{"id":582,"date":"2026-10-03T14:46:00","date_gmt":"2026-10-03T13:46:00","guid":{"rendered":"https:\/\/wpcalc.com\/tr\/normal-dagilim-hesaplayici\/"},"modified":"2026-10-03T14:46:00","modified_gmt":"2026-10-03T13:46:00","slug":"normal-dagilim-hesaplayici","status":"publish","type":"post","link":"https:\/\/wpcalc.com\/tr\/istatistik\/normal-dagilim-hesaplayici\/","title":{"rendered":"Normal Da\u011f\u0131l\u0131m Hesaplay\u0131c\u0131"},"content":{"rendered":"<section class=\"not-prose calculator-box\" aria-labelledby=\"calculator-title\"><div class=\"flex items-baseline sm:items-center justify-between gap-2 sm:gap-3\"><div class=\"flex flex-col sm:flex-row sm:items-center gap-2\"><span class=\"icon icon-calculator text-primary-700! text-base! dark:text-primary-300!\" aria-hidden=\"true\"><\/span><h2 id=\"calculator-title\" class=\"text-lg font-display font-bold\">Normal Da\u011f\u0131l\u0131m Olas\u0131l\u0131klar\u0131n\u0131 Bulun<\/h2><\/div><div class=\"calcdash-favorite group\">\n  <button type=\"button\" class=\"favorite\" id=\"favorite\" data-favorite-id=\"582\" data-favorite-title=\"Normal Da\u011f\u0131l\u0131m\" data-favorite-url=\"https:\/\/wpcalc.com\/tr\/istatistik\/normal-dagilim-hesaplayici\/\" data-favorite-excerpt=\"Normal da\u011f\u0131l\u0131m i\u00e7in olas\u0131l\u0131k yo\u011funlu\u011funu, k\u00fcm\u00fclatif olas\u0131l\u0131klar\u0131 P(X &lt; x), P(X &gt; x), P(a &lt; X &lt; b) ve z-puan\u0131n\u0131 elde etmek \u00fczere bir ortalama, standart sapma ve bir de\u011fer (ya da iki s\u0131n\u0131r) girin.\" aria-label=\"Favorilere ekle\" data-favorite-icon=\"icon icon-wpcalc-distribution-histogram\">\n    <span class=\"icon icon-shape-star-empty\" aria-hidden=\"true\"><\/span>\n  <\/button>\n  <div class=\"calcdash-favorite__tip\" aria-hidden=\"true\">\n   <span class=\"favorite-tooltip\" id=\"favorite-tooltip\"><\/span>\n  <\/div>\n  <span class=\"sr-only\" role=\"status\" id=\"favorite-status\"><\/span>\n<\/div><\/div><form action=\"https:\/\/wpcalc.com\/tr\/istatistik\/normal-dagilim-hesaplayici\/\" method=\"POST\" class=\"calculator\" id=\"calculator-582\" data-post=\"582\"><fieldset class=\"fieldset-input is-1\"><legend class=\"sr-only\">Giri\u015f alanlar\u0131<\/legend><div class=\"field has-term\" id=\"input-1\"><label for=\"field-1\">Ortalama (\u03bc)<\/label><div class=\"term\">\u03bc<\/div>  <div class=\"absolute bottom-0 left-16 top-8 w-2 h-0.5 bg-blue-500\"><\/div><input type=\"number\" name=\"ortalama_\" id=\"field-1\" aria-describedby=\"calc-info-1\" placeholder=\"e.g. 100\" step=\"any\" value=\"100\"\/><small id=\"calc-info-1\">\u00c7an e\u011frisinin merkezi.<\/small><\/div><div class=\"field has-term\" id=\"input-2\"><label for=\"field-2\">Standart sapma (\u03c3)<\/label><div class=\"term\">\u03c3<\/div>  <div class=\"absolute bottom-0 left-16 top-8 w-2 h-0.5 bg-blue-500\"><\/div><input type=\"text\" name=\"standart_sapma_\" id=\"field-2\" aria-describedby=\"calc-info-2\" data-number inputmode=\"decimal\" autocomplete=\"off\" spellcheck=\"false\" placeholder=\"e.g. 15\" min=\"0\" value=\"15\"\/><small id=\"calc-info-2\">Da\u011f\u0131l\u0131m\u0131n yay\u0131l\u0131m\u0131 \u2014 0&#039;dan b\u00fcy\u00fck olmal\u0131d\u0131r.