{"id":79,"date":"2023-08-05T17:33:30","date_gmt":"2023-08-05T17:33:30","guid":{"rendered":"https:\/\/statorials.org\/tr\/standart-sapma-veya-standart-sapma\/"},"modified":"2023-08-05T17:33:30","modified_gmt":"2023-08-05T17:33:30","slug":"standart-sapma-veya-standart-sapma","status":"publish","type":"post","link":"https:\/\/statorials.org\/tr\/standart-sapma-veya-standart-sapma\/","title":{"rendered":"Standart sapma (veya standart sapma)"},"content":{"rendered":"<p>Bu makalede standart sapma olarak da adland\u0131r\u0131lan standart sapman\u0131n ne oldu\u011fu a\u00e7\u0131klanmaktad\u0131r. Herhangi bir veri \u00f6rne\u011finin standart sapmas\u0131n\u0131 bulmak i\u00e7in standart sapman\u0131n nas\u0131l hesaplanaca\u011f\u0131n\u0131, ad\u0131m ad\u0131m pratik bir \u00f6rne\u011fi ve \u00e7evrimi\u00e7i hesap makinesini \u00f6\u011freneceksiniz. <\/p>\n<h2 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"%c2%bfque-es-la-desviacion-estandar-o-desviacion-tipica\"><\/span> Standart sapma (veya standart sapma) nedir?<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p> <strong>Standart sapma olarak da adland\u0131r\u0131lan standart sapma<\/strong> <strong>,<\/strong> istatistiksel da\u011f\u0131l\u0131m\u0131n bir \u00f6l\u00e7\u00fcs\u00fcd\u00fcr. Ba\u015fka bir deyi\u015fle standart sapma, bir dizi istatistiksel verinin da\u011f\u0131l\u0131m\u0131n\u0131 g\u00f6steren bir de\u011ferdir.<\/p>\n<p> Bu nedenle <strong>standart sapma (veya standart sapma), bir pop\u00fclasyonun veya istatistiksel numunenin da\u011f\u0131l\u0131m\u0131n\u0131 \u00f6l\u00e7mek i\u00e7in kullan\u0131l\u0131r.<\/strong> Bir veri serisinin standart sapmas\u0131 ne kadar b\u00fcy\u00fck olursa, veriler o kadar da\u011f\u0131n\u0131k olur. Yorum ters y\u00f6nde de yap\u0131labilir, e\u011fer standart sapma d\u00fc\u015f\u00fckse bu, genel olarak verilerin ortalamaya \u00e7ok yak\u0131n oldu\u011fu anlam\u0131na gelir.<\/p>\n<p> Bir pop\u00fclasyon \u00fczerinden standart veya tipik sapma hesaplan\u0131rken <strong>standart sapman\u0131n sembol\u00fc<\/strong> Yunanca sigma (\u03c3) harfidir. Ancak \u00f6rnek standart sapmas\u0131 s\u00f6z konusu oldu\u011funda istatistiksel \u00f6l\u00e7\u00fcm\u00fc temsil etmek i\u00e7in s harfi kullan\u0131l\u0131r.<\/p>\n<p> Baz\u0131 istatistik ve olas\u0131l\u0131k kitaplar\u0131nda standart sapmaya standart sapma da denir. <\/p>\n<h2 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"formula-de-la-desviacion-estandar-o-desviacion-tipica\"><\/span> Standart sapma (veya standart sapma) form\u00fcl\u00fc<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p> Standart sapma (veya standart sapma), veri serisindeki sapmalar\u0131n karelerinin toplam\u0131n\u0131n karek\u00f6k\u00fcn\u00fcn toplam g\u00f6zlem say\u0131s\u0131na b\u00f6l\u00fcnmesine e\u015fittir.<\/p>\n<p> Bu nedenle <strong>standart sapmay\u0131 (veya standart sapmay\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\/ecart-type-ecart-type.png\" alt=\"standart sapma, standart sapma\" class=\"wp-image-1652\" width=\"334\" height=\"334\" srcset=\"\" sizes=\"auto, \"><\/figure>\n<p> \ud83d\udc49Herhangi <u style=\"text-decoration-color:#FF8A05;\">bir veri setinin standart sapmas\u0131n\u0131 hesaplamak i\u00e7in a\u015fa\u011f\u0131daki hesap makinesini kullanabilirsiniz.