{"id":2728,"date":"2014-04-06T22:52:38","date_gmt":"2014-04-06T14:52:38","guid":{"rendered":"http:\/\/caucanimax.com\/blog\/?p=2728"},"modified":"2014-04-06T23:09:21","modified_gmt":"2014-04-06T15:09:21","slug":"naked-statistics-reading-notes","status":"publish","type":"post","link":"https:\/\/caucanimax.com\/blog\/naked-statistics-reading-notes\/","title":{"rendered":"\u300a\u8d64\u88f8\u88f8\u7684\u7edf\u8ba1\u5b66\u300b\u8bfb\u4e66\u7b14\u8bb0"},"content":{"rendered":"<p><a href=\"http:\/\/caucanimax.com\/blog\/wordpress\/wp-content\/uploads\/2014\/04\/Naked_Statistics_01.jpg\"><img loading=\"lazy\" decoding=\"async\" class=\"alignnone size-full wp-image-2733\" alt=\"Naked_Statistics_01\" src=\"http:\/\/caucanimax.com\/blog\/wordpress\/wp-content\/uploads\/2014\/04\/Naked_Statistics_01.jpg\" width=\"650\" height=\"365\" srcset=\"https:\/\/caucanimax.com\/blog\/wordpress\/wp-content\/uploads\/2014\/04\/Naked_Statistics_01.jpg 650w, 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\u6570\u636e\u4e0e\u504f\u89c1<\/strong><\/p>\n<p>\u7edf\u8ba1\u5b66\u5f97\u4ee5\u83b7\u5f97\u6210\u529f\u5e94\u7528\u9664\u4e86\u5176\u6570\u5b66\u5de5\u5177\u4e4b\u5916\uff0c\u53e6\u4e00\u4e2a\u91cd\u8981\u7684\u90e8\u5206\u5c31\u662f\u88ab\u5206\u6790\u7684\u6570\u636e\uff0c\u751a\u81f3\u53ef\u4ee5\u8bf4\u8fd9\u662f\u57fa\u7840\u3002\u4e00\u822c\u6765\u8bf4\uff0c\u4f1a\u8981\u6c42\u6570\u636e\u505a3\u4ef6\u4e8b\uff1a<\/p>\n<ol>\n<li>\u5f97\u5230\u4e00\u4e2a\u5177\u6709\u4ee3\u8868\u6027\u6570\u636e\u6837\u672c\u3002\u9700\u8981\u6ce8\u610f\u7684\u662f\uff0c\u9996\u5148\u6837\u672c\u5bb9\u91cf\u5f88\u91cd\u8981\uff0c\u8d8a\u5927\u8d8a\u597d\uff08\u5728\u5927\u6570\u636e\u65f6\u4ee3\u751a\u81f3\u53ef\u4ee5100%\u53d6\u6837\uff09\uff0c\u7b2c\u4e8c\uff0c\u6837\u672c\u4e0d\u80fd\u6709\u504f\u89c1\uff0c\u5426\u5219\u4fbf\u4e0d\u8db3\u4ee5\u4ee3\u8868\u6574\u4f53\u7684\u60c5\u51b5\uff1b<\/li>\n<li>\u63d0\u4f9b\u6bd4\u8f83\uff0c\u627e\u5230\u5bf9\u7167\u7ec4\u3002\u81ea\u7136\u79d1\u5b66\u9886\u57df\u7684\u5bf9\u7167\u7ec4\u6bd4\u8f83\u5bb9\u6613\u5b9e\u73b0\uff0c\u4f46\u793e\u4f1a\u79d1\u5b66\u5c31\u5f88\u9ebb\u70e6\uff0c\u56e0\u4e3a\u5927\u591a\u6570\u65f6\u5019\u5e76\u4e0d\u80fd\u5bf9\u4eba\u505a\u5b9e\u9a8c\uff0c\u5c24\u5176\u662f\u9700\u8981\u7814\u7a76\u67d0\u9879\u6d88\u6781\u56e0\u7d20\u5bf9\u4eba\u7684\u5f71\u54cd\u7684\u65f6\u5019\u3002\u5982\u679c\u786e\u5b9e\u53ef\u4ee5\u8fdb\u884c\u5b9e\u9a8c\uff0c\u90a3\u4e48\u4e3a\u4e86\u4fdd\u8bc1\u53ea\u6709\u4e00\u4e2a\u56e0\u7d20\u4e0d\u540c\uff0c\u5728\u5bf9\u8c61\u7684\u9009\u62e9\u4e0a\u5e94\u8be5\u4e25\u683c\u201c\u968f\u673a\u53d6\u6837\u201d\uff1b<\/li>\n<li>\u5c3d\u53ef\u80fd\u591a\u6536\u96c6\u6570\u636e\uff0c\u56e0\u4e3a\u5f88\u591a\u6570\u636e\u4f1a\u6709\u610f\u60f3\u4e0d\u5230\u7684\u7528\u5904\u3002<\/li>\n<\/ol>\n<p>\u5982\u679c\u6570\u636e\u672c\u8eab\u662f\u4f2a\u9020\u7684\u6216\u662f\u4e0d\u6b63\u5f53\u7684\uff0c\u5c31\u7b97\u7edf\u8ba1\u65b9\u6cd5\u518d\u6b63\u786e\uff0c\u7ed3\u679c\u90fd\u4f1a\u975e\u5e38\u7cdf\u7cd5\uff0c\u8fd9\u751a\u81f3\u8d85\u8fc7\u4e86\u7531\u4e8e\u7edf\u8ba1\u65b9\u6cd5\u9519\u8bef\u800c\u5bfc\u81f4\u7684\u540e\u679c\u3002\u5e38\u89c1\u7684\u4e00\u4e9b\u6570\u636e\u9519\u8bef\u5982\u4e0b\uff1a<\/p>\n<ol>\n<li>\u9009\u62e9\u6027\u504f\u89c1\u3002\u5728\u9009\u62e9\u5bf9\u8c61\u7684\u65f6\u5019\uff0c\u6bcf\u4e2a\u5bf9\u8c61\u88ab\u9009\u7684\u6982\u7387\u4e0d\u5747\u7b49\uff0c\u4e00\u822c\u662f\u7531\u4e8e\u9009\u62e9\u6cd5\u6240\u80fd\u63a5\u89e6\u5230\u7684\u6837\u672c\u6709\u5c40\u9650\u6027\u3002<\/li>\n<li>\u53d1\u8868\u6027\u504f\u89c1\u3002\u80af\u5b9a\u6027\u7684\u7814\u7a76\u53d1\u73b0\u4e0e\u5426\u5b9a\u6027\u7684\u76f8\u6bd4\u66f4\u6709\u53ef\u80fd\u88ab\u53d1\u8868\uff0c\u56e0\u4e3a\u66f4\u5438\u5f15\u773c\u7403\uff0c\u4ece\u800c\u5f71\u54cd\u6211\u4eec\u5bf9\u4e8b\u5b9e\u771f\u76f8\u7684\u5224\u65ad\u3002<\/li>\n<li>\u8bb0\u5fc6\u6027\u504f\u89c1\u3002\u5f53\u7814\u7a76\u4e00\u4e9b\u7279\u522b\u597d\u6216\u7279\u522b\u574f\u7684\u7ed3\u679c\u65f6\uff0c\u6837\u672c\u5bf9\u8c61\u4f1a\u53d7\u5230\u7814\u7a76\u9898\u76ee\u7684\u5f71\u54cd\uff0c\u4ece\u800c\u65e0\u610f\u8bc6\u5730\u5f3a\u5316\u548c\u9009\u62e9\u6709\u5229\u4e8e\u9898\u76ee\u5047\u8bbe\u7684\u8bb0\u5fc6\u3002\u6b64\u65f6\u5c31\u4f53\u73b0\u51fa\u7eb5\u5411\u7814\u7a76\u76f8\u6bd4\u6a2a\u5411\u7814\u7a76\u7684\u4f18\u70b9\u4e86\u3002<\/li>\n<li>\u5e78\u5b58\u8005\u504