<\/small><\/div><div class=\"field\" id=\"input-3\"><label for=\"field-3\">\u0130stedi\u011finiz olas\u0131l\u0131k<\/label><div class=\"grid grid-cols-1\"><select id=\"field-3\" name=\"stediiniz_olaslk\"><option value=\"below\" selected>P(X &lt; x) \u2014 bir de\u011ferin alt\u0131nda<\/option><option value=\"above\">P(X &gt; x) \u2014 bir de\u011ferin \u00fcst\u00fcnde<\/option><option value=\"between\">P(a &lt; X &lt; b) \u2014 iki de\u011fer aras\u0131nda<\/option><option value=\"outside\">Bir aral\u0131\u011f\u0131n d\u0131\u015f\u0131 (iki kuyruk)<\/option><\/select><svg class=\"pointer-events-none col-start-1 row-start-1 mr-2 size-5 self-center justify-self-end text-gray-500 sm:size-4\" viewBox=\"0 0 16 16\" fill=\"currentColor\" aria-hidden=\"true\" data-slot=\"icon\">\n              <path fill-rule=\"evenodd\" d=\"M4.22 6.22a.75.75 0 0 1 1.06 0L8 8.94l2.72-2.72a.75.75 0 1 1 1.06 1.06l-3.25 3.25a.75.75 0 0 1-1.06 0L4.22 7.28a.75.75 0 0 1 0-1.06Z\" clip-rule=\"evenodd\" \/>\n            <\/svg><\/div><\/div><div class=\"field has-term\" id=\"input-4\"><label for=\"field-4\">De\u011fer (x)<\/label><div class=\"term\">x<\/div>  <div class=\"absolute bottom-0 left-16 top-8 w-2 h-0.5 bg-blue-500\"><\/div><input type=\"number\" name=\"deer_x\" id=\"field-4\" aria-describedby=\"calc-info-4\" placeholder=\"e.g. 110\" step=\"any\" value=\"110\"\/><small id=\"calc-info-4\">Yo\u011funlu\u011fun ve k\u00fcm\u00fclatif olas\u0131l\u0131klar\u0131n P(X &lt; x) ve P(X &gt; x) hesapland\u0131\u011f\u0131 nokta.<\/small><\/div><div class=\"field has-term\" id=\"input-5\" hidden><label for=\"field-5\">Alt s\u0131n\u0131r (a)<\/label><div class=\"term\">a<\/div>  <div class=\"absolute bottom-0 left-16 top-8 w-2 h-0.5 bg-blue-500\"><\/div><input type=\"number\" name=\"alt_snr_a\" id=\"field-5\" aria-describedby=\"calc-info-5\" placeholder=\"e.g. 85\" step=\"any\" value=\"85\"\/><small id=\"calc-info-5\">Aral\u0131\u011f\u0131n sol kenar\u0131.<\/small><\/div><div class=\"field has-term\" id=\"input-6\" hidden><label for=\"field-6\">\u00dcst s\u0131n\u0131r (b)<\/label><div class=\"term\">b<\/div>  <div class=\"absolute bottom-0 left-16 top-8 w-2 h-0.5 bg-blue-500\"><\/div><input type=\"number\" name=\"st_snr_b\" id=\"field-6\" aria-describedby=\"calc-info-6\" placeholder=\"e.g. 115\" step=\"any\" value=\"115\"\/><small id=\"calc-info-6\">Aral\u0131\u011f\u0131n sa\u011f kenar\u0131 \u2014 alt s\u0131n\u0131rdan b\u00fcy\u00fck olmal\u0131d\u0131r.<\/small><\/div><\/fieldset><div class=\"buttons\"><button type=\"submit\" data-text=\"Yeniden hesapla\" id=\"calculate-button\" data-post=\"582\">Hesapla<\/button><button type=\"reset\">S\u0131f\u0131rla<\/button><\/div><div class=\"field is-checkbox hidden!\" id=\"field-auto-calc\"><input type=\"checkbox\" id=\"auto-calc\"><label for=\"auto-calc\">Otomatik hesapla<\/label><small>Etkinle\u015ftirilirse, herhangi bir de\u011feri de\u011fi\u015ftirdi\u011finizde sonu\u00e7 otomatik olarak g\u00fcncellenir.