{"id":19862,"date":"2025-04-09T21:56:42","date_gmt":"2025-04-09T13:56:42","guid":{"rendered":"https:\/\/blog.iyatt.com\/?p=19862"},"modified":"2025-11-15T15:03:25","modified_gmt":"2025-11-15T07:03:25","slug":"%e6%a0%87%e5%87%86%e5%81%8f%e5%b7%ae-standard-deviation","status":"publish","type":"post","link":"https:\/\/blog.iyatt.com\/?p=19862","title":{"rendered":"\u6807\u51c6\u504f\u5dee Standard Deviation"},"content":{"rendered":"<div id=\"ez-toc-container\" class=\"ez-toc-v2_0_83 ez-toc-wrap-center counter-hierarchy ez-toc-counter ez-toc-light-blue ez-toc-container-direction\">\n<div class=\"ez-toc-title-container\">\n<p class=\"ez-toc-title ez-toc-toggle\" style=\"cursor:pointer\">\u76ee\u5f55<\/p>\n<span class=\"ez-toc-title-toggle\"><a href=\"#\" class=\"ez-toc-pull-right ez-toc-btn ez-toc-btn-xs ez-toc-btn-default ez-toc-toggle\" aria-label=\"Toggle Table of Content\"><span class=\"ez-toc-js-icon-con\"><span class=\"\"><span class=\"eztoc-hide\" style=\"display:none;\">Toggle<\/span><span class=\"ez-toc-icon-toggle-span\"><svg style=\"fill: #999;color:#999\" xmlns=\"http:\/\/www.w3.org\/2000\/svg\" class=\"list-377408\" width=\"20px\" height=\"20px\" viewBox=\"0 0 24 24\" fill=\"none\"><path d=\"M6 6H4v2h2V6zm14 0H8v2h12V6zM4 11h2v2H4v-2zm16 0H8v2h12v-2zM4 16h2v2H4v-2zm16 0H8v2h12v-2z\" fill=\"currentColor\"><\/path><\/svg><svg style=\"fill: #999;color:#999\" class=\"arrow-unsorted-368013\" xmlns=\"http:\/\/www.w3.org\/2000\/svg\" width=\"10px\" height=\"10px\" viewBox=\"0 0 24 24\" version=\"1.2\" baseProfile=\"tiny\"><path d=\"M18.2 9.3l-6.2-6.3-6.2 6.3c-.2.2-.3.4-.3.7s.1.5.3.7c.2.2.4.3.7.3h11c.3 0 .5-.1.7-.3.2-.2.3-.5.3-.7s-.1-.5-.3-.7zM5.8 14.7l6.2 6.3 6.2-6.3c.2-.2.3-.5.3-.7s-.1-.5-.3-.7c-.2-.2-.4-.3-.7-.3h-11c-.3 0-.5.1-.7.3-.2.2-.3.5-.3.7s.1.5.3.7z\"\/><\/svg><\/span><\/span><\/span><\/a><\/span><\/div>\n<nav><ul class='ez-toc-list ez-toc-list-level-1 ' ><li class='ez-toc-page-1 ez-toc-heading-level-1'><a class=\"ez-toc-link ez-toc-heading-1\" href=\"https:\/\/blog.iyatt.com\/?p=19862\/#%E6%80%BB%E4%BD%93%E6%A0%87%E5%87%86%E5%81%8F%E5%B7%AE_Population_Standard_Deviation\" >\u603b\u4f53\u6807\u51c6\u504f\u5dee Population Standard Deviation<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-1'><a class=\"ez-toc-link ez-toc-heading-2\" href=\"https:\/\/blog.iyatt.com\/?p=19862\/#%E6%A0%B7%E6%9C%AC%E6%A0%87%E5%87%86%E5%81%8F%E5%B7%AE_Sample_Standard_Deviation\" >\u6837\u672c\u6807\u51c6\u504f\u5dee Sample Standard Deviation<\/a><\/li><\/ul><\/nav><\/div>\n<h1><span class=\"ez-toc-section\" id=\"%E6%80%BB%E4%BD%93%E6%A0%87%E5%87%86%E5%81%8F%E5%B7%AE_Population_Standard_Deviation\"><\/span>\u603b\u4f53\u6807\u51c6\u504f\u5dee