{"id":1004547,"date":"2023-07-07T11:00:00","date_gmt":"2023-07-07T18:00:00","guid":{"rendered":"https:\/\/www.questionpro.com\/blog\/standart-sapma-nedir-nasil-hesaplanir-uygulama\/"},"modified":"2025-08-21T00:16:58","modified_gmt":"2025-08-21T07:16:58","slug":"standart-sapma-nedir-nasil-hesaplanir-uygulama","status":"publish","type":"post","link":"https:\/\/www.questionpro.com\/blog\/tr\/standart-sapma-nedir-nasil-hesaplanir-uygulama\/","title":{"rendered":"Standart sapma: nedir + nas\u0131l hesaplan\u0131r + uygulama"},"content":{"rendered":"\n<p>Standart sapma, ara\u015ft\u0131rma \u00f6rneklerini hesaplamak i\u00e7in kullan\u0131lan en \u00f6nemli istatistiksel \u00f6l\u00e7\u00fcmlerden biridir. Ayn\u0131 zamanda analistlerin bir risk \u00f6l\u00e7\u00fcs\u00fcd\u00fcr Portf\u00f6y y\u00f6neticileri ve dan\u0131\u015fmanlar\u0131 kullan\u0131r<\/p>\n\n\n\n<p>Bu blogda ne oldu\u011funu, ne i\u00e7in kullan\u0131labilece\u011fini ve hesaplamalar\u0131 i\u00e7in ad\u0131m ad\u0131m bir k\u0131lavuzu a\u00e7\u0131klayaca\u011f\u0131z.<\/p>\n\n\n\n\n\n<h2 class=\"wp-block-heading\">Standart sapma nedir?<\/h2>\n\n\n\n<p>Standart sapma, tan\u0131mlay\u0131c\u0131 istatistiklerdeki yay\u0131lma veya varyans\u0131n bir \u00f6l\u00e7\u00fcs\u00fcd\u00fcr. Her veri noktas\u0131n\u0131n ortalamadan farkl\u0131 oldu\u011fu varyans veya yay\u0131lmay\u0131 hesaplamak i\u00e7in kullan\u0131l\u0131r.<\/p>\n\n\n\n<p>D\u00fc\u015f\u00fck sapma, veri noktas\u0131n\u0131n ortalamaya \u00e7ok yak\u0131n oldu\u011fu anlam\u0131na gelirken, y\u00fcksek sapma, verilerin daha geni\u015f bir de\u011fer aral\u0131\u011f\u0131na yay\u0131ld\u0131\u011f\u0131n\u0131 g\u00f6sterir.  <\/p>\n\n\n\n<p>Pazarlamada varyans, \u00e7ok \u00e7e\u015fitli giderlerin veya gelirlerin muhasebele\u015ftirilmesine yard\u0131mc\u0131 olabilir. Ayr\u0131ca, varl\u0131k fiyatlar\u0131n\u0131n ortalama fiyat ve piyasa oynakl\u0131\u011f\u0131na g\u00f6re da\u011f\u0131l\u0131m\u0131n\u0131n belirlenmesine de yard\u0131mc\u0131 olur.<\/p>\n\n\n\n<h2 class=\"wp-block-heading\">Standart Sapman\u0131n \u00d6nemi<\/h2>\n\n\n\n<p>Standart sapma, istatistiksel analizde \u00f6nemli bir g\u00f6stergedir. Sebeplerden baz\u0131lar\u0131 \u015funlard\u0131r:<\/p>\n\n\n\n<ul>\n<li><h3>T\u00fcm g\u00f6zlemleri i\u00e7erir.