<\/small><\/div><div class=\"fieldset-result is-hidden\" aria-labelledby=\"result-title\" aria-live=\"polite\" role=\"region\"> <h3 class=\"result-title bg-gradient-to-r from-primary-50 to-gray-50 dark:from-primary-900 dark:to-gray-800\" id=\"result-title\"><span class=\"icon icon-s-pulse\" aria-hidden=\"true\"><\/span> Sonu\u00e7lar\u0131n\u0131z<\/h3><div class=\"result-box\"><div class=\"field-result\" id=\"output-1\"><span class=\"field-title\"><span>Olas\u0131l\u0131k yo\u011funlu\u011fu<\/span><span class=\"result-term\">f(x)<\/span><\/span><span class=\"field-value\" id=\"result-1\"><\/span><button type=\"button\" class=\"copy-result\" data-tooltip=\"Sonucu kopyala\" aria-label=\"Sonucu kopyala\"><span class=\"copy-icon icon icon-document-copy\" aria-hidden=\"true\"><\/span><\/button><\/div><div class=\"field-result\" id=\"output-2\"><span class=\"field-title\"><span>K\u00fcm\u00fclatif P(X &lt; x)<\/span><span class=\"result-term\">F(x)<\/span><\/span><span class=\"field-value\" id=\"result-2\"><\/span><button type=\"button\" class=\"copy-result\" data-tooltip=\"Sonucu kopyala\" aria-label=\"Sonucu kopyala\"><span class=\"copy-icon icon icon-document-copy\" aria-hidden=\"true\"><\/span><\/button><\/div><div class=\"field-result\" id=\"output-3\"><span class=\"field-title\"><span>P(X &gt; x)<\/span><\/span><span class=\"field-value\" id=\"result-3\"><\/span><button type=\"button\" class=\"copy-result\" data-tooltip=\"Sonucu kopyala\" aria-label=\"Sonucu kopyala\"><span class=\"copy-icon icon icon-document-copy\" aria-hidden=\"true\"><\/span><\/button><\/div><div class=\"field-result\" id=\"output-4\"><span class=\"field-title\"><span>a ile b aras\u0131ndaki alan<\/span><span class=\"result-term\">P(a<X<b)<\/span><\/span><span class=\"field-value\" id=\"result-4\"><\/span><button type=\"button\" class=\"copy-result\" data-tooltip=\"Sonucu kopyala\" aria-label=\"Sonucu kopyala\"><span class=\"copy-icon icon icon-document-copy\" aria-hidden=\"true\"><\/span><\/button><\/div><div class=\"field-result\" id=\"output-5\"><span class=\"field-title\"><span>z-skoru<\/span><span class=\"result-term\">z<\/span><\/span><span class=\"field-value\" id=\"result-5\"><\/span><button type=\"button\" class=\"copy-result\" data-tooltip=\"Sonucu kopyala\" aria-label=\"Sonucu kopyala\"><span class=\"copy-icon icon icon-document-copy\" aria-hidden=\"true\"><\/span><\/button><\/div><div class=\"field-result is-column\" id=\"output-6\"><span class=\"field-title\"><span>Yorum<\/span><\/span><span class=\"field-value\" id=\"result-6\"><\/span><button type=\"button\" class=\"copy-result\" data-tooltip=\"Sonucu kopyala\" aria-label=\"Sonucu kopyala\"><span class=\"copy-icon icon icon-document-copy\" aria-hidden=\"true\"><\/span><\/button><\/div><\/div><div class=\"result-actions\"><button type=\"button\" class=\"copy-link\"><svg viewBox=\"0 0 20 20\" fill=\"currentColor\" aria-hidden=\"true\"><path d=\"M12.232 4.232a2.5 2.5 0 0 1 3.536 3.536l-1.225 1.224a.75.75 0 0 0 1.061 1.06l1.224-1.224a4 4 0 0 0-5.656-5.656l-3 3a4 4 0 0 0 .225 5.865.75.75 0 0 0 .977-1.138 2.5 2.5 0 0 1-.142-3.667l3-3Z\"\/><path d=\"M11.603 7.963a.75.75 0 0 0-.977 1.138 2.5 2.5 0 0 1 .142 3.667l-3 