<\/u><\/p>\n<p> Sonu\u00e7 olarak, bir veri k\u00fcmesinin standart sapmas\u0131n\u0131 bulmak i\u00e7in t\u00fcm sapmalar\u0131 (veri noktas\u0131 ile aritmetik ortalama aras\u0131ndaki fark olarak tan\u0131mlan\u0131r) hesaplaman\u0131z, sapmalar\u0131 ikiye \u00e7\u0131karman\u0131z, hepsini toplaman\u0131z ve ard\u0131ndan say\u0131ya b\u00f6lmeniz gerekir. Toplam. veri say\u0131s\u0131n\u0131 ve son olarak karek\u00f6k\u00fcn\u00fc al\u0131n. <\/p>\n<h2 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"ejemplo-de-desviacion-estandar-o-desviacion-tipica\"><\/span> Standart sapma \u00f6rne\u011fi (veya standart sapma)<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p> A\u015fa\u011f\u0131da standart sapman\u0131n (veya tipik sapman\u0131n) tan\u0131m\u0131 g\u00f6z \u00f6n\u00fcne al\u0131nd\u0131\u011f\u0131nda, bir veri serisinin standart sapmas\u0131n\u0131n nas\u0131l hesapland\u0131\u011f\u0131n\u0131 g\u00f6rebilmeniz i\u00e7in ad\u0131m ad\u0131m bir \u00f6rnek verilmi\u015ftir.<\/p>\n<ul>\n<li> A\u015fa\u011f\u0131daki de\u011ferlerin standart sapmas\u0131n\u0131 hesaplay\u0131n: 3, 6, 2, 9, 4.<\/li>\n<\/ul>\n<p> Yapmam\u0131z gereken ilk \u015fey \u00f6rnek ortalamas\u0131n\u0131 belirlemektir. Bunu yapmak i\u00e7in t\u00fcm verileri toplay\u0131p toplam g\u00f6zlem say\u0131s\u0131na b\u00f6l\u00fcyoruz ki bu da be\u015ftir:<\/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-29d93bdafc53afa6ed1e684cdf0ed8cf_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\overline{x}=\\cfrac{3+6+2+9+4}{5}=4,8\" title=\"Rendered by QuickLaTeX.com\" height=\"38\" width=\"216\" style=\"vertical-align: -12px;\"><\/p>\n<\/p>\n<p> \u015eimdi standart sapma form\u00fcl\u00fcn\u00fc 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-94d7422dac6b694a42e1dcd6485e681e_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle\\sigma=\\sqrt{\\frac{\\displaystyle\\sum_{i=1}^N(x_i-\\overline{x})^2}{N}}\" title=\"Rendered by QuickLaTeX.com\" height=\"86\" width=\"152\" style=\"vertical-align: -16px;\"><\/p>\n<\/p>\n<p> 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-049d3262c2c56e3c39cae6c520dd2e67_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle\\sigma =\\sqrt{\\frac{(3-4,8)^2+(6-4,8)^2+(2-4,8)^2+(9-4,8)^2+(4-4,8)^2}{5}}\" title=\"Rendered by QuickLaTeX.com\" height=\"43\" width=\"531\" style=\"vertical-align: -13px;\"><\/p>\n<\/p>\n<p> Son olarak standart sapmay\u0131 hesapl\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-d52b5396ff383310226cf152a9bf87ea_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\begin{aligned}\\displaystyle\\sigma &amp; = \\sqrt{\\frac{(-1,8)^2+1,2^2+(-2,8)^2+4,2^2+(-0,8)^2}{5}}\\\\[2ex]&amp;=\\sqrt{\\frac{3,24+1,44+7,84+17,64+0,64}{5}}\\\\[2ex]&amp;= \\sqrt{\\frac{30,8}{5}}=\\sqrt{6,16}=2,48 \\end{aligned}\" title=\"Rendered by QuickLaTeX.com\" height=\"173\" width=\"392\" style=\"vertical-align: 