<\/h3><\/li>\n<\/ul>\n\n\n\n<p>\u00d6nyarg\u0131 ile ilgili iyi bir \u015fey, ara\u015ft\u0131rmada her bilginin dikkate al\u0131nmas\u0131d\u0131r. Aral\u0131k gibi sapmay\u0131 \u00f6l\u00e7menin di\u011fer yollar\u0131, yaln\u0131zca birbirinden uzak olan noktalara bakar ve orta konumu dikkate almaz. Sonu\u00e7 olarak, standart sapmalar genellikle di\u011fer verilere g\u00f6re daha do\u011fru ve g\u00fcvenilir bir \u00f6l\u00e7\u00fcm y\u00f6ntemi olarak g\u00f6r\u00fcl\u00fcr.<\/p>\n\n\n\n<ul>\n<li><h3>Birlikte kullan\u0131labilir.<\/h3><\/li>\n<\/ul>\n\n\n\n<p>Belirli y\u00f6ntemler kullan\u0131larak, iki veri k\u00fcmesinin standart sapmas\u0131 bir araya getirilebilir. \u0130statistikte di\u011fer g\u00f6zlemsel da\u011f\u0131l\u0131m \u00f6l\u00e7\u00fcmleri i\u00e7in b\u00f6yle bir y\u00f6ntem yoktur. Ayr\u0131ca di\u011fer g\u00f6zlem y\u00f6ntemlerinden farkl\u0131 olarak di\u011fer matematiksel hesaplamalarda da kullan\u0131labilir.<\/p>\n\n\n\n<ul>\n<li><h3>K\u00fcmenin ne zaman e\u015fit olmayan bir \u015fekilde da\u011f\u0131ld\u0131\u011f\u0131n\u0131 bize s\u00f6yler.<\/h3><\/li>\n<\/ul>\n\n\n\n<p>Sapma, veri k\u00fcmenizin ne kadar e\u015fit olmayan bir \u015fekilde da\u011f\u0131ld\u0131\u011f\u0131n\u0131 d\u00fc\u015f\u00fcn\u00fcrken \u00e7ok kullan\u0131\u015fl\u0131d\u0131r. Yaln\u0131zca verilerinizin geni\u015fli\u011fini de\u011fil, ayn\u0131 zamanda e\u015fit olmayan da\u011f\u0131l\u0131m\u0131 da s\u00f6yler.<\/p>\n\n\n\n<ul>\n<li><h3>Matematiksel ve istatistiksel analizi destekler<\/h3><\/li>\n<\/ul>\n\n\n\n<p>Standart sapmalar her zaman belirlenir ve iyi tan\u0131mlan\u0131r, bu da hem matematiksel hem de istatistiksel analize olanak tan\u0131r.<\/p>\n\n\n\n<ul>\n<li><h3>Bir yat\u0131r\u0131m\u0131n risklerini belirlememizi sa\u011flar.<\/h3><\/li>\n<\/ul>\n\n\n\n<p>Ortalaman\u0131n d\u0131\u015f\u0131ndaki veri noktalar\u0131n\u0131n say\u0131s\u0131, bir yat\u0131r\u0131m\u0131n riskini hesaplamak i\u00e7in kullan\u0131labilir. Ortalamadan ne kadar fazla sapma olursa, yat\u0131r\u0131m o kadar riskli olur.<\/p>\n\n\n\n<h2 class=\"wp-block-heading\">Numunenin standart sapmas\u0131n\u0131 hesaplamak i\u00e7in form\u00fcl<\/h2>\n\n\n\n<p>Standart sapma, ara\u015ft\u0131rma \u00f6rnekleminin b\u00fcy\u00fckl\u00fc\u011f\u00fcn\u00fc belirlemede \u00f6nemli bir fakt\u00f6rd\u00fcr. Hesaplama form\u00fcl\u00fc a\u015fa\u011f\u0131daki gibidir:<\/p>\n\n\n\n<figure class=\"wp-block-image