3a2.5 2.5 0 0 1-3.536-3.536l1.225-1.224a.75.75 0 0 0-1.061-1.06l-1.224 1.224a4 4 0 1 0 5.656 5.656l3-3a4 4 0 0 0-.225-5.865Z\"\/><\/svg><span class=\"copy-link__text\">Bu hesaplaman\u0131n ba\u011flant\u0131s\u0131n\u0131 kopyala<\/span><\/button><span class=\"sr-only\" role=\"status\" id=\"copy-link-status\"><\/span><\/div><\/div><a href=\"#respond\" class=\"hidden transition-opacity duration-300 opacity-0 w-50 text-sm justify-center items-center gap-2 px-4 py-2 rounded bg-gray-200 text-gray-700 hover:bg-gray-300\" id=\"leave-comment\"><span class=\"icon icon-comments\" aria-hidden=\"true\"><\/span>Yorum b\u0131rak<\/a><\/form><\/section><section id=\"calc-reactions\" class=\"not-prose hidden my-12 bg-gradient-to-r from-primary-50 to-gray-50 border border-indigo-100 rounded-xl px-6 py-4 shadow-sm\" data-post=\"582\" aria-live=\"polite\" aria-labelledby=\"calc-reactions-title\"><p id=\"calc-reactions-title\" class=\"text-sm text-gray-500 text-center mb-2\">Bu sonu\u00e7 hakk\u0131nda ne d\u00fc\u015f\u00fcn\u00fcyorsunuz?<\/p><div role=\"group\" aria-labelledby=\"calc-reactions-title\" class=\"grid grid-cols-3 sm:flex sm:flex-row sm:justify-around gap-4 sm:items-center sm:flex-wrap\"><button type=\"button\" aria-pressed=\"false\" class=\"reaction-btn flex flex-col items-center gap-1 text-sm text-gray-700 hover:text-primary-600 cursor-pointer transition-transform hover:scale-105\" data-reaction=\"like\"><span class=\"reaction-count\" data-reaction-count=\"like\">0<\/span><span class=\"reaction text-3xl\" aria-hidden=\"true\">\ud83d\ude00 <\/span><span class=\"reaction-description font-medium\">Be\u011fendim <\/span><\/button><button type=\"button\" aria-pressed=\"false\" class=\"reaction-btn flex flex-col items-center gap-1 text-sm text-gray-700 hover:text-primary-600 cursor-pointer transition-transform hover:scale-105\" data-reaction=\"helpful\"><span class=\"reaction-count\" data-reaction-count=\"helpful\">0<\/span><span class=\"reaction text-3xl\" aria-hidden=\"true\">\ud83d\udca1 <\/span><span class=\"reaction-description font-medium\">Faydal\u0131 <\/span><\/button><button type=\"button\" aria-pressed=\"false\" class=\"reaction-btn flex flex-col items-center gap-1 text-sm text-gray-700 hover:text-primary-600 cursor-pointer transition-transform hover:scale-105\" data-reaction=\"confused\"><span class=\"reaction-count\" data-reaction-count=\"confused\">0<\/span><span class=\"reaction text-3xl\" aria-hidden=\"true\">\ud83d\ude15 <\/span><span class=\"reaction-description font-medium\">Kafam kar\u0131\u015ft\u0131 <\/span><\/button><button type=\"button\" aria-pressed=\"false\" class=\"reaction-btn flex flex-col items-center gap-1 text-sm text-gray-700 hover:text-primary-600 cursor-pointer transition-transform hover:scale-105\" data-reaction=\"disappointed\"><span class=\"reaction-count\" data-reaction-count=\"disappointed\">0<\/span><span class=\"reaction text-3xl\" aria-hidden=\"true\">\ud83d\ude1e <\/span><span class=\"reaction-description font-medium\">Hayal k\u0131r\u0131kl\u0131\u011f\u0131 <\/span><\/button><button type=\"button\" aria-pressed=\"false\" class=\"reaction-btn