{"id":79,"date":"2023-08-05T17:33:30","date_gmt":"2023-08-05T17:33:30","guid":{"rendered":"https:\/\/statorials.org\/cn\/%e6%a0%87%e5%87%86%e5%b7%ae%e6%88%96%e6%a0%87%e5%87%86%e5%b7%ae\/"},"modified":"2023-08-05T17:33:30","modified_gmt":"2023-08-05T17:33:30","slug":"%e6%a0%87%e5%87%86%e5%b7%ae%e6%88%96%e6%a0%87%e5%87%86%e5%b7%ae","status":"publish","type":"post","link":"https:\/\/statorials.org\/cn\/%e6%a0%87%e5%87%86%e5%b7%ae%e6%88%96%e6%a0%87%e5%87%86%e5%b7%ae\/","title":{"rendered":"\u6807\u51c6\u5dee\uff08\u6216\u6807\u51c6\u5dee\uff09"},"content":{"rendered":"<p>\u672c\u6587\u89e3\u91ca\u4ec0\u4e48\u662f\u6807\u51c6\u5dee\uff0c\u4e5f\u79f0\u4e3a\u6807\u51c6\u5dee\u3002\u60a8\u5c06\u5b66\u4e60\u5982\u4f55\u8ba1\u7b97\u6807\u51c6\u5dee\u3001\u5206\u6b65\u5b9e\u8df5\u793a\u4f8b\u4ee5\u53ca\u7528\u4e8e\u67e5\u627e\u4efb\u4f55\u6570\u636e\u6837\u672c\u7684\u6807\u51c6\u5dee\u7684\u5728\u7ebf\u8ba1\u7b97\u5668\u3002 <\/p>\n<h2 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"%c2%bfque-es-la-desviacion-estandar-o-desviacion-tipica\"><\/span>\u4ec0\u4e48\u662f\u6807\u51c6\u5dee\uff08\u6216\u6807\u51c6\u5dee\uff09\uff1f<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p><strong>\u6807\u51c6\u5dee<\/strong>\uff0c\u4e5f\u79f0\u4e3a<strong>\u6807\u51c6\u504f\u5dee<\/strong>\uff0c\u662f\u7edf\u8ba1\u79bb\u6563\u5ea6\u7684\u5ea6\u91cf\u3002\u6362\u53e5\u8bdd\u8bf4\uff0c\u6807\u51c6\u5dee\u662f\u8868\u793a\u4e00\u7ec4\u7edf\u8ba1\u6570\u636e\u5206\u6563\u7a0b\u5ea6\u7684\u503c\u3002<\/p>\n<p>\u56e0\u6b64\uff0c<strong>\u6807\u51c6\u5dee\uff08\u6216\u6807\u51c6\u5dee\uff09\u7528\u4e8e\u91cf\u5316\u603b\u4f53\u6216\u7edf\u8ba1\u6837\u672c\u7684\u79bb\u6563\u7a0b\u5ea6\u3002<\/strong>\u6570\u636e\u7cfb\u5217\u7684\u6807\u51c6\u5dee\u8d8a\u5927\uff0c\u8868\u660e\u6570\u636e\u8d8a\u5206\u6563\u3002\u4e5f\u53ef\u4ee5\u4ece\u53e6\u4e00\u4e2a\u65b9\u5411\u8fdb\u884c\u89e3\u91ca\uff0c\u5982\u679c\u6807\u51c6\u5dee\u5f88\u4f4e\uff0c\u8fd9\u610f\u5473\u7740\u901a\u5e38\u6570\u636e\u975e\u5e38\u63a5\u8fd1\u5176\u5e73\u5747\u503c\u3002<\/p>\n<p>\u8ba1\u7b97\u603b\u4f53\u7684\u6807\u51c6\u504f\u5dee\u6216\u5178\u578b\u504f\u5dee\u65f6\uff0c<strong>\u6807\u51c6\u504f\u5dee\u7684\u7b26\u53f7<\/strong>\u662f\u5e0c\u814a\u5b57\u6bcd sigma (\u03c3)\u3002\u4f46\u5f53\u6d89\u53ca\u6837\u672c\u6807\u51c6\u5dee\u65f6\uff0c\u5b57\u6bcd s \u7528\u4e8e\u8868\u793a\u7edf\u8ba1\u6d4b\u91cf\u3002<\/p>\n<p>\u5728\u4e00\u4e9b\u7edf\u8ba1\u5b66\u548c\u6982\u7387\u4e66\u7c4d\u4e2d\uff0c\u6807\u51c6\u5dee\u4e5f\u79f0\u4e3a\u6807\u51c6\u5dee\u3002 <\/p>\n<h2 