f\u89c1\u3002\u6837\u672c\u5728\u7edf\u8ba1\u8fc7\u7a0b\u4e2d\u6709\u4e00\u4e9b\u6216\u5f88\u591a\u6570\u636e\u7f3a\u5931\uff0c\u5bfc\u81f4\u6837\u672c\u6210\u5206\u53d1\u751f\u53d8\u5316\uff0c\u6240\u4ee5\u7ed3\u679c\u5e76\u4e0d\u51c6\u786e\u3002\u5171\u540c\u57fa\u91d1\u7684\u4f8b\u5b50\u5f88\u6709\u610f\u601d\u3002<\/li>\n<li>\u5065\u5eb7\u7528\u6237\u504f\u89c1\u3002\u5b9e\u9a8c\u7ec4\u548c\u5bf9\u7167\u7ec4\u7684\u5bf9\u8c61\u5e76\u4e0d\u662f\u968f\u673a\u53d6\u6837\uff0c\u800c\u662f\u88ab\u7814\u7a76\u5047\u8bbe\u5206\u4e3a\u4e86\u4e0d\u540c\u7684\u4e24\u7ec4\uff0c\u4ed6\u4eec\u53ef\u80fd\u9664\u4e86\u7814\u7a76\u5047\u8bbe\u7684\u4e0d\u540c\uff0c\u8fd8\u5b58\u5728\u5176\u4ed6\u7cfb\u5217\u7684\u5dee\u522b\uff0c\u8fd9\u6837\u5c31\u4e0d\u80fd\u65ad\u5b9a\u662f\u5355\u4e00\u539f\u56e0\u8d77\u4f5c\u7528\u4e86\u3002<\/li>\n<\/ol>\n<p>\u6240\u4ee5\uff0c\u53ef\u4ee5\u770b\u51fa\uff0c\u5728\u6574\u4e2a\u7edf\u8ba1\u7814\u7a76\u4e2d\uff0c\u4f18\u8d28\u6570\u636e\u662f\u591a\u4e48\u91cd\u8981\uff0c\u800c\u4e14\u5f80\u5f80\u6bd4\u770b\u4e0a\u53bb\u56f0\u96be\u7684\u591a\u3002<\/p>\n<p><strong>\u7b2c9\u7ae0 \u4e2d\u5fc3\u6781\u9650\u5b9a\u7406<\/strong><\/p>\n<p>\u5728\u5927\u6570\u636e\u65f6\u4ee3\u4e4b\u524d\uff0c\u7edf\u8ba1\u5b66\u83b7\u5f97\u6570\u636e\u7684\u57fa\u672c\u65b9\u6cd5\u662f\u62bd\u6837\u8c03\u67e5\uff0c\u90a3\u4e3a\u4ec0\u4e48\u62bd\u6837\u8c03\u67e5\u7684\u7ed3\u8bba\u80fd\u591f\u53cd\u6620\u6574\u4f53\u7684\u60c5\u51b5\u5462\uff1f\u4e2d\u5fc3\u6781\u9650\u5b9a\u7406\u4e3a\u5176\u4f53\u73b0\u4e86\u7406\u8bba\u4f9d\u636e\uff0c\u5176\u6838\u5fc3\u8981\u4e49\u5c31\u662f\uff1a\u4e00\u4e2a\u5927\u578b\u6837\u672c\u7684\u6b63\u786e\u62bd\u6837\u4e0e\u5176\u4ee3\u8868\u7684\u7fa4\u4f53\u5b58\u5728\u76f8\u4f3c\u5173\u7cfb\u3002<\/p>\n<p>\u7531\u4e2d\u5fc3\u6781\u9650\u5b9a\u7406\u53ef\u4ee5\u5f97\u5230\u4e00\u4e9b\u63a8\u8bba\uff1a<\/p>\n<ol>\n<li>\u5df2\u77e5\u7fa4\u4f53\u4fe1\u606f\uff0c\u53ef\u63a8\u65ad\u51fa\u5176\u4e2d\u6b63\u786e\u968f\u673a\u62bd\u6837\u7684\u60c5\u51b5\uff1b<\/li>\n<li>\u5df2\u77e5\u6b63\u786e\u968f\u673a\u62bd\u6837\u7684\u60c5\u51b5\uff0c\u53ef\u63a8\u7406\u51fa\u7fa4\u4f53\u7684\u4fe1\u606f\uff1b<\/li>\n<li>\u5df2\u77e