flex flex-col items-center gap-1 text-sm text-gray-700 hover:text-primary-600 cursor-pointer transition-transform hover:scale-105\" data-reaction=\"inaccurate\"><span class=\"reaction-count\" data-reaction-count=\"inaccurate\">0<\/span><span class=\"reaction text-3xl\" aria-hidden=\"true\">\u274c <\/span><span class=\"reaction-description font-medium\">Hatal\u0131 <\/span><\/button><\/div><div id=\"reaction-message\" class=\"hidden mt-8 rounded-md border border-primary-100 bg-white\/50 backdrop-blur-sm px-4 py-2 text-sm text-center shadow-sm\"><\/div><\/section><div class=\"calcdash-ad not-prose calcdash-ad--calc_result calcdash-ad--in-article\"><ins class=\"adsbygoogle\" style=\"display:block\" data-ad-client=\"ca-pub-1721569815777345\" data-ad-slot=\"6317458308\" data-ad-layout=\"in-article\" data-ad-format=\"fluid\"><\/ins><script>(adsbygoogle = window.adsbygoogle || []).push({});<\/script><\/div>\n<style id=\"wpcoderpro-inline-1\">.formula-box {\r\n\tborder-bottom: none !important;\r\n}<\/style><section class=\"formula-box\" aria-labelledby=\"formula-title\">\r\n\t<div id=\"formula-title\" class=\"not-prose font-display mb-4\"><span class=\"icon icon-formula\" aria-hidden=\"true\"><\/span><h2>Normal Da\u011f\u0131l\u0131m Form\u00fcl\u00fc<\/h2><\/div>\r\n\t<figure class=\"not-prose formula\">\r\n\t\t<figcaption class=\"formula-title\">Form\u00fcl<\/figcaption>\r\n\t\t<div class=\"text-base text-gray-800\" id=\"formula\">\n\\[ f(x)=\\frac{1}{\\sigma\\sqrt{2\\pi}}\\,e^{-\\frac{(x-\\mu)^2}{2\\sigma^2}} \\\\ F(x)=P(X&lt;x)=\\Phi(z)=\\frac{1}{2}\\left[1+\\operatorname{erf}\\!\\left(\\frac{z}{\\sqrt{2}}\\right)\\right] \\\\ z=\\frac{x-\\mu}{\\sigma} \\]\n<\/div>\r\n\t<\/figure>\r\n\t<\/p>\n<p><strong>Burada:<\/strong><\/p>\n<ul>\n<li>\\(\\mu\\) \u2014 ortalama, \u00e7an e\u011frisinin merkezi<\/li>\n<li>\\(\\sigma\\) \u2014 standart sapma, da\u011f\u0131l\u0131m\u0131n yay\u0131l\u0131m\u0131 (pozitif olmal\u0131d\u0131r)<\/li>\n<li>\\(x\\) \u2014 yo\u011funlu\u011fun ve olas\u0131l\u0131klar\u0131n hesapland\u0131\u011f\u0131 de\u011fer<\/li>\n<li>\\(f(x)\\) \u2014 olas\u0131l\u0131k yo\u011funluk fonksiyonu (PDF), e\u011frinin \\(x\\) noktas\u0131ndaki y\u00fcksekli\u011fi<\/li>\n<li>\\(F(x)\\) \u2014 k\u00fcm\u00fclatif da\u011f\u0131l\u0131m fonksiyonu (CDF), e\u011frinin \\(x\\)'in solunda kalan alan\u0131<\/li>\n<li>\\(z\\) \u2014 z-puan\u0131, ortalaman\u0131n standart sapma cinsinden uzakl\u0131\u011f\u0131<\/li>\n<li>\\(\\Phi\\) \u2014 <em>standart<\/em> normal da\u011f\u0131l\u0131m\u0131n k\u00fcm\u00fclatif da\u011f\u0131l\u0131m fonksiyonu (\\(\\mu=0,\\ \\sigma=1\\))<\/li>\n<\/ul>\n<p>\u0130lk denklem \u00e7an e\u011frisinin kendisini tan\u0131mlar. \u0130kincisi herhangi bir de\u011feri z-puan\u0131na \u00e7evirir ve olas\u0131l\u0131\u011f\u0131 standart normal e\u011friden okur; b\u00f6ylece tek bir evrensel tablo (veya hata fonksiyonu) her ortalama ve standart sapma i\u00e7in i\u015f g\u00f6r\u00fcr.