size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"1410\" height=\"1182\" src=\"https:\/\/www.questionpro.com\/blog\/wp-content\/uploads\/2023\/07\/formula-to-calculate-standard-deviation.jpg\" alt=\"formula-to-calculate-standard-deviation\" class=\"wp-image-1035625\"\/><\/figure>\n\n\n\n<p>nerede<\/p>\n\n\n\n<ul>\n<li><strong>S<\/strong> = Standart Sapma<\/li>\n\n\n\n<li><strong>\u2211<\/strong> = Toplam\u0131<\/li>\n\n\n\n<li><strong>X<\/strong> = Her de\u011fer<\/li>\n\n\n\n<li><strong>x\u0305<\/strong> = \u00d6rnek ortalamas\u0131<\/li>\n\n\n\n<li><strong>n<\/strong> = \u00f6rnekteki de\u011ferlerin say\u0131s\u0131.<\/li>\n<\/ul>\n\n\n\n<h2 class=\"wp-block-heading\">Standart sapmay\u0131 hesaplamak i\u00e7in ad\u0131m ad\u0131m talimatlar<\/h2>\n\n\n\n<p>\u00d6rne\u011fin standart sapmas\u0131n\u0131 hesaplamak i\u00e7in \u015fu ad\u0131mlar\u0131 izleyin:<\/p>\n\n\n\n<h3 class=\"wp-block-heading\">Ad\u0131m 01: Bilgilerinizi Toplay\u0131n<\/h3>\n\n\n\n<p>Standart sapmay\u0131 hesaplayacak bir veri k\u00fcmesi toplay\u0131n. Diyelim ki bir veri k\u00fcmeniz (45, 67, 30, 58, 50) ve \u00f6rneklem b\u00fcy\u00fckl\u00fc\u011f\u00fcn\u00fcz n = 5.<\/p>\n\n\n\n<h3 class=\"wp-block-heading\">Ad\u0131m 02: Ortalamay\u0131 Bulun<\/h3>\n\n\n\n<p>T\u00fcm veri noktalar\u0131n\u0131 toplayarak ve \u00f6rneklem b\u00fcy\u00fckl\u00fc\u011f\u00fc n&#8217;ye b\u00f6lerek \u00f6rnek ortalamas\u0131n\u0131 (ortalama) hesaplay\u0131n.<\/p>\n\n\n\n<ul>\n<li>Ortalama \u00f6rne\u011fi x\u0305 = (45+67+30+58+50)\/n = 250\/5 = 50<\/li>\n<\/ul>\n\n\n\n<h3 class=\"wp-block-heading\">Ad\u0131m 03: Ortalamadan Fark\u0131 Hesaplay\u0131n<\/h3>\n\n\n\n<p>Her veri noktas\u0131ndan (X) \u00f6rnek ortalamas\u0131n\u0131 (x\u0305) \u00e7\u0131kar\u0131n.<\/p>\n\n\n\n<p>Fark = X &#8211; x\u0305<\/p>\n\n\n\n<ul>\n<li>45, Fark = X &#8211; x\u0305 = 45 &#8211; 50 = &#8211; 4<\/li>\n\n\n\n<li>67, Fark = X &#8211; x\u0305 = 67 &#8211; 50 = 17<\/li>\n\n\n\n<li>30, Fark = X &#8211; x\u0305 = 30 &#8211; 50 = &#8211; 20<\/li>\n\n\n\n<li>58, Fark = X &#8211; x\u0305 = 58 &#8211; 50 = 8<\/li>\n\n\n\n<li>50, Fark = X &#8211; x\u0305 = 50 &#8211; 50 = 0<\/li>\n<\/ul>\n\n\n\n<h3 class=\"wp-block-heading\">Ad\u0131m 04: Fark\u0131n Karesini Al\u0131n<\/h3>\n\n\n\n<p>\u00d6nceki ad\u0131mda elde edilen farkl\u0131l\u0131klar\u0131n her birinin karesini al\u0131n.