{"id":136,"date":"2023-08-05T02:21:20","date_gmt":"2023-08-05T02:21:20","guid":{"rendered":"https:\/\/statorials.org\/cn\/%e5%88%87%e6%af%94%e9%9b%aa%e5%a4%ab%e5%ae%9a%e7%90%86\/"},"modified":"2023-08-05T02:21:20","modified_gmt":"2023-08-05T02:21:20","slug":"%e5%88%87%e6%af%94%e9%9b%aa%e5%a4%ab%e5%ae%9a%e7%90%86","status":"publish","type":"post","link":"https:\/\/statorials.org\/cn\/%e5%88%87%e6%af%94%e9%9b%aa%e5%a4%ab%e5%ae%9a%e7%90%86\/","title":{"rendered":"\u5207\u6bd4\u96ea\u592b\u5b9a\u7406"},"content":{"rendered":"<p>\u672c\u6587\u89e3\u91ca\u4ec0\u4e48\u662f\u5207\u6bd4\u96ea\u592b\u5b9a\u7406\u3002\u5728\u8fd9\u91cc\u60a8\u53ef\u4ee5\u627e\u5230\u5207\u6bd4\u96ea\u592b\u5b9a\u7406\u516c\u5f0f\u3001\u5df2\u89e3\u51b3\u7684\u7ec3\u4e60\uff0c\u6b64\u5916\u8fd8\u6709\u5728\u7ebf\u5207\u6bd4\u96ea\u592b\u5b9a\u7406\u8ba1\u7b97\u5668\u3002\u6700\u540e\u8bf4\u660e\u4e86\u5207\u6bd4\u96ea\u592b\u5b9a\u7406\u4e0e\u7ecf\u9a8c\u6cd5\u5219\u7684\u533a\u522b\u3002 <\/p>\n<h2 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"%c2%bfque-es-el-teorema-de-chebyshev\"><\/span>\u4ec0\u4e48\u662f\u5207\u6bd4\u96ea\u592b\u5b9a\u7406\uff1f<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p><strong>\u5207\u6bd4\u96ea\u592b\u5b9a\u7406<\/strong>\uff0c\u4e5f\u79f0\u4e3a<strong>\u5207\u6bd4\u96ea\u592b\u4e0d\u7b49\u5f0f<\/strong>\uff0c\u662f\u4e00\u79cd\u7edf\u8ba1\u89c4\u5219\uff0c\u7528\u4e8e\u8ba1\u7b97\u968f\u673a\u53d8\u91cf\u7684\u503c\u4e0e\u5176\u5e73\u5747\u503c\u5728\u4e00\u5b9a\u8ddd\u79bb\u5185\u7684\u6982\u7387\u3002<\/p>\n<p>\u6362\u53e5\u8bdd\u8bf4\uff0c\u5728\u7edf\u8ba1\u5b66\u4e2d\uff0c\u5207\u6bd4\u96ea\u592b\u5b9a\u7406\u7528\u4e8e\u786e\u5b9a\u67d0\u4e2a\u503c\u4f4d\u4e8e\u7f6e\u4fe1\u533a\u95f4\u5185\u7684\u6982\u7387\u3002<\/p>\n<p>\u6b64\u5916\uff0c\u5207\u6bd4\u96ea\u592b\u5b9a\u7406\u8fd8\u7528\u4e8e\u8bc1\u660e\u5176\u4ed6\u7edf\u8ba1\u5b9a\u7406\uff0c\u4f8b\u5982\u5927\u6570\u5b9a\u5f8b\u3002<\/p>\n<p>\u867d\u7136\u5207\u6bd4\u96ea\u592b\u5b9a\u7406\u6700\u521d\u662f\u7531\u6cd5\u56fd\u4eba Ir\u00e9n\u00e9e-Jules Bienaym\u00e9 \u63d0\u51fa\u7684\uff0c\u4f46\u8be5\u5b9a\u7406\u4e4b\u6240\u4ee5\u5982\u6b64\u547d\u540d\uff0c\u662f\u56e0\u4e3a\u5b83\u662f\u7531\u4fc4\u7f57\u65af\u4eba\u5e15\u592b\u52aa\u8482\u00b7\u5207\u5e03\u4ec0\u592b\u4e8e 1867 \u5e74\u63d0\u51fa\u7684\u3002<\/p>\n<h2 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"formula-del-teorema-de-chebyshev\"><\/span>\u5207\u6bd4\u96ea\u592b\u5b9a\u7406\u7684\u516c\u5f0f<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p>\u5207\u6bd4\u96ea\u592b\u5b9a\u7406\u6307\u51fa\uff0c\u67d0\u4e2a\u503c\u7b49\u4e8e\u5e73\u5747\u503c<em> k \u4e2a<\/em>\u6807\u51c6\u5dee\u7684\u6982\u7387\u5927\u4e8e\u6216\u7b49\u4e8e 1 \u51cf\u53bb 1 \u9664\u4ee5<em>k<\/em>\u5e73\u65b9\u7684\u6bd4\u7387\u3002<\/p>\n<p>\u56e0\u6b64\uff0c<strong>\u5207\u6bd4\u96ea\u592b\u5b9a\u7406\u7684\u516c\u5f0f<\/strong>\u5982\u4e0b\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-f13ff7c0d76ea2442ecd978dbfc457a4_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle P(\\mu-k\\sigma\\leq X \\leq \\mu+k\\sigma)\\geq 1 -\\frac{1}{k^2}\" title=\"Rendered by