{"id":2105,"date":"2023-07-23T16:34:09","date_gmt":"2023-07-23T16:34:09","guid":{"rendered":"https:\/\/statorials.org\/cn\/%e6%80%bb%e4%bd%93%e4%b8%8e%e6%a0%b7%e6%9c%ac%e6%a0%87%e5%87%86%e5%b7%ae%e7%9a%84%e6%af%94%e8%be%83\/"},"modified":"2023-07-23T16:34:09","modified_gmt":"2023-07-23T16:34:09","slug":"%e6%80%bb%e4%bd%93%e4%b8%8e%e6%a0%b7%e6%9c%ac%e6%a0%87%e5%87%86%e5%b7%ae%e7%9a%84%e6%af%94%e8%be%83","status":"publish","type":"post","link":"https:\/\/statorials.org\/cn\/%e6%80%bb%e4%bd%93%e4%b8%8e%e6%a0%b7%e6%9c%ac%e6%a0%87%e5%87%86%e5%b7%ae%e7%9a%84%e6%af%94%e8%be%83\/","title":{"rendered":"\u4eba\u53e3\u5bf9\u6bd4\u6837\u672c\u6807\u51c6\u5dee\uff1a\u4f55\u65f6\u4f7f\u7528\u6bcf\u4e2a\u6807\u51c6\u5dee"},"content":{"rendered":"<p><\/p>\n<hr>\n<p><span style=\"color: #000000;\"><strong>\u6807\u51c6\u5dee<\/strong>\u662f\u8861\u91cf\u6570\u636e\u96c6\u4e2d\u503c\u5206\u5e03\u7684\u6700\u5e38\u89c1\u65b9\u6cd5\u4e4b\u4e00\u3002<\/span><\/p>\n<p><span style=\"color: #000000;\">\u4e8b\u5b9e\u8bc1\u660e\uff0c\u60a8\u53ef\u4ee5\u8ba1\u7b97\u4e24\u79cd\u4e0d\u540c\u7c7b\u578b\u7684\u6807\u51c6\u5dee\uff0c\u5177\u4f53\u53d6\u51b3\u4e8e\u60a8\u4f7f\u7528\u7684\u6570\u636e\u7c7b\u578b\u3002<\/span><\/p>\n<p> <span style=\"color: #000000;\"><strong>1.\u603b\u4f53\u6807\u51c6\u5dee<\/strong><\/span><\/p>\n<p><span style=\"color: #000000;\">\u5f53\u60a8\u4f7f\u7528\u7684\u6570\u636e\u96c6\u4ee3\u8868\u6574\u4e2a\u603b\u4f53\uff08\u5373\u60a8\u611f\u5174\u8da3\u7684\u6bcf\u4e2a\u503c\uff09\u65f6\uff0c\u60a8\u5e94\u8be5\u8ba1\u7b97\u603b\u4f53\u6807\u51c6\u5dee\u3002<\/span><\/p>\n<p><span style=\"color: #000000;\">\u8ba1\u7b97\u603b\u4f53\u6807\u51c6\u5dee\uff08\u8868\u793a\u4e3a \u03c3\uff09\u7684\u516c\u5f0f\u4e3a\uff1a<\/span><\/p>\n<p> <span style=\"color: #000000;\"><strong>\u03c3 = \u221a <span style=\"border-top: 1px solid black;\">\u03a3( <sub>xi<\/sub> \u2013 \u03bc) <sup>2<\/sup> \/ N<\/span><\/strong><\/span><\/p>\n<p><span style=\"color: #000000;\">\u91d1\u5b50\uff1a<\/span><\/p>\n<ul>\n<li> <span style=\"color: #000000;\"><strong>\u03a3<\/strong> \uff1a\u8868\u793a\u201c\u548c\u201d\u7684\u7b26\u53f7<\/span><\/li>\n<li><span style=\"color: #000000;\"><strong>x <sub>i<\/sub><\/strong> \uff1a\u6570\u636e\u96c6\u4e2d\u7684\u7b2c i<sup>\u4e2a<\/sup>\u503c<\/span><\/li>\n<li><span