<\/p>\n\n\n\n<p>Kare Fark\u0131 = (X &#8211; x\u0305)<sup>2<\/sup><\/p>\n\n\n\n<ul>\n<li>45, Kare Fark\u0131 = (X &#8211; x\u0305)<sup>2<\/sup> = (45 &#8211; 50)<sup>2<\/sup> = (- 4)<sup>2<\/sup> = 16<\/li>\n\n\n\n<li>67, Kare Fark\u0131 = (X &#8211; x\u0305)<sup>2<\/sup> = (67 &#8211; 50)<sup>2<\/sup> = (17)<sup>2<\/sup> = 289<\/li>\n\n\n\n<li>30, Kare Fark\u0131 = (X &#8211; x\u0305)<sup>2<\/sup> = (30 &#8211; 50)<sup>2<\/sup> = (- 20)<sup>2<\/sup> = 400<\/li>\n\n\n\n<li>58, Kare Fark\u0131 = (X &#8211; x\u0305)<sup>2<\/sup> = (58 &#8211; 50)<sup>2<\/sup> = (8)<sup>2<\/sup> = 64<\/li>\n\n\n\n<li>50, Kare Fark\u0131 = (X &#8211; x\u0305)<sup>2<\/sup> = (50 &#8211; 50)<sup>2<\/sup> = (0)<sup>2<\/sup> = 0<\/li>\n<\/ul>\n\n\n\n<h3 class=\"wp-block-heading\">Ad\u0131m 05: Fark\u0131n Karesini Toplay\u0131n<\/h3>\n\n\n\n<p>T\u00fcm kare farklar\u0131n\u0131 bir araya getirin.<\/p>\n\n\n\n<p>\u2211(Kare Fark\u0131) = \u2211[(X &#8211; x\u0305)<sup>2<\/sup>]= 16 + 289 + 400 + 64 + 0 = 769<\/p>\n\n\n\n<h3 class=\"wp-block-heading\">Ad\u0131m 06: Varyans\u0131 hesaplay\u0131n<\/h3>\n\n\n\n<p>Varyans\u0131 elde etmek i\u00e7in, farklar\u0131n karelerinin toplam\u0131n\u0131 (n &#8211; 1) ile b\u00f6l\u00fcn.<\/p>\n\n\n\n<ul>\n<li>Varyans (S\u00b2) = \u03c3(fark\u0131n karesi) \/ (n &#8211; 1) = 769\/4 = 192.25<\/li>\n<\/ul>\n\n\n\n<h3 class=\"wp-block-heading\">Ad\u0131m 07: Standart Sapmay\u0131 Hesaplay\u0131n<\/h3>\n\n\n\n<p>Son olarak, varyans\u0131n karek\u00f6k\u00fcn\u00fc kullanarak standart sapmay\u0131 hesaplay\u0131n.<\/p>\n\n\n\n<ul>\n<li>Standart Sapma (S) = \u221a Varyans = \u221a 192.25 = 13.875<\/li>\n<\/ul>\n\n\n\n<blockquote class=\"wp-block-quote\">\n<p class=\"has-text-align-center\"> <em>\n  <strong>\u015eunlar hakk\u0131nda bilgi edinin:<\/strong>\n<\/em> <em>\n  <a href=\"https:\/\/www.questionpro.com\/blog\/tr\/5-arastirma-ve-analiz-icin-istatistiksel-analiz-yontemleri\/\">\u0130statistiksel Analiz Y\u00f6ntemleri<\/a>\n<\/em><\/p>\n<\/blockquote>\n\n\n\n<h2 class=\"wp-block-heading\">Standart Sapmalar\u0131 Kullanma<\/h2>\n\n\n\n<p>Standart sapma, \u00e7e\u015fitli faydalar\u0131 olan yararl\u0131 bir istatistiksel \u00f6l\u00e7\u00fcd\u00fcr. \u0130\u015fte be\u015f yayg\u0131n kullan\u0131m:<\/p>\n\n\n\n<h3 class=\"wp-block-heading\">01. Yat\u0131r\u0131m riskini \u00f6l\u00e7\u00fcn<\/h3>\n\n\n\n<p>Bir\u00e7ok yat\u0131r\u0131m firmas\u0131, bir fonun performans\u0131n\u0131n beklenen getirilerinden ne kadar sapt\u0131\u011f\u0131n\u0131 belirlemek i\u00e7in standart sapmalar\u0131 kullan\u0131r. Bu bilgiler, anla\u015f\u0131lmas\u0131 kolay oldu\u011fu i\u00e7in son kullan\u0131c\u0131lara ve yat\u0131r\u0131mc\u0131lara iletilebilir.