Population Standard Deviation<span class=\"ez-toc-section-end\"><\/span><\/h1>\n<p><code class=\"katex-inline\">\\sigma=\\sqrt{\\frac{1}{n}\\sum_{i=1}^{n}(x_i-\\mu)^2}<\/code><br \/>\n<code class=\"katex-inline\">n<\/code>\uff1a\u6570\u636e\u603b\u4e2a\u6570<br \/>\n<code class=\"katex-inline\">x_i<\/code>\uff1a\u7b2c i \u4e2a\u6570\u636e<br \/>\n<code class=\"katex-inline\">\\mu<\/code>\uff1a\u6570\u636e\u5e73\u5747\u503c<\/p>\n<p>Excel \u4e2d\u53ef\u4ee5\u4f7f\u7528 <strong>STDEV.P<\/strong> \u51fd\u6570\u8ba1\u7b97<br \/>\n<img decoding=\"async\" data-src=\"https:\/\/blog.iyatt.com\/wp-content\/uploads\/2025\/04\/image-1744206503706.png\" alt=\"file\" src=\"data:image\/svg+xml;base64,PHN2ZyB3aWR0aD0iMSIgaGVpZ2h0PSIxIiB4bWxucz0iaHR0cDovL3d3dy53My5vcmcvMjAwMC9zdmciPjwvc3ZnPg==\" class=\"lazyload\" style=\"--smush-placeholder-width: 341px; --smush-placeholder-aspect-ratio: 341\/123;\" \/><\/p>\n<pre><code class=\"language-katex\">\\begin{array}{l}\nn=4 \\\\\n\\mu=\\frac{3+9+4+10}{9}=6.5 \\\\\n\\sigma=\\sqrt{\\frac{1}{4}[(3-6.5)^2+(9-6.5)^2+(4-6.5)^2+(10-6.5)^2]}\\approx3.041381265\n\\end{array}<\/code><\/pre>\n<p><img decoding=\"async\" data-src=\"https:\/\/blog.iyatt.com\/wp-content\/uploads\/2025\/04\/image-1744206756944.png\" alt=\"file\" src=\"data:image\/svg+xml;base64,PHN2ZyB3aWR0aD0iMSIgaGVpZ2h0PSIxIiB4bWxucz0iaHR0cDovL3d3dy53My5vcmcvMjAwMC9zdmciPjwvc3ZnPg==\" class=\"lazyload\" style=\"--smush-placeholder-width: 603px; --smush-placeholder-aspect-ratio: 603\/409;\" \/><\/p>\n<h1><span class=\"ez-toc-section\" id=\"%E6%A0%B7%E6%9C%AC%E6%A0%87%E5%87%86%E5%81%8F%E5%B7%AE_Sample_Standard_Deviation\"><\/span>\u6837\u672c\u6807\u51c6\u504f\u5dee Sample Standard Deviation<span class=\"ez-toc-section-end\"><\/span><\/h1>\n<p><code class=\"katex-inline\">s=\\sqrt{\\frac{1}{n-1}\\sum_{i=1}^{n}(x_i-\\mu)^2}<\/code><br \/>\n<code class=\"katex-inline\">n<\/code>\uff1a\u6570\u636e\u603b\u4e2a\u6570<br \/>\n<code class=\"katex-inline\">x_i<\/code>\uff1a\u7b2c i \u4e2a\u6570\u636e<br \/>\n<code class=\"katex-inline\">\\mu<\/code>\uff1a\u6570\u636e\u5e73\u5747\u503c<\/p>\n<p>Excel \u4e2d\u53ef\u4ee5\u4f7f\u7528 <strong>STDEV.S<\/strong> \u51fd\u6570\u8ba1\u7b97<br \/>\n<img decoding=\"async\" data-src=\"https:\/\/blog.iyatt.com\/wp-content\/uploads\/2025\/04\/image-1744206895241.png\" alt=\"file\" src=\"data:image\/svg+xml;base64,PHN2ZyB3aWR0aD0iMSIgaGVpZ2h0PSIxIiB4bWxucz0iaHR0cDovL3d3dy53My5vcmcvMjAwMC9zdmciPjwvc3ZnPg==\" class=\"lazyload\" style=\"--smush-placeholder-width: 353px; --smush-placeholder-aspect-ratio: 353\/108;\" \/><\/p>\n<pre><code class=\"language-katex\">\\begin{array}{l}\nn=4 \\\\\n\\mu=\\frac{3+9+4+10}{9}=6.5 \\\\\n\\sigma=\\sqrt{\\frac{1}{4-1}[(3-6.5)^2+(9-6.5)^2+(4-6.5)^2+(10-6.5)^2]}\\approx3.511884584\n\\end{array}<\/code><\/pre>\n<p><img decoding=\"async\" data-src=\"https:\/\/blog.iyatt.com\/wp-content\/uploads\/2025\/04\/image-1744206934790.png\" alt=\"file\" src=\"data:image\/svg+xml;base64,PHN2ZyB3aWR0aD0iMSIgaGVpZ2h0PSIxIiB4bWxucz0iaHR0cDovL3d3dy53My5vcmcvMjAwMC9zdmciPjwvc3ZnPg==\" class=\"lazyload\" style=\"--smush-placeholder-width: 594px; --smush-placeholder-aspect-ratio: 594\/400;\" \/><\/p>\n","protected":false},"excerpt":{"rendered":"<p>\u603b\u4f53\u6807\u51c6\u504f\u5dee Population Standard Deviation \\sigma=\\sqrt{\\frac [&hellip;]<\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"closed","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":{"zakra_page_container_layout":"customizer","zakra_page_sidebar_layout":"customizer","zakra_remove_content_margin":false,"zakra_sidebar":"customizer","zakra_transparent_header":"customizer","zakra_logo":0,"zakra_main_header_style":"default","zakra_menu_item_color":"","zakra_menu_item_hover_color":"","zakra_menu_item_active_color":"","zakra_menu_active_style":"","zakra_page_header":true,"_lmt_disableupdate":"no","_lmt_disable":"no","footnotes":""},"categories":[1,649,648,612],"tags":[],"class_list":["post-19862","post","type-post","status-publish","format-standard","hentry","category-all","category-excel","category-office","category-612"],"modified_by":"IYATT-yx","_links":{"self":[{"href":"https:\/\/blog.iyatt.com\/index.php?rest_route=\/wp\/v2\/posts\/19862","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/blog.iyatt.com\/index.php?rest_route=\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/blog.iyatt.com\/index.php?rest_route=\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/blog.iyatt.com\/index.php?rest_route=\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/blog.iyatt.com\/index.php?rest_route=%2Fwp%2Fv2%2Fcomments&post=19862"}],"version-history":[{"count":2,"href":"https:\/\/blog.iyatt.com\/index.php?rest_route=\/wp\/v2\/posts\/19862\/revisions"}],"predecessor-version":[{"id":19869,"href":"https:\/\/blog.iyatt.com\/index.php?rest_route=\/wp\/v2\/posts\/19862\/revisions\/19869"}],"wp:attachment":[{"href":"https:\/\/blog.iyatt.com\/index.php?rest_route=%2Fwp%2Fv2%2Fmedia&parent=19862"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/blog.iyatt.com\/index.php?rest_route=%2Fwp%2Fv2%2Fcategories&post=19862"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/blog.iyatt.com\/index.php?rest_route=%2Fwp%2Fv2%2Ftags&post=19862"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}