0px;\"><\/p>\n<\/p>\n<h2 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"calculadora-de-la-desviacion-estandar-o-desviacion-tipica\"><\/span> Standart Sapma (veya Standart Sapma) Hesaplay\u0131c\u0131<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p> Standart sapmas\u0131n\u0131 (veya standart sapmas\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<form action=\"\" method=\"post\"><textarea name=\"datos\" style=\"border:1.5px solid #4FC3F7; border-radius:15px;\" placeholder=\"3 6 2 9 0.7 4 ...\" 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=\"Standart sapmay\u0131 hesaplay\u0131n\"><\/div>\n<\/form>\n<h2 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"desviacion-estandar-o-tipica-para-datos-agrupados\"><\/span> Grupland\u0131r\u0131lm\u0131\u015f veriler i\u00e7in standart (veya tipik) sapma<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p> <strong>Aral\u0131klara g\u00f6re grupland\u0131r\u0131lm\u0131\u015f verilerin standart sapmas\u0131n\u0131 (veya standart sapmas\u0131n\u0131) hesaplamak i\u00e7in<\/strong> a\u015fa\u011f\u0131daki ad\u0131mlar izlenmelidir:<\/p>\n<ol style=\"color:#FF8A05; font-weight: bold;\">\n<li style=\"margin-bottom:12px\"> <span style=\"color:#101010;font-weight: normal;\">Grupland\u0131r\u0131lm\u0131\u015f verilerin ortalamas\u0131n\u0131 bulun.<\/span><\/li>\n<li style=\"margin-bottom:12px\"> <span style=\"color:#101010;font-weight: normal;\">Grupland\u0131r\u0131lm\u0131\u015f verilerin sapmalar\u0131n\u0131 hesaplay\u0131n.<\/span><\/li>\n<li style=\"margin-bottom:12px\"> <span style=\"color:#101010;font-weight: normal;\">Her bo\u015flu\u011fun karesini al\u0131n.<\/span><\/li>\n<li style=\"margin-bottom:12px\"> <span style=\"color:#101010;font-weight: normal;\">\u00d6nceki her sonucu aral\u0131\u011f\u0131n\u0131n frekans\u0131yla \u00e7arp\u0131n.<\/span><\/li>\n<li style=\"margin-bottom:12px\"> <span style=\"color:#101010;font-weight: normal;\">\u00d6nceki ad\u0131mda elde edilen t\u00fcm de\u011ferlerin toplam\u0131n\u0131 ekleyin.<\/span><\/li>\n<li style=\"margin-bottom:12px\"> <span style=\"color:#101010;font-weight: normal;\">Toplam g\u00f6zlem say\u0131s\u0131na b\u00f6l\u00fcn.<\/span><\/li>\n<li> <span style=\"color:#101010;font-weight: normal;\">\u00d6nceki de\u011ferin karek\u00f6k\u00fcn\u00fc al\u0131n. Ortaya \u00e7\u0131kan say\u0131, grupland\u0131r\u0131lm\u0131\u015f verilerin standart sapmas\u0131d\u0131r.<\/span><\/li>\n<\/ol>\n<p> Sonu\u00e7 olarak, aral\u0131klara g\u00f6re grupland\u0131r\u0131lm\u0131\u015f verilerin standart sapmas\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-6a435319a8eafa0c374dc44e85709b4c_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle\\sigma=\\sqrt{\\frac{\\displaystyle\\sum_{i=1}^N\\left(x_i-\\overline{x}\\right)^2\\cdot f_i }{N}}\" title=\"Rendered by QuickLaTeX.com\" height=\"86\" width=\"182\" style=\"vertical-align: -16px;\"><\/p>\n<\/p>\n<p> Normalde yukar\u0131daki form\u00fcl kullan\u0131lsa da ayn\u0131 sonu\u00e7 elde edildi\u011fi i\u00e7in a\u015fa\u011f\u0131daki cebirsel ifade de