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"formula-de-la-desviacion-estandar-o-desviacion-tipica\"><\/span>\u6807\u51c6\u5dee\uff08\u6216\u6807\u51c6\u5dee\uff09\u516c\u5f0f<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p>\u6807\u51c6\u5dee\uff08\u6216\u6807\u51c6\u5dee\uff09\u7b49\u4e8e\u6570\u636e\u7cfb\u5217\u504f\u5dee\u5e73\u65b9\u548c\u9664\u4ee5\u89c2\u6d4b\u503c\u603b\u6570\u7684\u5e73\u65b9\u6839\u3002<\/p>\n<p>\u56e0\u6b64<strong>\uff0c\u8ba1\u7b97\u6807\u51c6\u5dee\uff08\u6216\u6807\u51c6\u5dee\uff09\u7684\u516c\u5f0f<\/strong>\u4e3a\uff1a <\/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=\"\u6807\u51c6\u5dee, \u6807\u51c6\u5dee\" class=\"wp-image-1652\" width=\"334\" height=\"334\" srcset=\"\" sizes=\"auto, \"><\/figure>\n<p> \ud83d\udc49<u style=\"text-decoration-color:#FF8A05;\">\u60a8\u53ef\u4ee5\u4f7f\u7528\u4e0b\u9762\u7684\u8ba1\u7b97\u5668\u6765\u8ba1\u7b97\u4efb\u4f55\u6570\u636e\u96c6\u7684\u6807\u51c6\u5dee\u3002<\/u><\/p>\n<p>\u603b\u4e4b\uff0c\u8981\u627e\u5230\u6570\u636e\u96c6\u7684\u6807\u51c6\u5dee\uff0c\u60a8\u9700\u8981\u8ba1\u7b97\u6240\u6709\u504f\u5dee\uff08\u5b9a\u4e49\u4e3a\u6570\u636e\u70b9\u4e0e\u7b97\u672f\u5e73\u5747\u503c\u4e4b\u95f4\u7684\u5dee\uff09\uff0c\u5c06\u504f\u5dee\u589e\u52a0\u5230\u4e24\u500d\uff0c\u5c06\u5b83\u4eec\u5168\u90e8\u76f8\u52a0\uff0c\u7136\u540e\u9664\u4ee5\u5168\u90e8\u7684\u3002\u6570\u636e\u4e2a\u6570\uff0c\u6700\u540e\u53d6\u5e73\u65b9\u6839\u3002 <\/p>\n<h2 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"ejemplo-de-desviacion-estandar-o-desviacion-tipica\"><\/span>\u6807\u51c6\u5dee\uff08\u6216\u6807\u51c6\u5dee\uff09\u793a\u4f8b<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p>\u8003\u8651\u5230\u6807\u51c6\u5dee\uff08\u6216\u5178\u578b\u5dee\uff09\u7684\u5b9a\u4e49\uff0c\u4e0b\u9762\u662f\u4e00\u4e2a\u5206\u6b65\u793a\u4f8b\uff0c\u4ee5\u4fbf\u60a8\u53ef\u4ee5\u4e86\u89e3\u5982\u4f55\u8ba1\u7b97\u6570\u636e\u7cfb\u5217\u7684\u6807\u51c6\u5dee\u3002<\/p>\n<ul>\n<li>\u8ba1\u7b97\u4ee5\u4e0b\u503c\u7684\u6807\u51c6\u5dee\uff1a3\u30016\u30012\u30019\u30014\u3002<\/li>\n<\/ul>\n<p>\u6211\u4eec\u9700\u8981\u505a\u7684\u7b2c\u4e00\u4ef6\u4e8b\u662f\u786e\u5b9a\u6837\u672c\u5747\u503c\u3002\u4e3a\u6b64\uff0c\u6211\u4eec\u5c06\u6240\u6709\u6570\u636e\u76f8\u52a0\u5e76\u9664\u4ee5\u89c2\u5bdf\u603b\u6570\uff08\u5373 5\uff09\uff1a<\/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>\u6211\u4eec\u73b0\u5728\u4f7f\u7528\u6807\u51c6\u5dee\u516c\u5f0f\uff1a<\/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>\u6211\u4eec\u5c06\u6570\u636e\u4ee3\u5165\u516c\u5f0f\uff1a<\/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>\u6700\u540e\u6211\u4eec\u8ba1\u7b97\u6807\u51c6\u5dee\uff1a <\/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>\u6807\u51c6\u5dee\uff08\u6216\u6807\u51c6\u5dee\uff09\u8ba1\u7b97\u5668<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p>\u5c06\u4e00\u7ec4\u7edf\u8ba1\u6570\u636e\u8f93\u5165\u5230\u4e0b\u9762\u7684\u5728\u7ebf\u8ba1\u7b97\u5668\u4e2d\uff0c\u8ba1\u7b97\u5176\u6807\u51c6\u5dee\uff08\u6216\u6807\u51c6\u5dee\uff09\u3002\u6570\u636e\u5fc5\u987b\u7528\u7a7a\u683c\u5206\u9694\uff0c\u5e76\u4f7f\u7528\u53e5\u70b9\u4f5c\u4e3a\u5c0f\u6570\u70b9\u5206\u9694\u7b26\u8f93\u5165\u3002 <\/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=\"\u8ba1\u7b97\u6807\u51c6\u5dee\"><\/div>\n<\/form>\n<h2 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"desviacion-estandar-o-tipica-para-datos-agrupados\"><\/span>\u5206\u7ec4\u6570\u636e\u7684\u6807\u51c6\uff08\u6216\u5178\u578b\uff09\u504f\u5dee<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p><strong>\u8981\u8ba1\u7b97\u5206\u7ec4\u4e3a\u533a\u95f4 \u7684\u6570\u636e\u7684\u6807\u51c6\u5dee\uff08\u6216\u6807\u51c6\u5dee\uff09<\/strong> \uff0c\u5fc5\u987b\u9075\u5faa\u4ee5\u4e0b\u6b65\u9aa4\uff1a<\/p>\n<ol style=\"color:#FF8A05; font-weight: bold;\">\n<li style=\"margin-bottom:12px\"><span style=\"color:#101010;font-weight: normal;\">\u6c42\u5206\u7ec4\u6570\u636e\u7684\u5e73\u5747\u503c\u3002<\/span><\/li>\n<li style=\"margin-bottom:12px\"><span style=\"color:#101010;font-weight: normal;\">\u8ba1\u7b97\u5206\u7ec4\u6570\u636e\u7684\u504f\u5dee\u3002<\/span><\/li>\n<li style=\"margin-bottom:12px\"><span style=\"color:#101010;font-weight: normal;\">\u5c06\u6bcf\u4e2a\u95f4\u9699\u5e73\u65b9\u3002<\/span><\/li>\n<li style=\"margin-bottom:12px\"><span style=\"color:#101010;font-weight: normal;\">\u5c06\u4e4b\u524d\u7684\u6bcf\u4e2a\u7ed3\u679c\u4e58\u4ee5\u5176\u95f4\u9694\u7684\u9891\u7387\u3002<\/span><\/li>\n<li style=\"margin-bottom:12px\"><span style=\"color:#101010;font-weight: normal;\">\u5c06\u4e0a\u4e00\u6b65\u83b7\u5f97\u7684\u6240\u6709\u503c\u76f8\u52a0\u3002<\/span><\/li>\n<li style=\"margin-bottom:12px\"><span style=\"color:#101010;font-weight: normal;\">\u9664\u4ee5\u89c2\u5bdf\u603b\u6570\u3002<\/span><\/li>\n<li><span style=\"color:#101010;font-weight: normal;\">\u53d6\u524d\u4e00\u4e2a\u503c\u7684\u5e73\u65b9\u6839\u3002\u6240\u5f97\u6570\u5b57\u662f\u5206\u7ec4\u6570\u636e\u7684\u6807\u51c6\u5dee\u3002<\/span><\/li>\n<\/ol>\n<p>\u603b\u4e4b\uff0c\u6309\u533a\u95f4\u5206\u7ec4\u7684\u6570\u636e\u6807\u51c6\u5dee\u7684\u8ba1\u7b97\u516c\u5f0f\u4e3a\uff1a<\/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>\u867d\u7136\u901a\u5e38\u4f7f\u7528\u4e0a\u9762\u7684\u516c\u5f0f\uff0c\u4f46\u662f\u4e5f\u53ef\u4ee5\u4f7f\u7528\u4e0b\u9762\u7684\u4ee3\u6570\u8868\u8fbe\u5f0f\uff0c\u56e0\u4e3a\u53ef\u4ee5\u5f97\u5230\u76f8\u540c\u7684\u7ed3\u679c\uff1a<\/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>\u56e0\u6b64\uff0c\u60a8\u53ef\u4ee5\u770b\u5230\u8fd9\u662f\u5982\u4f55\u5b8c\u6210\u7684\uff0c\u4e0b\u9762\u662f\u5bf9\u5206\u7ec4\u4e3a\u533a\u95f4\u7684\u6570\u636e\u6807\u51c6\u5dee\u7684\u5206\u6b65\u7ec3\u4e60\u3002\u66f4\u51c6\u786e\u5730\u8bf4\uff0c\u5c06\u8ba1\u7b97\u4ee5\u4e0b\u7edf\u8ba1\u6570\u636e\u7684\u6807\u51c6\u5dee\uff1a <\/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=\"\u6309\u533a\u95f4\u5206\u7ec4\u7684\u6570\u636e\u793a\u4f8b\" class=\"wp-image-1679\" width=\"244\" height=\"180\" srcset=\"\" sizes=\"auto, \"><\/figure>\n<p>\u9996\u5148\uff0c\u6211\u4eec\u5c06\u6bcf\u4e2a\u533a\u95f4\u7684\u73ed\u7ea7\u5206\u6570\u4e58\u4ee5\u5176\u9891\u7387\u6765\u8ba1\u7b97\u7b97\u672f\u5e73\u5747\u503c\uff1a <\/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>\u56e0\u6b64\u5206\u7ec4\u6570\u636e\u7684\u5e73\u5747\u503c\u5c06\u662f\uff1a<\/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>\u73b0\u5728\u6211\u4eec\u77e5\u9053\u5e73\u5747\u503c\u7684\u503c\uff0c\u6211\u4eec\u9700\u8981\u5c06\u4ee5\u4e0b\u4e09\u5217\u6dfb\u52a0\u5230\u6570\u636e\u8868\u4e2d\uff1a <\/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=\"\u89e3\u51b3\u4e86\u6807\u51c6\u5dee\u6216\u5206\u7ec4\u6570\u636e\u6807\u51c6\u5dee\u7684\u7ec3\u4e60\" class=\"wp-image-1683\" width=\"606\" height=\"180\" srcset=\"\" sizes=\"auto, \"><\/figure>\n<p>\u90a3\u4e48\u5206\u7ec4\u6570\u636e\u7684\u6807\u51c6\u5dee\u5c06\u662f\u6700\u540e\u4e00\u5217\u603b\u6570\u9664\u4ee5\u89c2\u6d4b\u603b\u6570\u7684\u5e73\u65b9\u6839\u7684\u7ed3\u679c\uff1a <\/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>\u6807\u51c6\uff08\u6216\u5178\u578b\uff09\u504f\u5dee\u548c\u65b9\u5dee<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p><strong>\u6807\u51c6\u5dee\uff08\u6216\u5178\u578b\u5dee\uff09\u4e0e\u65b9\u5dee\u7684\u5173\u7cfb<\/strong>\u662f\u6807\u51c6\u5dee\u662f\u65b9\u5dee\u7684\u5e73\u65b9\u6839\u3002<\/p>\n<p>\u56e0\u6b64\uff0c\u5982\u679c\u6211\u4eec\u77e5\u9053\u6570\u636e\u96c6\u7684\u65b9\u5dee\u503c\uff0c\u6211\u4eec\u53ef\u4ee5\u901a\u8fc7\u5e73\u65b9\u6839\u8f7b\u677e\u8ba1\u7b97\u6807\u51c6\u5dee\u3002\u6216\u8005\u76f8\u53cd\uff0c\u5982\u679c\u6211\u4eec\u77e5\u9053\u6807\u51c6\u5dee\uff0c\u6211\u4eec\u53ef\u4ee5\u901a\u8fc7\u5bf9\u8be5\u503c\u8fdb\u884c\u5e73\u65b9\u6765\u627e\u5230\u65b9\u5dee\u3002<\/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>\u4e8b\u5b9e\u4e0a\uff0c\u65b9\u5dee\u53ef\u4ee5\u7b80\u5355\u5730\u7528\u5e73\u65b9\u6807\u51c6\u5dee\u7b26\u53f7\u6765\u8868\u793a\u3002\u56e0\u6b64\uff0c\u603b\u4f53\u65b9\u5dee\u7684\u7b26\u53f7\u4e3a sigma \u5e73\u65b9 (\u03c3 <sup>2<\/sup> )\uff0c\u6837\u672c\u65b9\u5dee\u7684\u7b26\u53f7\u4e3a s \u5e73\u65b9 (s <sup>2<\/sup> )\u3002<\/p>\n<p>\u6b64\u5916\uff0c\u6807\u51c6\u5dee\u548c\u65b9\u5dee\u7684\u6982\u5ff5\u5177\u6709\u76f8\u4f3c\u7684\u89e3\u91ca\uff0c\u56e0\u4e3a\u4e24\u8005\u90fd\u663e\u793a\u4e86\u4e00\u7cfb\u5217\u7edf\u8ba1\u6570\u636e\u7684\u5206\u6563\u6027\u3002 <\/p>\n<h2 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"propiedades-de-la-desviacion-estandar-o-desviacion-tipica\"><\/span>\u6807\u51c6\u5dee\uff08\u6216\u6807\u51c6\u5dee\uff09\u7684\u6027\u8d28<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p>\u6807\u51c6\u5dee\u5177\u6709\u4ee5\u4e0b\u5c5e\u6027\uff1a<\/p>\n<ul>\n<li>\u6570\u636e\u6837\u672c\u7684\u6807\u51c6\u5dee\u4e0d\u80fd\u4e3a\u8d1f\u3002<\/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>\u5982\u679c\u6240\u6709\u6570\u636e\u90fd\u76f8\u540c\uff0c\u6807\u51c6\u504f\u5dee\u5c06\u4e3a\u96f6\u3002<\/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>\u5982\u679c\u5c06\u5e38\u6570\u9879\u6dfb\u52a0\u5230\u6240\u6709\u6570\u636e\u4e2d\uff0c\u6807\u51c6\u5dee\u503c\u4e0d\u4f1a\u6539\u53d8\u3002<\/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>\u5982\u679c\u6240\u6709\u6570\u636e\u4e58\u4ee5\u4e00\u4e2a\u6570\u5b57\uff0c\u5219\u6807\u51c6\u5dee\u5c06\u4e58\u4ee5\u8be5\u6570\u5b57\u7684\u7edd\u5bf9\u503c\u3002<\/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>\u4e24\u4e2a\u968f\u673a\u53d8\u91cf\u4e4b\u548c\u7684\u6807\u51c6\u5dee\u7b49\u4e8e\u53d8\u91cf\u65b9\u5dee\u4e4b\u548c\u7684\u5e73\u65b9\u6839\u52a0\u4e0a\u4e24\u4e2a\u53d8\u91cf\u4e4b\u95f4\u534f\u65b9\u5dee\u7684\u4e24\u500d\u3002<\/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>\u5982\u679c\u6211\u4eec\u77e5\u9053\u4e0d\u540c\u5206\u5e03\u7684\u6807\u51c6\u5dee (\u03c3 <sub>i<\/sub> ) \u53ca\u5176\u6570\u636e\u6570\u91cf (n <sub>i<\/sub> )\uff0c\u6211\u4eec\u53ef\u4ee5\u901a\u8fc7\u5e94\u7528\u4ee5\u4e0b\u516c\u5f0f\u8ba1\u7b97\u603b\u6807\u51c6\u5dee\uff1a<\/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>\u672c\u6587\u89e3\u91ca\u4ec0\u4e48\u662f\u6807\u51c6\u5dee\uff0c\u4e5f\u79f0\u4e3a\u6807\u51c6\u5dee\u3002\u60a8\u5c06\u5b66\u4e60\u5982\u4f55\u8ba1\u7b97\u6807\u51c6\u5dee\u3001\u5206\u6b65\u5b9e\u8df5\u793a\u4f8b\u4ee5\u53ca\u7528\u4e8e\u67e5\u627e\u4efb\u4f55\u6570\u636e\u6837\u672c\u7684\u6807\u51c6\u5dee\u7684\u5728\u7ebf [&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-14"],"yoast_head":"<!-- This site is optimized with the Yoast SEO plugin v21.5 - https:\/\/yoast.com\/wordpress\/plugins\/seo\/ -->\n<title>\u25b7\u6807\u51c6\u5dee\uff08\u6216\u6807\u51c6\u5dee\uff09<\/title>\n<meta name=\"description\" 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