<\/p>\n\n\n\n<p>Bu \u015fekilde sapma, piyasadaki menkul k\u0131ymetlerin riskini \u00f6l\u00e7memize ve gelecekteki performans modellerini tahmin etmemize olanak tan\u0131r.<\/p>\n\n\n\n<h3 class=\"wp-block-heading\">02. Veri k\u00fcmelerinin daha iyi anla\u015f\u0131lmas\u0131<\/h3>\n\n\n\n<p>Bireyler ve i\u015fletmeler, veri k\u00fcmesini daha iyi anlamak i\u00e7in sekt\u00f6rler aras\u0131nda her zaman \u00f6nyarg\u0131y\u0131 kullan\u0131r.<\/p>\n\n\n\n<h3 class=\"wp-block-heading\">03. Reklam\u0131n\u0131z\u0131n performans\u0131n\u0131 anlay\u0131n<\/h3>\n\n\n\n<p>Pazarlamac\u0131lar, belirli bir reklam i\u00e7in beklenen gelirdeki dalgalanmalar\u0131 anlamak i\u00e7in genellikle her bir reklam i\u00e7in kazan\u0131lan gelirin standart sapmas\u0131n\u0131 hesaplar.  <\/p>\n\n\n\n<p>Ayr\u0131ca, rakiplerinizin bu alanda kulland\u0131klar\u0131 reklam say\u0131s\u0131ndaki de\u011fi\u015fikli\u011fi hesaplayabilir ve belirli bir s\u00fcre boyunca normal reklamlar\u0131ndan daha fazla m\u0131 yoksa daha az m\u0131 kulland\u0131klar\u0131n\u0131 g\u00f6rebilirsiniz.<\/p>\n\n\n\n<h3 class=\"wp-block-heading\">04. \u0130nsan Kaynaklar\u0131nda<\/h3>\n\n\n\n<p>\u0130\u015fe al\u0131m y\u00f6neticisinin sorumluluklar\u0131 aras\u0131nda, belirli bran\u015flardaki \u00fccretlerin standart sapmas\u0131n\u0131n hesaplanmas\u0131, yeni \u00e7al\u0131\u015fana sa\u011flanacak maa\u015f de\u011fi\u015fikli\u011finin t\u00fcr\u00fcn\u00fcn belirlenmesi yer al\u0131r.<\/p>\n\n\n\n<blockquote class=\"wp-block-quote\">\n<p class=\"has-text-align-center\"><em><strong>\u015eunlar hakk\u0131nda bilgi edinin:<\/strong> <a href=\"https:\/\/www.questionpro.com\/blog\/tr\/ortalama-siparis-degeri-nedir-ve-nasil-hesaplanir\/\">Ortalama Sipari\u015f De\u011feri<\/a><\/em><\/p>\n<\/blockquote>\n\n\n\n<h2 class=\"wp-block-heading\">son<\/h2>\n\n\n\n<p>Standart sapma, bir veri k\u00fcmesi i\u00e7indeki veri noktalar\u0131n\u0131n varyans\u0131n\u0131 ve da\u011f\u0131l\u0131m\u0131n\u0131 belirlemek i\u00e7in yararl\u0131 bir istatistiksel \u00f6l\u00e7\u00fcd\u00fcr.<\/p>\n\n\n\n<p>Standart sapmalar, veri de\u011fi\u015fkenli\u011fini tan\u0131mlar, risk ve oynakl\u0131\u011f\u0131 de\u011ferlendirir, performans de\u011ferlendirme s\u00fcre\u00e7lerini inceler ve ortalama etraf\u0131ndaki veri da\u011f\u0131l\u0131m\u0131n\u0131 nicelle\u015ftirerek hipotez testlerini ve istatistiksel \u00e7\u0131kar\u0131mlar\u0131 destekler.