kullan\u0131labilir:<\/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-b2a1493ab90f08b0bc32dfa9a4108590_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle\\sigma=\\sqrt{\\frac{\\displaystyle\\sum_{i=1}^n x_i^2\\cdot f_i }{N}-\\overline{x}^2}\" title=\"Rendered by QuickLaTeX.com\" height=\"85\" width=\"170\" style=\"vertical-align: -17px;\"><\/p>\n<\/p>\n<p> Bunun nas\u0131l yap\u0131ld\u0131\u011f\u0131n\u0131 g\u00f6rebilirsiniz, a\u015fa\u011f\u0131da aral\u0131klara g\u00f6re grupland\u0131r\u0131lm\u0131\u015f verilerin standart sapmas\u0131na ili\u015fkin ad\u0131m ad\u0131m bir al\u0131\u015ft\u0131rma bulunmaktad\u0131r. Daha kesin olarak a\u015fa\u011f\u0131daki istatistiksel verilerin standart sapmas\u0131 hesaplanacakt\u0131r: <\/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\/exemple-de-donnees-regroupees-en-intervalles.png\" alt=\"aral\u0131klarla grupland\u0131r\u0131lm\u0131\u015f verilere \u00f6rnek\" class=\"wp-image-1679\" width=\"244\" height=\"180\" srcset=\"\" sizes=\"auto, \"><\/figure>\n<p> Aritmetik ortalamay\u0131 hesaplamak i\u00e7in \u00f6ncelikle her aral\u0131\u011f\u0131n s\u0131n\u0131f puan\u0131n\u0131 frekans\u0131yla \u00e7arp\u0131yoruz: <\/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\/calcul-de-table-de-donnees.png\" alt=\"\" class=\"wp-image-1682\" width=\"326\" height=\"180\" srcset=\"\" sizes=\"auto, \"><\/figure>\n<p> Yani grupland\u0131r\u0131lm\u0131\u015f verilerin ortalamas\u0131 \u015f\u00f6yle olacakt\u0131r:<\/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-ce59b9a32c04cd7349126ce0539db196_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\overline{x}=\\cfrac{\\displaystyle\\sum_{i=1}^n x_i\\cdot f_i}{N}=\\cfrac{46200}{100}=462\" title=\"Rendered by QuickLaTeX.com\" height=\"70\" width=\"229\" style=\"vertical-align: -12px;\"><\/p>\n<\/p>\n<p> Art\u0131k ortalaman\u0131n de\u011ferini bildi\u011fimize g\u00f6re, a\u015fa\u011f\u0131daki \u00fc\u00e7 s\u00fctunu veri tablosuna eklememiz gerekiyor: <\/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\/exercice-resolu-ecart-type-donnees-groupees.png\" alt=\"Grupland\u0131r\u0131lm\u0131\u015f veriler i\u00e7in standart sapma veya standart sapman\u0131n \u00e7\u00f6z\u00fcml\u00fc al\u0131\u015ft\u0131rmas\u0131\" class=\"wp-image-1683\" width=\"606\" height=\"180\" srcset=\"\" sizes=\"auto, \"><\/figure>\n<p> Daha sonra grupland\u0131r\u0131lm\u0131\u015f verilerin standart sapmas\u0131, son s\u00fctunun toplam\u0131n\u0131n karek\u00f6k\u00fcn\u00fcn toplam g\u00f6zlem say\u0131s\u0131na b\u00f6l\u00fcnmesinin sonucu olacakt\u0131r: <\/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-71f6868fe660a5b263f7dba58b823e4d_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle\\sigma=\\sqrt{\\frac{\\displaystyle\\sum_{i=1}^N\\left(x_i-\\overline{x}\\right)^2\\cdot f_i }{N}}=\\sqrt{\\frac{1445600}{100}}=120,23\" title=\"Rendered by QuickLaTeX.com\" height=\"86\" width=\"365\" style=\"vertical-align: -16px;\"><\/p>\n<\/p>\n<h2 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"desviacion-estandar-o-tipica-y-varianza\"><\/span> Standart (veya tipik) sapma ve varyans<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p> <strong>Standart sapma (veya tipik sapma) ile varyans aras\u0131ndaki ili\u015fki,<\/strong> standart sapman\u0131n varyans\u0131n karek\u00f6k\u00fc olmas\u0131d\u0131r.