style=\"color: #000000;\"><strong>\u03bc<\/strong> \uff1a\u4eba\u53e3\u5e73\u5747\u503c<\/span><\/li>\n<li><span style=\"color: #000000;\"><strong>N<\/strong> \uff1a\u4eba\u53e3\u89c4\u6a21<\/span><\/li>\n<\/ul>\n<p><span style=\"color: #000000;\"><strong>2. \u6807\u51c6\u5dee\u793a\u4f8b<\/strong><\/span><\/p>\n<p><span style=\"color: #000000;\">\u5f53\u60a8\u4f7f\u7528\u7684\u6570\u636e\u96c6\u4ee3\u8868\u53d6\u81ea\u8f83\u5927\u611f\u5174\u8da3\u7fa4\u4f53\u7684\u6837\u672c\u65f6\uff0c\u60a8\u5e94\u8be5\u8ba1\u7b97\u6837\u672c\u6807\u51c6\u5dee\u3002<\/span><\/p>\n<p><span style=\"color: #000000;\">\u8ba1\u7b97\u6837\u672c\u6807\u51c6\u5dee\uff08\u8868\u793a\u4e3a<em>s \uff09<\/em>\u7684\u516c\u5f0f\u4e3a\uff1a<\/span><\/p>\n<p> <span style=\"color: #000000;\"><strong>s = \u221a <span style=\"border-top: 1px solid black;\">\u03a3( <sub>xi<\/sub> \u2013 x\u0304) <sup>2<\/sup> \/ (n \u2013 1)<\/span><\/strong><\/span><\/p>\n<p><span style=\"color: #000000;\">\u91d1\u5b50\uff1a<\/span><\/p>\n<ul>\n<li> <span style=\"color: #000000;\"><strong>\u03a3<\/strong> \uff1a\u8868\u793a\u201c\u548c\u201d\u7684\u7b26\u53f7<\/span><\/li>\n<li><span style=\"color: #000000;\"><strong>x <sub>i<\/sub><\/strong> \uff1a\u6570\u636e\u96c6\u4e2d\u7684\u7b2c i<sup>\u4e2a<\/sup>\u503c<\/span><\/li>\n<li><span style=\"color: #000000;\"><strong>x\u0304<\/strong> : \u6837\u672c\u5e73\u5747\u503c<\/span><\/li>\n<li><span style=\"color: #000000;\"><strong>n<\/strong> \uff1a\u6837\u672c\u5927\u5c0f<\/span><\/li>\n<\/ul>\n<h3><strong>\u603b\u4f53\u4e0e\u6837\u672c\u7684\u6807\u51c6\u5dee\uff1a\u5dee\u503c<\/strong><\/h3>\n<p><span style=\"color: #000000;\">\u4ece\u4e0a\u9762\u7684\u516c\u5f0f\u4e2d\uff0c\u6211\u4eec\u53ef\u4ee5\u770b\u5230\u603b\u4f53\u548c\u6837\u672c\u6807\u51c6\u5dee\u4e4b\u95f4\u5b58\u5728\u5fae\u5c0f\u7684\u5dee\u5f02\uff1a<strong>\u5728\u8ba1\u7b97\u6837\u672c\u6807\u51c6\u5dee\u65f6\uff0c\u6211\u4eec\u9664\u4ee5n-1\u800c\u4e0d\u662fN\u3002<\/strong><\/span><\/p>\n<p><span style=\"color: #000000;\">\u539f\u56e0\u662f\uff0c\u5f53\u6211\u4eec\u8ba1\u7b97\u6837\u672c\u6807\u51c6\u5dee\u65f6\uff0c\u6211\u4eec\u5f80\u5f80\u4f1a\u4f4e\u4f30\u771f\u5b9e\u7684\u603b\u4f53\u53d8\u5f02\u6027\u3002\u6362\u53e5\u8bdd\u8bf4\uff0c\u6211\u4eec\u5bf9\u771f\u5b9e\u603b\u4f53\u6807\u51c6\u5dee\u7684\u4f30\u8ba1\u662f\u6709\u504f\u5dee\u7684\u3002*<\/span><\/p>\n<p><span