<\/p>\n<p>\r\n<\/section>\n<style id=\"wpcoderpro-inline-2\">.calculation-box {\r\n\tborder-bottom: none !important;\r\n}<\/style><section id=\"calculation\" class=\"calculation-box\" aria-labelledby=\"calculation-title\">\r\n\t<div id=\"calculation-title\" class=\"not-prose font-display\"><span class=\"icon icon-unordered-list\" aria-hidden=\"true\"><\/span><h2>Normal Da\u011f\u0131l\u0131m \u2013 Hesaplama \u00d6rne\u011fi<\/h2><\/div>\r\n\r\n<\/p>\n<p><strong>\u00d6rnek:<\/strong> IQ puanlar\u0131 yakla\u015f\u0131k olarak ortalalamas\u0131 100 ve standart sapmas\u0131 15 olan normal da\u011f\u0131l\u0131m g\u00f6sterir. Rastgele se\u00e7ilen bir ki\u015finin IQ'sunun 110'un alt\u0131nda olma olas\u0131l\u0131\u011f\u0131 nedir?<\/p>\n<p>\\[ z=\\frac{x-\\mu}{\\sigma}=\\frac{110-100}{15}=0.6667 \\]<\/p>\n<p>\\[ P(X&lt;110)=\\Phi(0.6667)=\\frac{1}{2}\\left[1+\\operatorname{erf}\\!\\left(\\frac{0.6667}{\\sqrt{2}}\\right)\\right]\\approx 0.7475 \\]<\/p>\n<p>Bu noktadaki olas\u0131l\u0131k yo\u011funlu\u011fu \\( f(110)=\\frac{1}{15\\sqrt{2\\pi}}e^{-0.6667^2\/2}\\approx 0.0213 \\) de\u011feridir.<\/p>\n<p><strong>Sonu\u00e7:<\/strong> P(X &gt; 110) \u2248 %25,25 ve z-puan\u0131 0,6667'dir.<\/p>\n<p>\n\r\n<\/section>\n<h2>Hesaplay\u0131c\u0131 nas\u0131l kullan\u0131l\u0131r<\/h2>\n<ol>\n<li><strong>Ortalamay\u0131 (\u03bc)<\/strong> girin \u2014 da\u011f\u0131l\u0131m\u0131n\u0131z\u0131n merkezi (\u00f6rn. 100).<\/li>\n<li><strong>Standart sapmay\u0131 (\u03c3)<\/strong> girin \u2014 0'dan b\u00fcy\u00fck olmal\u0131d\u0131r.<\/li>\n<li>\u0130stedi\u011finiz <strong>olas\u0131l\u0131k t\u00fcr\u00fcn\u00fc se\u00e7in<\/strong>: bir de\u011ferin alt\u0131nda, bir de\u011ferin \u00fcst\u00fcnde, iki de\u011fer aras\u0131nda veya bir aral\u0131\u011f\u0131n d\u0131\u015f\u0131nda (iki kuyruk).<\/li>\n<li>\"Alt\u0131nda\" ve \"\u00fcst\u00fcnde\" modlar\u0131 i\u00e7in olas\u0131l\u0131klar\u0131n hesaplanaca\u011f\u0131 <strong>De\u011feri (x)<\/strong> girin.<\/li>\n<li>\"Aras\u0131nda\" ve \"d\u0131\u015f\u0131nda\" modlar\u0131 i\u00e7in <strong>Alt s\u0131n\u0131r\u0131 (a)<\/strong> ve <strong>\u00dcst s\u0131n\u0131r\u0131 (b)<\/strong> girin; \u00fcst s\u0131n\u0131r alt s\u0131n\u0131rdan b\u00fcy\u00fck olmal\u0131d\u0131r. Yo\u011funlu\u011fu ve k\u00fcm\u00fclatif olas\u0131l\u0131klar\u0131 da o noktada elde etmek i\u00e7in yine de x'i doldurabilirsiniz.<\/li>\n<li>Sonu\u00e7lar\u0131 okuyun: olas\u0131l\u0131k yo\u011funlu\u011fu, k\u00fcm\u00fclatif olas\u0131l\u0131k, \u00fcst kuyruk olas\u0131l\u0131\u011f\u0131, s\u0131n\u0131rlar aras\u0131ndaki alan, z-puan\u0131 ve sade dille bir yorum.<\/li>\n<\/ol>\n<h2>Normal da\u011f\u0131l\u0131m nedir?<\/h2>\n<p>Normal da\u011f\u0131l\u0131m (Gauss da\u011f\u0131l\u0131m\u0131 veya \u00e7an e\u011frisi olarak da adland\u0131r\u0131l\u0131r) istatistikte en yayg\u0131n kullan\u0131lan olas\u0131l\u0131k da\u011f\u0131l\u0131m\u0131d\u0131r. Yaln\u0131zca iki say\u0131yla tam olarak tan\u0131mlan\u0131r: e\u011frinin merkezini belirleyen ortalama \\(\\mu\\) ve e\u011frinin ne kadar geni\u015f veya dar oldu\u011funu denetleyen standart sapma \\(\\sigma\\). Bir\u00e7ok do\u011fal \u00f6l\u00e7\u00fcm \u2014 boylar, \u00f6l\u00e7\u00fcm hatalar\u0131, test puanlar\u0131, tansiyon \u2014 yakla\u015f\u0131k olarak normal da\u011f\u0131l\u0131m g\u00f6sterir; bunun ba\u015fl\u0131ca nedeni merkezi limit teoremidir: bir\u00e7ok k\u00fc\u00e7\u00fck ba\u011f\u0131ms\u0131z etki topland\u0131\u011f\u0131nda, toplam bir \u00e7an e\u011frisine yak\u0131nsar.