<\/p>\n<p> Yani bir veri setinin varyans de\u011ferini biliyorsak karek\u00f6k\u00fcn\u00fc alarak standart sapmay\u0131 kolayl\u0131kla hesaplayabiliriz. Ya da tam tersi, e\u011fer standart sapmay\u0131 biliyorsak, de\u011ferin karesini alarak varyans\u0131 bulabiliriz.<\/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-0c71ab111d7c483a2ad04cb5e9618da4_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"Var(X)=\\sigma^2\" title=\"Rendered by QuickLaTeX.com\" height=\"20\" width=\"103\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<p> Asl\u0131nda varyans, karesi al\u0131nm\u0131\u015f standart sapma sembol\u00fc kullan\u0131larak basit bir \u015fekilde temsil edilebilir. Bu nedenle pop\u00fclasyon varyans\u0131n\u0131n sembol\u00fc sigma karedir (\u03c3 <sup>2<\/sup> ) ve \u00f6rneklem varyans\u0131n\u0131n sembol\u00fc s karedir (s <sup>2<\/sup> ).<\/p>\n<p> Ek olarak, standart sapma ve varyans kavramlar\u0131 da benzer bir yoruma sahiptir \u00e7\u00fcnk\u00fc her ikisi de bir dizi istatistiksel verinin da\u011f\u0131l\u0131m\u0131n\u0131 g\u00f6sterir. <\/p>\n<h2 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"propiedades-de-la-desviacion-estandar-o-desviacion-tipica\"><\/span> Standart sapman\u0131n (veya standart sapman\u0131n) \u00f6zellikleri<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p> Standart sapma a\u015fa\u011f\u0131daki \u00f6zelliklere sahiptir:<\/p>\n<ul>\n<li> Bir veri \u00f6rne\u011finin standart sapmas\u0131 negatif olamaz.<\/li>\n<\/ul>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/statorials.org\/wp-content\/ql-cache\/quicklatex.com-6dc2fa2a98bf03919de68092ecd42e0d_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\sigma \\ge 0\" title=\"Rendered by QuickLaTeX.com\" height=\"15\" width=\"43\" style=\"vertical-align: -3px;\"><\/p>\n<\/p>\n<ul>\n<li> T\u00fcm veriler ayn\u0131ysa standart sapma s\u0131f\u0131r olacakt\u0131r.<\/li>\n<\/ul>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/statorials.org\/wp-content\/ql-cache\/quicklatex.com-5771378afa7d193b85b4075fea1ddbca_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\sigma =0\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"43\" style=\"vertical-align: 0px;\"><\/p>\n<\/p>\n<ul>\n<li> T\u00fcm verilere sabit terim eklenirse standart sapma de\u011feri de\u011fi\u015fmez.<\/li>\n<\/ul>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/statorials.org\/wp-content\/ql-cache\/quicklatex.com-12ed23ebb645e96aa0b8262997874bf1_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\sigma (X+k)=\\sigma (X)\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"135\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<ul>\n<li> T\u00fcm veriler bir say\u0131yla \u00e7arp\u0131l\u0131rsa standart sapma, s\u00f6z konusu say\u0131n\u0131n mutlak de\u011feriyle \u00e7arp\u0131lacakt\u0131r.