<\/p>\n\n\n\n<p>QuestionPro, anket olu\u015fturmak, yay\u0131nlamak ve analiz etmek i\u00e7in \u00e7ok \u00e7e\u015fitli ara\u00e7lar ve yetenekler sunan pop\u00fcler bir \u00e7evrimi\u00e7i anket ve ara\u015ft\u0131rma platformudur.<\/p>\n\n\n\n<p>QuestionPro, analiz i\u00e7in veri toplamak ve standart sapmalar gibi istatistiksel \u00f6l\u00e7\u00fcmleri hesaplamak i\u00e7in kullan\u0131labilir. Ara\u015ft\u0131rmac\u0131lar ve analistler, Likert \u00f6l\u00e7e\u011fi sorular\u0131, puanlama \u00f6l\u00e7ekleri veya di\u011fer veri toplama y\u00f6ntemlerini kullanarak anketler geli\u015ftirebilirler.<\/p>\n\n\n\n<p>Kullan\u0131c\u0131lar, ara\u015ft\u0131rma s\u00fcrecinde QuestionPro&#8217;yu kullanarak standart sapmalar\u0131 yap\u0131land\u0131rmak i\u00e7in gereken veriler de dahil olmak \u00fczere verileri verimli bir \u015fekilde toplayabilir ve ek bilgiler i\u00e7indeki kal\u0131plar\u0131, e\u011filimleri ve korelasyonlar\u0131 inceleyebilir.<\/p>\n\n\n\n<p><\/p><p style=\"text-align: center;\"> <a href=\"https:\/\/www.questionpro.com\/research-edition-survey-software\/\" target=\"_blank\" rel=\"noopener\">\n<button>Daha fazla bilgi edin\u00dccretsiz<\/button>\n  <\/a> <a href=\"https:\/\/www.questionpro.com\/a\/showEntry.do?classID=1053&#038;sourceRef=blog\" target=\"_blank\" rel=\"noopener\">\n<button>deneme<\/button>  \n<\/a>       <\/p>\n","protected":false},"excerpt":{"rendered":"<p>Standart sapma, ara\u015ft\u0131rma \u00f6rneklerini hesaplamak i\u00e7in kullan\u0131lan en \u00f6nemli istatistiksel \u00f6l\u00e7\u00fcmlerden biridir. Ayn\u0131 zamanda analistlerin bir risk \u00f6l\u00e7\u00fcs\u00fcd\u00fcr Portf\u00f6y y\u00f6neticileri [&hellip;]<\/p>\n","protected":false},"author":51,"featured_media":801471,"comment_status":"closed","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":{"_genesis_hide_title":false,"_genesis_hide_breadcrumbs":false,"_genesis_hide_singular_image":false,"_genesis_hide_footer_widgets":false,"_genesis_custom_body_class":"","_genesis_custom_post_class":"","_genesis_layout":"","footnotes":""},"categories":[1114],"tags":[],"yoast_head":"<!-- This site is optimized with the Yoast SEO plugin v20.4 - https:\/\/yoast.com\/wordpress\/plugins\/seo\/ -->\n<title>Standart sapma: nedir + nas\u0131l hesaplan\u0131r + uygulama<\/title>\n<meta name=\"description\" content=\"Standart sapma, tan\u0131mlay\u0131c\u0131 istatistiksel de\u011fi\u015fkenli\u011fi \u00f6l\u00e7er. 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