QuickLaTeX.com\" height=\"36\" width=\"271\" style=\"vertical-align: -12px;\"><\/p>\n<\/p>\n<p>\u91d1\u5b50<\/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-996ff7036e644e89f8ac379fa58d0cf7_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"X\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"16\" style=\"vertical-align: 0px;\"><\/p>\n<p>\u662f\u968f\u673a\u53d8\u91cf\u7684\u503c\uff0c<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/statorials.org\/wp-content\/ql-cache\/quicklatex.com-05d9eae892416bd34247a25207f8b718_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\mu\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"11\" style=\"vertical-align: -4px;\"><\/p>\n<p>\u53d8\u91cf\u7684<a href=\"https:\/\/statorials.org\/cn\/\u7b97\u672f\u5e73\u5747\u6570\/\">\u7b97\u672f\u5e73\u5747\u503c<\/a>\uff0c<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/statorials.org\/wp-content\/ql-cache\/quicklatex.com-eaaf379fee5e67946f3fedf5631047b1_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\sigma\" title=\"Rendered by QuickLaTeX.com\" height=\"8\" width=\"11\" style=\"vertical-align: 0px;\"><\/p>\n<p>\u5176<a href=\"https:\/\/statorials.org\/cn\/\u6807\u51c6\u5dee\u6216\u6807\u51c6\u5dee\/\">\u6807\u51c6\u5dee<\/a>\u548c<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/statorials.org\/wp-content\/ql-cache\/quicklatex.com-d42bc2203d6f76ad01b27ac9acc0bee1_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"k\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"9\" style=\"vertical-align: 0px;\"><\/p>\n<p>\u8981\u8ba1\u7b97\u6982\u7387\u7684\u5e73\u5747\u503c\u7684\u6807\u51c6\u504f\u5dee\u6570\u3002<\/p>\n<p>\u8bf7\u6ce8\u610f\uff0c\u4ec5\u5f53\u6267\u884c\u8ba1\u7b97\u7684\u6807\u51c6\u5dee\u6570\u5927\u4e8e 1\uff0c\u6216\u8005\u6362\u53e5\u8bdd\u8bf4\uff0c\u5982\u679c<em>k<\/em>\u5927\u4e8e 1 \u65f6\uff0c\u624d\u80fd\u4f7f\u7528\u6b64\u516c\u5f0f\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-76b1d6dbe5ee35b66ff33156e238ad73_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"k>1&#8243; title=&#8221;Rendered by QuickLaTeX.com&#8221; height=&#8221;14&#8243; width=&#8221;41&#8243; style=&#8221;vertical-align: -2px;&#8221;><\/p>\n<\/p>\n<p> \ud83d\udc49<u style=\"text-decoration-color:#FF8A05;\">\u60a8\u53ef\u4ee5\u4f7f\u7528\u4e0b\u9762\u7684\u5728\u7ebf\u5207\u6bd4\u96ea\u592b\u5b9a\u7406\u8ba1\u7b97\u5668\u6765\u8ba1\u7b97\u6982\u7387\u3002<\/u><\/p>\n<h2 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"ejemplo-del-teorema-de-chebyshev\"><\/span>\u5207\u6bd4\u96ea\u592b\u5b9a\u7406\u7684\u793a\u4f8b<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p>\u4e00\u65e6\u6211\u4eec\u4e86\u89e3\u4e86\u5207\u6bd4\u96ea\u592b\u5b9a\u7406\u7684\u5b9a\u4e49\u53ca\u5176\u516c\u5f0f\u662f\u4ec0\u4e48\uff0c\u4e0b\u9762\u662f\u8be5\u7edf\u8ba1\u5b9a\u7406\u7684\u4e00\u4e2a\u5df2\u89e3\u51b3\u7684\u793a\u4f8b\uff0c\u4ee5\u4fbf\u66f4\u597d\u5730\u7406\u89e3\u8be5\u6982\u5ff5\u3002<\/p>\n<ul>\n<li>\u5982\u679c\u5927\u5b66\u8bfe\u7a0b\u7edf\u8ba1\u4e2d\u7684\u6210\u7ee9\u6309\u7167\u5e73\u5747\u503c\u4e3a 65\u3001\u6807\u51c6\u5dee\u4e3a 10 \u7684\u5206\u5e03\u6765\u5b9a\u4e49\uff0c\u90a3\u4e48\u83b7\u5f97 