style=\"color: #000000;\">\u4e3a\u4e86\u7ea0\u6b63\u8fd9\u79cd\u504f\u5dee\uff0c\u6211\u4eec\u9664\u4ee5 n-1\u3002\u4e8b\u5b9e\u8bc1\u660e\uff0c\u8fd9\u4f7f\u5f97\u6837\u672c\u6807\u51c6\u5dee\u6210\u4e3a\u603b\u4f53\u6807\u51c6\u5dee\u7684\u65e0\u504f\u4f30\u8ba1\u3002<\/span><\/p>\n<p> <span style=\"color: #000000;\">*\u8fd9\u4e00\u70b9\u7684\u8bc1\u660e\u8d85\u51fa\u4e86\u672c\u6587\u7684\u8303\u56f4\u3002\u6709\u5173\u6570\u5b66\u8bc1\u660e\uff0c\u8bf7\u53c2\u9605<a href=\"https:\/\/stats.stackexchange.com\/questions\/11707\/why-is-sample-standard-deviation-a-biased-estimator-of-sigma\" target=\"_blank\" rel=\"noopener\">\u8fd9\u7bc7 Stack Exchange \u6587\u7ae0<\/a>\u3002<\/span><\/p>\n<h3><strong>\u4eba\u53e3\u5bf9\u6bd4\u6837\u672c\u6807\u51c6\u5dee\uff1a\u4f55\u65f6\u4f7f\u7528\u6bcf\u4e2a\u6807\u51c6\u5dee<\/strong><\/h3>\n<p><span style=\"color: #000000;\">\u4f7f\u7528\u4ee5\u4e0b\u7ec3\u4e60\u9898\u53ef\u4ee5\u66f4\u597d\u5730\u7406\u89e3\u4f55\u65f6\u5e94\u8be5\u4f7f\u7528\u603b\u4f53\u6807\u51c6\u5dee\u4e0e\u6837\u672c\u6807\u51c6\u5dee\u3002<\/span><\/p>\n<p><span style=\"color: #000000;\"><strong>\u7ec3\u4e60\u98981\uff1a\u4f53\u80b2<\/strong><\/span><\/p>\n<p><span style=\"color: #000000;\">\u5047\u8bbe\u4e00\u4f4d\u7bee\u7403\u6559\u7ec3\u60f3\u8981\u603b\u7ed3\u5176\u7403\u961f 12 \u540d\u7403\u5458\u5f97\u5206\u7684\u5e73\u5747\u503c\u548c\u6807\u51c6\u5dee\u3002<\/span><\/p>\n<p><span style=\"color: #000000;\">\u5728\u8ba1\u7b97\u5f97\u5206\u6807\u51c6\u5dee\u65f6\uff0c\u5e94\u8be5\u4f7f\u7528\u603b\u4f53\u6807\u51c6\u5dee\u516c\u5f0f\u8fd8\u662f\u6837\u672c\u6807\u51c6\u5dee\u516c\u5f0f\uff1f<\/span><\/p>\n<p><span style=\"color: #000000;\">\u7b54\u6848\uff1a\u4ed6\u5fc5\u987b\u4f7f\u7528<strong>\u603b\u4f53\u6807\u51c6\u5dee<\/strong>\uff0c\u56e0\u4e3a\u4ed6\u53ea\u5bf9\u81ea\u5df1\u7403\u5458\u7684\u5f97\u5206\u611f\u5174\u8da3\uff0c\u800c\u4e0d\u5bf9\u53e6\u4e00\u652f\u7403\u961f\u7684\u5176\u4ed6\u7403\u5458\u5f97\u5206\u611f\u5174\u8da3\u3002<\/span><\/p>\n<p><span style=\"color: #000000;\"><strong>\u7ec3\u4e60\u98982\uff1a\u9ad8\u5ea6<\/strong><\/span><\/p>\n<p><span style=\"color: #000000;\">\u5047\u8bbe\u4e00\u4f4d\u4f53\u80b2\u8001\u5e08\u60f3\u8981\u603b\u7ed3\u4ed6\u73ed\u4e0a\u5b66\u751f\u8eab\u9ad8\u7684\u5e73\u5747\u503c\u548c\u6807\u51c6\u5dee\u3002<\/span><\/p>\n<p><span