<\/li>\n<\/ul>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/statorials.org\/wp-content\/ql-cache\/quicklatex.com-2464c848bfc171c1800da25602ac68bc_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\sigma (k\\cdot X)=|k|\\cdot \\sigma (X)\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"159\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<ul>\n<li> \u0130ki rastgele de\u011fi\u015fkenin toplam\u0131n\u0131n standart sapmas\u0131, de\u011fi\u015fkenlerin varyanslar\u0131n\u0131n toplam\u0131n\u0131n karek\u00f6k\u00fcne art\u0131 iki de\u011fi\u015fken aras\u0131ndaki kovaryans\u0131n iki kat\u0131na e\u015fittir.<\/li>\n<\/ul>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/statorials.org\/wp-content\/ql-cache\/quicklatex.com-7a5efdb8faca6ce59563063a6a8d9bc0_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\" \\sigma(X+Y)=\\sqrt{Var(X)+Var(Y)+2\\cdot Cov(X,Y)}\" title=\"Rendered by QuickLaTeX.com\" height=\"22\" width=\"388\" style=\"vertical-align: -6px;\"><\/p>\n<\/p>\n<ul>\n<li> Farkl\u0131 da\u011f\u0131l\u0131mlar\u0131n standart sapmalar\u0131n\u0131 ( <sub>\u03c3i<\/sub> ) ve veri say\u0131s\u0131n\u0131 ( <sub>ni<\/sub> ) biliyorsak, a\u015fa\u011f\u0131daki form\u00fcl\u00fc uygulayarak toplam standart sapmay\u0131 hesaplayabiliriz:<\/li>\n<\/ul>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/statorials.org\/wp-content\/ql-cache\/quicklatex.com-7d2dca2d1ca2836361422677310d960a_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle\\sigma=\\sqrt{\\frac{\\displaystyle \\sum_{i=1}^N n_i\\cdot \\sigma_i^2}{\\displaystyle \\sum_{i=1}^N n_i}}=\\sqrt{\\frac{\\displaystyle n_1\\cdot \\sigma_1^2+n_2\\cdot \\sigma_2^2+\\dots +n_N\\cdot \\sigma_N^2}{\\displaystyle n_1+n_2+\\dots+n_N}}\" title=\"Rendered by QuickLaTeX.com\" height=\"128\" width=\"423\" style=\"vertical-align: -58px;\"><\/p><\/p>\n","protected":false},"excerpt":{"rendered":"<p>Bu makalede standart sapma olarak da adland\u0131r\u0131lan standart sapman\u0131n ne oldu\u011fu a\u00e7\u0131klanmaktad\u0131r. Herhangi bir veri \u00f6rne\u011finin standart sapmas\u0131n\u0131 bulmak i\u00e7in standart sapman\u0131n nas\u0131l hesaplanaca\u011f\u0131n\u0131, ad\u0131m ad\u0131m pratik bir \u00f6rne\u011fi ve \u00e7evrimi\u00e7i hesap makinesini \u00f6\u011freneceksiniz. Standart sapma (veya standart sapma) nedir? Standart sapma olarak da adland\u0131r\u0131lan standart sapma , istatistiksel da\u011f\u0131l\u0131m\u0131n bir \u00f6l\u00e7\u00fcs\u00fcd\u00fcr. Ba\u015fka bir deyi\u015fle [&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-79","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>\u25b7Standart sapma (veya standart sapma)<\/title>\n<meta name=\"description\" content=\"Standart sapman\u0131n (veya standart sapman\u0131n) ne oldu\u011funu ve nas\u0131l hesapland\u0131\u011f\u0131n\u0131 (form\u00fcl) a\u00e7\u0131kl\u0131yoruz. \u00c7evrimi\u00e7i standart sapma hesaplay\u0131c\u0131yla.\" \/>\n<meta name=\"robots\" content=\"index, follow, max-snippet:-1, max-image-preview:large, max-video-preview:-1\" \/>\n<link rel=\"canonical\" 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