50 \u5230 80 \u4e4b\u95f4\u6210\u7ee9\u7684\u5b66\u751f\u6240\u5360\u7684\u767e\u5206\u6bd4\u662f\u591a\u5c11\uff1f<\/li>\n<\/ul>\n<p>\u4e3a\u4e86\u89e3\u51b3\u8fd9\u4e2a\u95ee\u9898\uff0c\u6211\u4eec\u9700\u8981\u5e94\u7528\u5207\u6bd4\u96ea\u592b\u5b9a\u7406\u7684\u516c\u5f0f\u3002\u7136\u800c\uff0c\u6211\u4eec\u5fc5\u987b\u9996\u5148\u786e\u5b9a\u503c 50 \u548c 80 \u4e0e\u53d8\u91cf\u5e73\u5747\u503c\u6709\u591a\u5c11\u6807\u51c6\u5dee\uff0c\u4e3a\u6b64\uff0c\u6211\u4eec\u53ea\u9700\u8fdb\u884c\u4ee5\u4e0b\u8ba1\u7b97\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-23a555d6493c0a0be742097fe319932d_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"k=\\cfrac{\\text{valor}-\\text{media}}{\\text{desviaci\\'on t\\'ipica}}\" title=\"Rendered by QuickLaTeX.com\" height=\"42\" width=\"165\" style=\"vertical-align: -16px;\"><\/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-edee4613c11e3eebd7e1158ad7f7b5c4_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"k=\\cfrac{50-65}{10}=-1,5\" title=\"Rendered by QuickLaTeX.com\" height=\"39\" width=\"155\" style=\"vertical-align: -12px;\"><\/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-7668ffc75752b84a5fdfe4de807efe0d_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"k=\\cfrac{80-65}{10}=1,5\" title=\"Rendered by QuickLaTeX.com\" height=\"39\" width=\"141\" style=\"vertical-align: -12px;\"><\/p>\n<\/p>\n<p>\u56e0\u6b64\uff0c\u503c 50 \u548c 80 \u5206\u522b\u5bf9\u5e94\u4e8e\u4e0b\u5747\u503c\u548c\u4e0a\u5747\u503c\u7684 1.5 \u4e2a\u6807\u51c6\u5dee\u3002\u56e0\u6b64\uff0c\u6211\u4eec\u4f7f\u7528 k=1.5 \u65f6\u5207\u6bd4\u96ea\u5a03\u5b9a\u7406\u7684\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-6dede501857215fec033905b64a01431_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle P(\\mu-k\\sigma\\leq X \\leq \\mu+k\\sigma)\\leq 1 -\\frac{1}{k^2}\" title=\"Rendered by QuickLaTeX.com\" height=\"36\" width=\"271\" style=\"vertical-align: -12px;\"><\/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-ace95ab1310d82dc6a6275b123556c07_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle P(\\mu-1,5\\sigma\\leq X \\leq \\mu+1,5\\sigma)\\leq 1 -\\frac{1}{1,5^2}\" title=\"Rendered by QuickLaTeX.com\" height=\"40\" width=\"319\" style=\"vertical-align: -16px;\"><\/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-aa011250591257ffebf651292398d016_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle P(50\\leq X \\leq 80)\\leq 0,5556\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"203\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<p>\u56e0\u6b64\uff0c\u81f3\u5c11 55.56% \u7684\u5b66\u751f\u83b7\u5f97\u4e86 50 \u81f3 80 \u5206\u4e4b\u95f4\u7684\u6210\u7ee9\u3002 <\/p>\n<h2 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"calculadora-del-teorema-de-chebyshev\"><\/span>\u5207\u6bd4\u96ea\u592b\u5b9a\u7406\u8ba1\u7b97\u5668<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p>\u8f93\u5165\u76f8\u5173\u503c\u4e0e\u5e73\u5747\u503c<em>(k)<\/em>\u4e4b\u95f4\u7684\u6807\u51c6\u5dee\u6570\uff0c\u7136\u540e\u5355\u51fb\u201c\u8ba1\u7b97\u201d\u3002\u7136\u540e\u8ba1\u7b97\u5668\u5c06\u8fd4\u56de\u7f6e\u4fe1\u533a\u95f4\u7684\u6700\u5c0f\u6982\u7387\u3002<\/p>\n<p>\u60a8\u5fc5\u987b\u4f7f\u7528\u70b9\u4f5c\u4e3a\u5c0f\u6570\u70b9\u5206\u9694\u7b26\u6765\u8f93\u5165\u6807\u51c6\u5dee\u6570\u3002 <\/p>\n<form action=\"\" method=\"post\">\n<ul style=\"color:#1C2C92;\">\n<li style=\"margin-bottom:15px\"><span style=\"color:#101010;font-weight: normal;\">\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/statorials.org\/wp-content\/ql-cache\/quicklatex.com-f4c08f6419fa469da3aa1c832f5c6b2b_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"k = \" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"28\" style=\"vertical-align: 0px;\"><\/p>\n<p><input name=\"datos\" style=\"border:1.5px solid #1C2C92; border-radius:5px;  padding:7px; color:#000000; background-color:#EBF5FB; width:60px\" placeholder=\"1.5\" required=\"\" oninvalid=\"this.setCustomValidity('Introduce el n\u00famero total de datos aqu\u00ed')\" oninput=\"this.setCustomValidity('')\"><\/span><\/li>\n<\/ul>\n<div style=\"text-align:center\"><input align=\"center\" style=\"font-size:105%; border-radius:30px; margin: 20px\" type=\"submit\" name=\"submit\" value=\"\u8ba1\u7b97\"><\/div>\n<\/form>\n<h2 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"el-teorema-de-chebyshev-y-la-regla-empirica\"><\/span>\u5207\u6bd4\u96ea\u592b\u5b9a\u7406\u548c\u7ecf\u9a8c\u6cd5\u5219<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p>\u7edf\u8ba1\u5b66\u4e2d\u4e24\u4e2a\u5bc6\u5207\u76f8\u5173\u7684\u6982\u5ff5\u662f\u5207\u6bd4\u96ea\u592b\u5b9a\u7406\u548c\u7ecf\u9a8c\u89c4\u5219\uff0c\u56e0\u4e3a\u4e24\u8005\u90fd\u7528\u4e8e\u8ba1\u7b97\u7f6e\u4fe1\u533a\u95f4\u7684\u6982\u7387\u3002<\/p>\n<p><strong>\u5207\u6bd4\u96ea\u592b\u5b9a\u7406\u4e0e\u7ecf\u9a8c\u89c4\u5219\u4e4b\u95f4\u7684\u533a\u522b<\/strong>\u5728\u4e8e\uff0c\u5207\u6bd4\u96ea\u592b\u5b9a\u7406\u53ef\u4ee5\u7528\u4e8e\u4efb\u4f55\u7c7b\u578b\u7684\u5206\u5e03\uff0c\u800c\u7ecf\u9a8c\u89c4\u5219\u4ec5\u5bf9\u6b63\u6001\u5206\u5e03\u6709\u6548\u3002<\/p>\n<p>\u56e0\u6b64\uff0c\u5207\u6bd4\u96ea\u592b\u5b9a\u7406\u7684\u7528\u9014\u66f4\u5e7f\u6cdb\uff0c\u4f46\u7ecf\u9a8c\u89c4\u5219\u4e3a\u6b63\u6001\u5206\u5e03\u63d0\u4f9b\u4e86\u66f4\u7cbe\u786e\u7684\u7ed3\u679c\u3002<\/p>\n<p>\u5355\u51fb\u6b64\u5904\u67e5\u770b\u5177\u4f53\u7684\u7ecf\u9a8c\u6cd5\u5219\u662f\u4ec0\u4e48\uff1a <\/p>\n<div style=\"background-color:#FFFDE7; padding-top: 10px; padding-bottom: 10px; padding-right: 20px; padding-left: 30px; border: 2.5px dashed #FFB74D; border-radius:20px;\"> <span style=\"color:#ff951b\">\u27a4<\/span><strong>\u8bf7\u53c2\u9605\uff1a<\/strong><a href=\"https:\/\/statorials.org\/cn\/\u7ecf\u9a8c\u6cd5\u5219\/\">\u4e00\u822c\u89c4\u5219<\/a><\/div>\n","protected":false},"excerpt":{"rendered":"<p>\u672c\u6587\u89e3\u91ca\u4ec0\u4e48\u662f\u5207\u6bd4\u96ea\u592b\u5b9a\u7406\u3002\u5728\u8fd9\u91cc\u60a8\u53ef\u4ee5\u627e\u5230\u5207\u6bd4\u96ea\u592b\u5b9a\u7406\u516c\u5f0f\u3001\u5df2\u89e3\u51b3\u7684\u7ec3\u4e60\uff0c\u6b64\u5916\u8fd8\u6709\u5728\u7ebf\u5207\u6bd4\u96ea\u592b\u5b9a\u7406\u8ba1\u7b97\u5668\u3002\u6700 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