<\/p>\n<p>E\u011fri ortalamaya g\u00f6re simetriktir ve hi\u00e7bir zaman s\u0131f\u0131ra de\u011fmez, her iki y\u00f6nde sonsuza kadar uzan\u0131r. Herhangi bir <em>kesin<\/em> de\u011ferin olas\u0131l\u0131\u011f\u0131 s\u0131f\u0131rd\u0131r; olas\u0131l\u0131klar bunun yerine e\u011frinin alt\u0131ndaki <em>alanlara<\/em> kar\u015f\u0131l\u0131k gelir. K\u00fcm\u00fclatif olas\u0131l\u0131k \\(F(x)=P(X&lt;x)\\) e\u011frinin solunda kalan aland\u0131r; \\(P(X&gt;x)=1-F(x)\\) ise sa\u011f\u0131nda kalan aland\u0131r. Olas\u0131l\u0131k yo\u011funlu\u011fu \\(f(x)\\) tek ba\u015f\u0131na bir olas\u0131l\u0131k de\u011fildir \u2014 e\u011frinin y\u00fcksekli\u011fidir ve farkl\u0131 b\u00f6lgelerin birbirine g\u00f6re ne kadar olas\u0131 oldu\u011funu kar\u015f\u0131la\u015ft\u0131rmak i\u00e7in yararl\u0131d\u0131r.<\/p>\n<p>z-puan\u0131 \\(z=(x-\\mu)\/\\sigma\\) bir de\u011feri ortalaman\u0131n standart sapma cinsinden uzakl\u0131\u011f\u0131 olarak ifade eder. 2'lik bir z-puan\u0131 \"ortalaman\u0131n iki standart sapma \u00fcst\u00fcnde\" demektir. z-puan\u0131na \u00e7evirmek anahtar noktad\u0131r: hangi ortalama ve standart sapmaya sahip olursa olsun, her normal da\u011f\u0131l\u0131m ayn\u0131 standart normal e\u011friye d\u00f6n\u00fc\u015f\u00fcr; b\u00f6ylece olas\u0131l\u0131klar tek bir evrensel fonksiyondan okunabilir.<\/p>\n<h2>Sonucun yorumlanmas\u0131<\/h2>\n<p>68-95-99,7 kural\u0131 (ampirik kural) herhangi bir yan\u0131t i\u00e7in h\u0131zl\u0131 bir sa\u011flama sa\u011flar:<\/p>\n<table>\n<thead>\n<tr>\n<th>Ortalama etraf\u0131ndaki aral\u0131k<\/th>\n<th>\u0130\u00e7eride kalan veri pay\u0131<\/th>\n<th>D\u0131\u015far\u0131da kalan pay (iki kuyruk)<\/th>\n<\/tr>\n<\/thead>\n<tbody>\n<tr>\n<td>\\(\\mu \\pm 1\\sigma\\)<\/td>\n<td>68.27%<\/td>\n<td>31.73%<\/td>\n<\/tr>\n<tr>\n<td>\\(\\mu \\pm 2\\sigma\\)<\/td>\n<td>95.45%<\/td>\n<td>4.55%<\/td>\n<\/tr>\n<tr>\n<td>\\(\\mu \\pm 3\\sigma\\)<\/td>\n<td>99.73%<\/td>\n<td>0.27%<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<p>Hesaplad\u0131\u011f\u0131n\u0131z olas\u0131l\u0131k bu k\u0131staslarla ciddi bi\u00e7imde \u00e7eli\u015fiyorsa girdilerinizi iki kez kontrol edin. \u00d6rne\u011fin, varsay\u0131lan ayarlarla 110'un alt\u0131ndaki bir de\u011ferin olas\u0131l\u0131\u011f\u0131 (z = 0,67) %68'den biraz fazla olmal\u0131d\u0131r, \u00e7\u00fcnk\u00fc 110 ortalamadan birden fazla standart sapma yukar\u0131dad\u0131r \u2014 ve %74,75 bu beklentiye uyar.<\/p>\n<h2>Varsay\u0131mlar, s\u0131n\u0131rlamalar ve pratik ipu\u00e7lar\u0131<\/h2>\n<ul>\n<li><strong>Normallik varsay\u0131m\u0131:<\/strong> hesaplay\u0131c\u0131, verilerinizin ger\u00e7ekten normal da\u011f\u0131l\u0131m izledi\u011fini varsayar. Ger\u00e7ek veriler \u00e7o\u011fu zaman \u00e7arp\u0131k, s\u0131n\u0131rl\u0131 veya kal\u0131n kuyrukludur; u\u00e7 de\u011ferlere ait olas\u0131l\u0131klar bu varsay\u0131ma \u00f6zellikle duyarl\u0131d\u0131r.