\/p>\n<p> \u03b1\/2 olas\u0131l\u0131kla n-1 serbestlik derecesinin \u00d6\u011frenci t da\u011f\u0131l\u0131m\u0131n\u0131n de\u011feridir. B\u00fcy\u00fck \u00f6rneklem b\u00fcy\u00fckl\u00fckleri ve %95 g\u00fcven d\u00fczeyi i\u00e7in genellikle 1,96&#8217;ya, %99 g\u00fcven d\u00fczeyi i\u00e7in ise genellikle 2,576&#8217;ya yak\u0131nd\u0131r.<\/li>\n<li style=\"margin-bottom:5px\">\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/statorials.org\/wp-content\/ql-cache\/quicklatex.com-1edc883862ceed1a21913f60358e31d8_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"s\" title=\"Rendered by QuickLaTeX.com\" height=\"8\" width=\"8\" style=\"vertical-align: 0px;\"><\/p>\n<p> \u00f6rnek standart sapmas\u0131d\u0131r.<\/li>\n<li style=\"margin-bottom:5px\">\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> \u00f6rneklem b\u00fcy\u00fckl\u00fc\u011f\u00fcd\u00fcr. <\/li>\n<\/ul>\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\/ortalama-icin-guven-araligi\/\">Pop\u00fclasyon ortalamas\u0131 i\u00e7in g\u00fcven aral\u0131\u011f\u0131n\u0131 hesaplama \u00f6rne\u011fi<\/a> <\/div>\n<h2 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"media-poblacional-y-media-muestral\"><\/span> N\u00fcfus ortalamas\u0131 ve \u00f6rnek ortalamas\u0131<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p> Son olarak, \u00f6zet olarak, bu iki istatistiksel kavram\u0131n net olmas\u0131 i\u00e7in pop\u00fclasyon ortalamas\u0131 ile \u00f6rnek ortalamas\u0131 aras\u0131ndaki farklar\u0131 g\u00f6zden ge\u00e7irece\u011fiz.<\/p>\n<p> <strong>Pop\u00fclasyon ortalamas\u0131 ile \u00f6rnek ortalamas\u0131 aras\u0131ndaki fark,<\/strong> ortalaman\u0131n hesapland\u0131\u011f\u0131 de\u011fer aral\u0131\u011f\u0131d\u0131r. Pop\u00fclasyon ortalamas\u0131 t\u00fcm istatistiksel pop\u00fclasyonun ortalamas\u0131d\u0131r, \u00f6rnek ortalamas\u0131 ise pop\u00fclasyonun bir \u00f6rne\u011finin ortalamas\u0131d\u0131r.<\/p>\n<p> Ayr\u0131ca pop\u00fclasyon ortalamas\u0131n\u0131 \u00f6rnek ortalamas\u0131ndan ay\u0131rt etmek i\u00e7in farkl\u0131 sembollerle temsil edilirler. N\u00fcfus anlam\u0131na gelen sembol<\/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-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> , di\u011fer taraftan, \u00f6rnek ortalaman\u0131n sembol\u00fc<\/p>\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> .<\/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-f812349b186d7c1a8abdd1d2807f0a60_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\begin{array}{c}\\mu =\\text{Media poblacional}\\\\[2ex]\\overline{x} = \\text{Media muestral}\\end{array}\" title=\"Rendered by QuickLaTeX.com\" height=\"51\" width=\"177\" style=\"vertical-align: 0px;\"><\/p>\n<\/p>\n<p> Bu iki ortalama t\u00fcr\u00fc aras\u0131ndaki farklar konusunda h\u00e2l\u00e2 \u015f\u00fcpheleriniz varsa veya \u00f6rneklem ortalamas\u0131n\u0131n hesaplanmas\u0131 hakk\u0131nda daha fazla bilgi edinmek istiyorsan\u0131z a\u015fa\u011f\u0131daki makaleye ba\u015fvurabilirsiniz: <\/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\/ornek-ortalama\/\">\u00d6rnek ne anlama geliyor?<\/a><\/div>\n","protected":false},"excerpt":{"rendered":"<p>Bu makale istatistikte n\u00fcfusun ne anlama geldi\u011fini a\u00e7\u0131klamaktad\u0131r. Ayn\u0131 \u015fekilde pop\u00fclasyon ortalamas\u0131 form\u00fcl\u00fcn\u00fcn ne oldu\u011funu, pop\u00fclasyon ortalamas\u0131n\u0131n g\u00fcven aral\u0131\u011f\u0131n\u0131n nas\u0131l hesapland\u0131\u011f\u0131n\u0131 ve ayr\u0131ca pop\u00fclasyon ortalamas\u0131 ile &#8216;\u00f6rneklem&#8217; ortalamas\u0131 aras\u0131ndaki fark\u0131n ne oldu\u011funu \u00f6\u011freneceksiniz. N\u00fcfus ortalamas\u0131 nedir? N\u00fcfus ortalamas\u0131, istatistiksel pop\u00fclasyonun t\u00fcm \u00f6\u011felerinin aritmetik ortalamas\u0131d\u0131r. Bu nedenle pop\u00fclasyon ortalamas\u0131n\u0131 hesaplamak i\u00e7in t\u00fcm pop\u00fclasyon de\u011ferlerinin toplanmas\u0131 ve [&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-265","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 N\u00fcfus ortalamas\u0131 - Olas\u0131l\u0131klar ve istatistikler<\/title>\n<meta name=\"description\" content=\"Bu makale istatistikte n\u00fcfusun ne anlama geldi\u011fini a\u00e7\u0131klamaktad\u0131r. 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