style=\"color: #000000;\">\u8ba1\u7b97\u8eab\u9ad8\u6807\u51c6\u5dee\u65f6\uff0c\u5e94\u8be5\u4f7f\u7528\u603b\u4f53\u6807\u51c6\u5dee\u516c\u5f0f\u8fd8\u662f\u6837\u672c\u6807\u51c6\u5dee\u516c\u5f0f\uff1f<\/span><\/p>\n<p><span style=\"color: #000000;\">\u7b54\u6848\uff1a\u5b83\u5e94\u8be5\u4f7f\u7528<strong>\u603b\u4f53\u6807\u51c6\u5dee\uff0c<\/strong>\u56e0\u4e3a\u5b83\u53ea\u5bf9\u7279\u5b9a\u73ed\u7ea7\u7684\u5b66\u751f\u4eba\u6570\u611f\u5174\u8da3\u3002<\/span><\/p>\n<p><span style=\"color: #000000;\"><strong>\u7ec3\u4e60\u98983\uff1a\u751f\u7269\u5b66<\/strong><\/span><\/p>\n<p><span style=\"color: #000000;\">\u5047\u8bbe\u751f\u7269\u5b66\u5bb6\u60f3\u8981\u603b\u7ed3\u7279\u5b9a\u79cd\u7c7b\u6d77\u9f9f\u7684\u4f53\u91cd\u5e73\u5747\u503c\u548c\u6807\u51c6\u5dee\u3002\u5979\u51b3\u5b9a\u51fa\u53bb\u4ece\u79cd\u7fa4\u4e2d\u968f\u673a\u62bd\u53d6 20 \u53ea\u6d77\u9f9f\u3002<\/span><\/p>\n<p><span style=\"color: #000000;\">\u5728\u8ba1\u7b97\u6743\u91cd\u7684\u6807\u51c6\u5dee\u65f6\uff0c\u5979\u5e94\u8be5\u4f7f\u7528\u603b\u4f53\u6807\u51c6\u5dee\u516c\u5f0f\u8fd8\u662f\u6837\u672c\u6807\u51c6\u5dee\u516c\u5f0f\uff1f<\/span><\/p>\n<p><span style=\"color: #000000;\">\u7b54\u6848\uff1a\u5979\u5e94\u8be5\u4f7f\u7528<strong>\u6837\u672c\u6807\u51c6\u5dee<\/strong>\uff0c\u56e0\u4e3a\u5979\u5bf9\u6574\u4e2a\u6d77\u9f9f\u79cd\u7fa4\u7684\u91cd\u91cf\u611f\u5174\u8da3\uff0c\u800c\u4e0d\u4ec5\u4ec5\u662f\u6837\u672c\u4e2d\u6d77\u9f9f\u7684\u91cd\u91cf\u3002<\/span><\/p>\n<p><span style=\"color: #000000;\"><strong>\u7ec3\u4e60\u9898 4\uff1a\u5236\u9020<\/strong><\/span><\/p>\n<p><span style=\"color: #000000;\">\u5047\u8bbe\u68c0\u67e5\u5458\u60f3\u8981\u6c47\u603b\u67d0\u4e2a\u5de5\u5382\u751f\u4ea7\u7684\u8f6e\u80ce\u91cd\u91cf\u7684\u5e73\u5747\u503c\u548c\u6807\u51c6\u5dee\u3002\u4ed6\u51b3\u5b9a\u4ece\u5de5\u5382\u968f\u673a\u62bd\u53d6 40 \u4e2a\u8f6e\u80ce\u6837\u672c\uff0c\u5e76\u5bf9\u6bcf\u4e2a\u8f6e\u80ce\u8fdb\u884c\u79f0\u91cd\u3002<\/span><\/p>\n<p><span style=\"color: #000000;\">\u8ba1\u7b97\u6743\u91cd\u6807\u51c6\u5dee\u65f6\uff0c\u5e94\u8be5\u4f7f\u7528\u603b\u4f53\u6807\u51c6\u5dee\u516c\u5f0f\u8fd8\u662f\u6837\u672c\u6807\u51c6\u5dee\u516c\u5f0f\uff1f<\/span><\/p>\n<p><span