<\/li>\n<li><strong>Kesin ve kesin olmayan e\u015fitsizlik:<\/strong> s\u00fcrekli bir da\u011f\u0131l\u0131m i\u00e7in \\(P(X&lt;x)\\) ve \\(P(X\\le x)\\) birbirinin ayn\u0131s\u0131d\u0131r, bu y\u00fczden hangi yaz\u0131m\u0131 kulland\u0131\u011f\u0131n\u0131z\u0131n \u00f6nemi yoktur.<\/li>\n<li><strong>K\u00fc\u00e7\u00fck olas\u0131l\u0131klar:<\/strong> kuyruklarda \u00e7ok uzaktaki de\u011ferler (|z| yakla\u015f\u0131k 4'\u00fc a\u015farsa) 0'a veya 1'e yak\u0131n olas\u0131l\u0131klar verir; hesaplay\u0131c\u0131 bunlar\u0131 yine de okuyabilmeniz i\u00e7in alt\u0131 ondal\u0131k basamak g\u00f6sterir.<\/li>\n<li><strong>\u00d6rneklem ve anakitle:<\/strong> anakitle ortalamas\u0131n\u0131 ve standart sapmas\u0131n\u0131 biliyorsan\u0131z bunlar\u0131 girin. Yaln\u0131zca \u00f6rneklem tahminleriniz varsa sonu\u00e7lar yakla\u015f\u0131kt\u0131r \u2014 k\u00fc\u00e7\u00fck \u00f6rneklemeler i\u00e7in t-da\u011f\u0131l\u0131m\u0131 daha uygundur.<\/li>\n<li><strong>Negatif veya s\u0131f\u0131r \u03c3:<\/strong> standart sapma kesinlikle pozitif olmal\u0131d\u0131r; hesaplay\u0131c\u0131 ba\u015fka hi\u00e7bir de\u011feri kabul etmez, \u00e7\u00fcnk\u00fc s\u0131f\u0131r yay\u0131l\u0131m e\u011friyi tek bir sivri noktaya indirgerdi.<\/li>\n<li><strong>Duyarl\u0131l\u0131k:<\/strong> olas\u0131l\u0131klar, yakla\u015f\u0131k 7 ondal\u0131k basamak duyarl\u0131kl\u0131 bir hata fonksiyonu yakla\u015f\u0131klamas\u0131yla hesaplan\u0131r; bu, pratik \u00e7al\u0131\u015fma i\u00e7in fazlas\u0131yla yeterlidir.<\/li>\n<\/ul>\n","protected":false},"excerpt":{"rendered":"<p>Normal da\u011f\u0131l\u0131m i\u00e7in olas\u0131l\u0131k yo\u011funlu\u011funu, k\u00fcm\u00fclatif olas\u0131l\u0131klar\u0131 P(X &lt; x), P(X &gt; x), P(a &lt; X &lt; b) ve z-puan\u0131n\u0131 elde etmek \u00fczere bir ortalama, standart sapma ve bir de\u011fer (ya da iki s\u0131n\u0131r) girin.<\/p>\n","protected":false},"author":3168,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"_acf_changed":false,"footnotes":""},"categories":[12],"tags":[34],"class_list":["post-582","post","type-post","status-publish","format-standard","hentry","category-istatistik","tag-dagilimlar"],"acf":[],"_links":{"self":[{"href":"https:\/\/wpcalc.com\/tr\/wp-json\/wp\/v2\/posts\/582","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/wpcalc.com\/tr\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/wpcalc.com\/tr\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/wpcalc.com\/tr\/wp-json\/wp\/v2\/users\/3168"}],"replies":[{"embeddable":true,"href":"https:\/\/wpcalc.com\/tr\/wp-json\/wp\/v2\/comments?post=582"}],"version-history":[{"count":0,"href":"https:\/\/wpcalc.com\/tr\/wp-json\/wp\/v2\/posts\/582\/revisions"}],"wp:attachment":[{"href":"https:\/\/wpcalc.com\/tr\/wp-json\/wp\/v2\/media?parent=582"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/wpcalc.com\/tr\/wp-json\/wp\/v2\/categories?post=582"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/wpcalc.com\/tr\/wp-json\/wp\/v2\/tags?post=582"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}