style=\"color: #000000;\">\u7b54\u6848\uff1a\u4ed6\u5e94\u8be5\u4f7f\u7528<strong>\u6837\u672c\u6807\u51c6\u5dee\uff0c<\/strong>\u56e0\u4e3a\u4ed6\u611f\u5174\u8da3\u7684\u662f\u8be5\u5de5\u5382\u751f\u4ea7\u7684\u6240\u6709\u8f6e\u80ce\u7684\u91cd\u91cf\uff0c\u800c\u4e0d\u4ec5\u4ec5\u662f\u6837\u672c\u4e2d\u8f6e\u80ce\u7684\u91cd\u91cf\u3002<\/span><\/p>\n<h3><span style=\"color: #000000;\"><strong>\u5176\u4ed6\u8d44\u6e90<\/strong><\/span><\/h3>\n<p><span style=\"color: #000000;\">\u4ee5\u4e0b\u6559\u7a0b\u63d0\u4f9b\u6709\u5173\u6807\u51c6\u5dee\u7684\u5176\u4ed6\u4fe1\u606f\uff1a<\/span><\/p>\n<p><a href=\"https:\/\/statorials.org\/cn\/\u4e3a\u4ec0\u4e48\u6807\u51c6\u5dee\u5f88\u91cd\u8981\/\" target=\"_blank\" rel=\"noopener\">\u4e3a\u4ec0\u4e48\u6807\u51c6\u5dee\u5f88\u91cd\u8981\uff1f<\/a><br \/><a href=\"https:\/\/statorials.org\/cn\" target=\"_blank\" rel=\"noopener\">\u4ec0\u4e48\u88ab\u8ba4\u4e3a\u662f\u597d\u7684\u6807\u51c6\u5dee\uff1f<\/a><br \/><a href=\"https:\/\/statorials.org\/cn\/\u6807\u51c6\u5dee\u771f\u5b9e\u4f8b\u5b50\/\" target=\"_blank\" rel=\"noopener\">\u73b0\u5b9e\u751f\u6d3b\u4e2d\u4f7f\u7528\u6807\u51c6\u5dee\u7684 6 \u4e2a\u4f8b\u5b50<\/a><br \/><a href=\"https:\/\/statorials.org\/cn\/\u76f8\u5bf9\u4e8e\u6807\u51c6\u5dee\u7684\u53d8\u5f02\u7cfb\u6570\/\" target=\"_blank\" rel=\"noopener\">\u53d8\u5f02\u7cfb\u6570\u4e0e\u6807\u51c6\u5dee\uff1a\u5dee\u5f02<\/a><\/p>\n","protected":false},"excerpt":{"rendered":"<p>\u6807\u51c6\u5dee\u662f\u8861\u91cf\u6570\u636e\u96c6\u4e2d\u503c\u5206\u5e03\u7684\u6700\u5e38\u89c1\u65b9\u6cd5\u4e4b\u4e00\u3002 \u4e8b\u5b9e\u8bc1\u660e\uff0c\u60a8\u53ef\u4ee5\u8ba1\u7b97\u4e24\u79cd\u4e0d\u540c\u7c7b\u578b\u7684\u6807\u51c6\u5dee\uff0c\u5177\u4f53\u53d6\u51b3\u4e8e\u60a8\u4f7f\u7528\u7684\u6570\u636e [&hellip;]<\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[11],"tags":[],"class_list":["post-2105","post","type-post","status-publish","format-standard","hentry","category-11"],"yoast_head":"<!-- This site is optimized with the Yoast SEO plugin v21.5 - https:\/\/yoast.com\/wordpress\/plugins\/seo\/ -->\n<title>\u4eba\u53e3\u5bf9\u6bd4\u6807\u51c6\u5dee\u793a\u4f8b\uff1a\u4f55\u65f6\u4f7f\u7528\u6bcf\u4e2a\u6807\u51c6\u5dee - Statorials<\/title>\n<meta name=\"description\" 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