5\u7fa4\u4f53\u4fe1\u606f\u548c\u67d0\u4e2a\u6837\u672c\u7684\u6570\u636e\uff0c\u53ef\u5224\u65ad\u51fa\u6837\u672c\u662f\u5426\u5c5e\u4e8e\u8be5\u7fa4\u4f53\uff1b<\/li>\n<li>\u4e00\u76f4\u4e24\u4e2a\u6837\u672c\u7684\u6570\u636e\uff0c\u53ef\u5224\u65ad\u51fa\u662f\u5426\u5c5e\u4e8e\u540c\u4e00\u7fa4\u4f53\u3002<\/li>\n<\/ol>\n<p>\u4e0a\u8ff0\u63a8\u8bba\u8bf4\u7684\u901a\u4fd7\u4e00\u70b9\uff0c\u5c31\u662f\u770b\u957f\u5f97\u50cf\u4e0d\u50cf\u3002\u90a3\u4e48\u76f8\u50cf\u7a0b\u5ea6\u5982\u4f55\u6765\u63cf\u8ff0\uff0c\u4e2d\u5fc3\u6781\u9650\u5b9a\u7406\u7684\u6570\u5b66\u8868\u8fbe\u53ef\u4ee5\u544a\u8bc9\u6211\u4eec\uff0c\u8fd9\u5c31\u662f\u5927\u540d\u9f0e\u9f0e\u7684\u6b63\u6001\u5206\u5e03\u66f2\u7ebf\u3002\u5bf9\u7fa4\u4f53\u591a\u6b21\u968f\u673a\u62bd\u6837\uff0c\u4e0d\u7ba1\u7fa4\u4f53\u7684\u5206\u5e03\u5982\u4f55\uff0c\u8fd9\u4e9b\u6837\u672c\u7684\u5e73\u5747\u503c\u4f1a\u5728\u7fa4\u4f53\u5e73\u5747\u503c\u5468\u56f4\u5448\u6b63\u6001\u5206\u5e03\u3002<\/p>\n<p>\u6837\u672c\u5e73\u5747\u503c\u7684\u6807\u51c6\u5dee\uff0c\u6211\u4eec\u79f0\u4e4b\u4e3a\u201c\u6807\u51c6\u8bef\u5dee\u201d\uff0c\u7b26\u53f7\\[SE = \\frac{s}{{\\sqrt n }}\\]\uff0cs\u4e3a\u7fa4\u4f53\u6807\u51c6\u5dee\uff0cn\u4e3a\u6837\u672c\u6570\u91cf\u3002<\/p>\n<p>\u6b63\u6001\u5206\u5e03\u7684\u795e\u5947\u4e4b\u5904\u662f\uff0c\u6709\u5dee\u4e0d\u591a68%\u7684\u6837\u672c\u5e73\u5747\u503c\u4f1a\u5728\u7fa4\u4f53\u5e73\u5747\u503c\u76841\u4e2a\u6807\u51c6\u8bef\u5dee\u8303\u56f4\u5185\uff0c95%\u57282\u4e2a\u4e4b\u5185\uff0c99.7%\u57283\u4e2a\u4e4b\u5185\u3002\u6362\u8a00\u4e4b\uff0c3\u4e2a\u4e4b\u5916\u7684\u6982\u7387\u51e0\u4e4e\u4e3a0\u3002\u6240\u4ee5\uff0c\u8fd9\u5c31\u4e3a\u4e0a\u8ff0\u63a8\u8bba\u4e2d\u9700\u8981\u63cf\u8ff0\u7684\u76f8\u4f3c\u7a0b\u5ea6\u63d0\u4f9b\u4e86\u6570\u5b66\u65b9\u6cd5\u3002<\/p>\n<p><span style=\"color: #ff6600;\">\u672c\u7ae0\u6709\u4e00\u4e2a\u4e25\u91cd\u5370\u5237\u9519\u8bef\uff0c\u5c31\u662f164\u9875\u6807\u51c6\u8bef\u5dee\u7684\u516c\u5f0f\u662f\\[SE = s\\sqrt n \\]<\/span><span style=\"color: #ff6600;\">\uff0c\u5b9e\u9645\u4e0a\u5e94\u8be5\u662f\\[SE = \\frac{s}{{\\sqrt n }}\\]<\/span><span style=\"color: #ff6600;\">\uff0c\u5173\u7cfb\u5b8c\u5168\u9519\u4e86\u3002<\/span><\/p>\n<p><strong>\u7b2c10\u7ae0 \u7edf\u8ba1\u63a8\u65ad\u4e0e\u5047\u8bbe\u68c0\u9a8c<\/strong><\/p>\n<p>\u7edf\u8ba1\u63a8\u65ad\u4e0e\u5047\u8bbe\u68c0\u9a8c\u90fd\u662f\u57fa\u4e8e\u4e2d\u5fc3\u6781\u9650\u5b9a\u7406\u7684\u6838\u5fc3\u8981\u4e49\uff1a\u4e00\u4e2a\u5927\u578b\u6837\u672c\u7684\u6b63\u786e\u62bd\u6837\u4e0e\u5176\u6240\u4ee3\u8868\u7684\u7fa4\u4f53\u5b58\u5728\u76f8\u4f3c\u6027\u3002\u8fd9\u79cd\u76f8\u4f3c\u6027\u4f53\u73b0\u5728\u4e24\u4e2a\u6570\u636e\u6307\u6807\u4e0a\uff0c\u5373\u5e73\u5747\u503c\u548c\u6807\u51c6\u5dee\uff0c\u901a\u4fd7\u5730\u8bb2\u5c31\u662f\u5b83\u4eec\u5927\u5c0f\u5dee\u4e0d\u591a\uff0c\u8986\u76d6\u8303\u56f4\uff08\u79bb\u6563\u7a0b\u5ea6\uff09\u4e5f\u5dee\u4e0d\u591a\u3002\u6839\u636e\u4e0a\u4e00\u7ae0\u8bb2\u76844\u4e2a\u63a8\u8bba\u53ef\u4ee5\u770b\u51fa\uff0c\u5728\u4e00\u4e2a\u6574\u4f53\u53ca\u5176\u62bd\u6837\uff0c\u4ee5\u53ca\u4e24\u4e2a\u62bd\u6837\u4e4b\u95f4\u90fd\u5b58\u5728\u8fd9\u79cd\u76f8\u4f3c\u6027\uff0c\u6211\u4eec\u8981\u901a\u8fc7\u7edf\u8ba1\u5b66\u6765\u5224\u65ad\u4e24\u7ec4\u6570\u636e\u662f\u5426\u76f8\u4f3c\uff0c\u5c31\u662f\u770b\u5176\u5e73\u5747\u503c\u4e4b\u5dee\u662f\u5426\u5728\u5408\u7406\u7684\u79bb\u6563\u8303\u56f4\u4e4b\u5185\u3002\u6240\u4ee5\u5e94\u7528\u8d77\u6765\u4e00\u822c\u6709\u4e24\u79cd\uff1a<\/p>\n<ol>\n<li>\u5df2\u77e5\u7fa4\u4f53\u7684\u5e73\u5747\u503c\u548c\u79bb\u6563\u7a0b\u5ea6\u4ee5\u53ca\u6837\u672c\u7684\u5e73\u5747\u503c\uff0c\u5c31\u53ef\u4ee5\u5224\u65ad\u6837\u672c\u662f\u5426\u5c5e\u4e8e\u8be5\u7fa4\u4f53\u3002\u6837\u672c\u7684\u5e73\u5747\u503c\u5e94\u8be5\u5728\u4e00\u4e2a\u4ee5\u7fa4\u4f53\u5e73\u5747\u503c\u4e3a\u4e2d\u5fc3\uff0c\u4ee5\u4e0e\u6837\u672c\u5bb9\u91cf\u6709\u5173\u7684\u6807\u51c6\u8bef\u5dee\u6240\u786e\u5b9a\u7684\u6b63\u6001\u5206\u5e03\u7684\u5408\u7406\u8303\u56f4\u5185\uff0c\u5982\u679c\u4e0d\u5728\uff0c\u5219\u4e0d\u5c5e\u4e8e\u8fd9\u4e2a\u7fa4\u4f53\u3002\u516c\u5f0f\uff1a\\[SE = \\frac{s}{{\\sqrt n }}\\]<\/li>\n<li>\u5df2\u77e5\u4e24\u4e2a\u6837\u672c\u7684\u5e73\u5747\u503c\u4ee5\u53ca\u79bb\u6563\u7a0b\u5ea6\uff0c\u53ef\u4ee5\u5224\u65ad\u5b83\u4eec\u662f\u5426\u5c5e\u4e8e\u540c\u4e00\u4e2a\u7fa4\u4f53\u3002\u5982\u679c\u4e24\u4e2a\u6837\u672c\u5c5e\u4e8e\u540c\u4e00\u4e2a\u7fa4\u4f53\uff0c\u4e24\u4e2a\u6837\u672c\u7684\u5e73\u5747\u503c\u4e4b\u5dee\uff0c\u5e94\u8be5\u5728\u4e00\u4e2a\u6839\u636e\u4e24\u4e2a\u6837\u672c\u81ea\u8eab\u7684\u6807\u51c6\u5dee\u6240\u786e\u5b9a\u7684\u4e00\u4e2a\u5408\u6210\u6807\u51c6\u5dee\u7684\u5408\u7406\u8303\u56f4\u5185\uff0c\u6bd4\u59822\u4e2a\u62163\u4e2a\u4ee5\u5185\uff0c\u5982\u679c\u8d85\u8fc7\uff0c\u5219\u5e94\u8be5\u4e0d\u5c5e\u4e8e\u540c\u4e00\u4e2a\u7fa4\u4f53\u3002\u516c\u5f0f\uff1a\\[\\frac{{\\overline x &#8211; \\overline y }}{{\\sqrt {\\frac{{S_x^2}}{{{n_x}}} + \\frac{{S_y^2}}{{{n_y}}}} }}\\]<\/li>\n<\/ol>\n<p><span style=\"color: #ff6600;\">\u672c\u7ae0\u6709\u4e00\u4e2a\u8bf4\u660e\u4e0d\u6e05\u7684\u5730\u65b9\uff0c\u5728187\u9875\u63d0\u5230\u7684\u201c\u6807\u51c6\u8bef\u5dee\u4e3a22.7\u201d\uff0c\u8fd9\u4e2a22.7\u5728\u524d\u6587\u6ca1\u6709\u51fa\u73b0\uff0c\u662f\u5728\u7ae0\u672b\u7684\u201c\u8865\u5145\u77e5\u8bc6\u70b9\u201d\u4e2d\u8ba1\u7b97\u5f97\u51fa\u7684\uff0c\u4f46\u5947\u602a\u7684\u662f\uff0c\u6309\u7167\u4e66\u4e2d\u7ed9\u51fa\u7684\u516c\u5f0f\u548c\u6570\u636e\u5f97\u51fa\u7684\u4e5f\u4e0d\u662f22.7\u3002\u8fd9\u4e2a\u7591\u95ee\u6211\u4e00\u76f4\u6ca1\u80fd\u89e3\u51b3\u3002<\/span><\/p>\n<p><strong>\u7b2c11\u7ae0 \u6c11\u610f\u6d4b\u9a8c\u4e0e\u8bef\u5dee\u5e45\u5ea6<\/strong><\/p>\n<p>\u7edf\u8ba1\u63a8\u65ad\u53e6\u4e00\u79cd\u5e38\u7528\u7684\u5f62\u5f0f\u662f\u6c11\u610f\u8c03\u67e5\u3002\u4e0e\u5176\u4ed6\u62bd\u6837\u8c03\u67e5\u5f62\u5f0f\u4e4b\u95f4\u6700\u6839\u672c\u7684\u533a\u522b\u5728\u4e8e\uff0c\u6570\u636e\u4e0d\u662f\u5e73\u5747\u6570\uff0c\u800c\u662f\u767e\u5206\u6bd4\u3002\u9664\u6b64\u4e4b\u5916\uff0c\u5176\u4ed6\u6d41\u7a0b\u90fd\u662f\u76f8\u4f3c\u7684\u3002<\/p>\n<p>\u4e0e\u5176\u4ed6\u7edf\u8ba1\u63a8\u65ad\u76f8\u540c\uff0c\u6c11\u8c03\u503c\u4e5f\u6709\u4e00\u4e2a\u6807\u51c6\u8bef\u5dee\\[SE = \\sqrt {\\frac{{p(1 &#8211; p)}}{n}} \\]\u3002\u5f53\u7136\u8fd9\u662f\u572868%\u7684\u7f6e\u4fe1\u533a\u95f4\u5185\uff0c\u5982\u679c\u8981\u6269\u5927\u7f6e\u4fe1\u533a\u95f4\uff0c\u5219\u8981\u964d\u4f4e\u7cbe\u5ea6\uff0c\u5373\u5141\u8bb8\u67092\u4e2a\u62163\u4e2aSE\u3002\u4e3e\u4e2a\u4f8b\u5b50\uff0c\u6bd4\u5982\u670968%\u7684\u628a\u63e1\u8ba4\u4e3a\u5171\u548c\u515a\u4f1a\u83b7\u5f9753%\u00b12%\u7684\u9009\u7968\uff0c\u5176\u4e2d2%\u5c31\u662fSE\uff0c68%\u8868\u793a\u5728\u4e00\u4e2aSE\u4ee5\u5185\u7684\u533a\u95f4\u3002\u5982\u679c\u6269\u5927\u201c\u8bef\u5dee\u5e45\u5ea6\u201d\u5c31\u53ef\u4ee5\u8bf4\u201c\u670995%\u7684\u628a\u63e1\u2026\u2026\u83b7\u5f9753%\u00b14%\u7684\u9009\u7968\u201d\u3002\u603b\u4e4b\uff0c\u5728\u6ca1\u6709\u65b0\u6570\u636e\u8865\u5145\u7684\u60c5\u51b5\u4e0b\uff0c\u8981\u60f3\u63d0\u9ad8\u6c11\u8c03\u6b63\u786e\u7387\uff0c\u5c31\u53ea\u80fd\u964d\u4f4e\u9884\u6d4b\u7cbe\u5ea6\u3002<\/p>\n<p>\u57fa\u4e8e\u4e2d\u5fc3\u6781\u9650\u5b9a\u7406\uff0c\u4e00\u4e2a1000\u4eba\u7684\u6c11\u8c03\u8db3\u4ee5\u63d0\u4f9b\u6709\u5173\u6574\u4e2a\u7f8e\u56fd\u7684\u6709\u610f\u4e49\u548c\u51c6\u786e\u7684\u4fe1\u606f\u3002\u7edf\u8ba1\u5b66\u5e76\u4e0d\u590d\u6742\uff0c\u5173\u952e\u662f\u5728\u4e8e\u6837\u672c\u662f\u5426\u4f18\u8d28\u3002\u6240\u4ee5\u6c11\u8c03\u771f\u6b63\u7684\u6311\u6218\u5728\u4e8e\uff1a\u8bbe\u8ba1\u5e76\u9009\u53d6\u6b63\u786e\u7684\u6837\u672c\uff1b\u7528\u6070\u5f53\u7684\u65b9\u5f0f\u4ece\u8be5\u6837\u672c\u4e2d\u83b7\u53d6\u5408\u9002\u7684\u4fe1\u606f\uff0c\u4ee5\u51c6\u786e\u7684\u53cd\u6620\u4ed6\u4eec\u7684\u771f\u5b9e\u611f\u53d7\u3002<\/p>\n<p><span style=\"color: #ff6600;\">\u672c\u7ae0\u53c8\u51fa\u73b0\u4e00\u4e2a\u660e\u663e\u9519\u8bef\uff0c\u5728205\u9875\u201c\u5171\u548c\u515a\u5019\u9009\u4eba\u7684\u65b0\u6807\u51c6\u8bef\u5dee\u4e3a<\/span>\u00a0<span style=\"color: #ff6600;\">\\[\\sqrt {0.52 \\times 0.48\/2000} = 0.1\\]<\/span><span style=\"color: #ff6600;\">\u201d\uff0c\u800c\u5b9e\u9645\u4e0a\u5e94\u8be5\u7b49\u4e8e0.01\uff0c\u4e0b\u4e00\u6bb5\u4e2d\u76840.1\u4e5f\u5e94\u8be5\u662f0.01\uff0c\u771f\u662f\u4ee4\u4eba\u60ca\u8bb6\u7684\u9519\u8bef\u554a\u3002<\/span><\/p>\n<p><strong>\u7b2c12\u7ae0 \u56de\u5f52\u5206\u6790\u4e0e\u7ebf\u6027\u5173\u7cfb<\/strong><\/p>\n<p>\u56de\u5f52\u5206\u6790\u4e0e\u524d\u51e0\u7ae0\u8bb2\u7684\u7edf\u8ba1\u5b66\u65b9\u6cd5\u7684\u5f88\u5927\u4e00\u4e2a\u4e0d\u540c\u70b9\u662f\uff0c\u4e4b\u524d\u7684\u4f8b\u5b50\u91cc\uff0c\u9700\u8981\u7814\u7a76\u7684\u53d8\u91cf\u53ea\u6709\u4e24\u79cd\u72b6\u6001\uff0c\u662f\u6216\u5426\uff0c\u6709\u6216\u65e0\uff0c\u6bd4\u5982\u662f\u4e0d\u662f\u56fd\u9645\u9999\u80a0\u8282\u7684\u53c2\u52a0\u8005\uff0c\u662f\u4e0d\u662f\u7bee\u7403\u961f\u5458\uff0c\u6709\u6ca1\u6709\u4e00\u5929\u540320\u4e2a\u9eb8\u76ae\u997c\uff0c\u6709\u6ca1\u6709\u81ea\u95ed\u75c7\u3002\u8fd9\u79cd\u60c5\u51b5\u4e0b\u53ea\u9700\u8981\u7814\u7a76\u53d8\u91cf\u4e0e\u7ed3\u679c\u4e4b\u95f4\u662f\u5426\u6709\u76f8\u5173\u6027\u5373\u53ef\uff0c\u4e0d\u9700\u8981\u4e5f\u6ca1\u6709\u529e\u6cd5\u7814\u7a76\u56e0\u53d8\u91cf\u968f\u89e3\u91ca\u53d8\u91cf\u53d8\u5316\u7684\u5177\u4f53\u6570\u636e\u3002\u800c\u5728\u5f88\u591a\u7814\u7a76\u4e2d\uff0c\u53d8\u91cf\u5e76\u4e0d\u53ea\u662f\u7edd\u5bf9\u7684\u4e24\u79cd\u72b6\u6001\uff0c\u800c\u662f\u4e00\u7cfb\u5217\u6570\u503c\uff0c\u8fd9\u79cd\u60c5\u51b5\u4e0b\uff0c\u6ca1\u6709\u7edd\u5bf9\u7684\u591a\u5c11\u6216\u9ad8\u4f4e\u4e4b\u5206\uff0c\u5c31\u5fc5\u987b\u8981\u7814\u7a76\u7ed3\u679c\u968f\u53d8\u91cf\u7684\u53d8\u5316\u89c4\u5f8b\uff0c\u8fd9\u5c31\u662f\u56de\u5f52\u5206\u6790\u7684\u4e00\u4e2a\u91cd\u8981\u7279\u70b9\u3002<\/p>\n<p>\u56de\u5f52\u5206\u6790\u53ef\u4ee5\u4e3a\u6bcf\u4e2a\u89e3\u91ca\u53d8\u91cf\u7ed9\u51fa\u4e00\u4e2a\u56de\u5f52\u7cfb\u6570\uff0c\u8fd9\u6837\u5c31\u53ef\u4ee5\u5728\u5047\u8bbe\u5176\u4ed6\u89e3\u91ca\u53d8\u91cf\u4e0d\u6539\u53d8\u7684\u60c5\u51b5\u4e0b\uff0c\u770b\u51fa\u56e0\u53d8\u91cf\u4e0e\u67d0\u4e00\u4e2a\u89e3\u91ca\u53d8\u91cf\u4e4b\u95f4\u7684\u5173\u7cfb\uff0c\u6362\u53e5\u8bdd\u8bf4\uff0c\u8fd9\u5c31\u6392\u9664\u4e86\u5176\u4ed6\u53ef\u80fd\u7684\u56e0\u7d20\u3002\u8fd9\u662f\u56de\u5f52\u5206\u6790\u7684\u53e6\u4e00\u4e2a\u91cd\u8981\u7279\u70b9\u3002\u9700\u8981\u518d\u6b21\u91cd\u590d\u8bf4\u660e\u7684\u662f\uff0c\u7edf\u8ba1\u5b66\u8bc1\u660e\u7684\u76f8\u5173\u6027\u53ea\u662f\u4e00\u79cd\u8f85\u52a9\u7684\u5224\u65ad\uff0c\u5e76\u4e0d\u80fd\u8bc1\u660e\u5176\u4e2d\u6709\u56e0\u679c\u5173\u7cfb\u3002<\/p>\n<p>\u56de\u5f52\u5206\u6790\u4e2d\u6700\u6838\u5fc3\u7684\u4e00\u70b9\u662f\uff0c\u5b83\u5bfb\u627e\u7684\u662f\u4e24\u4e2a\u53d8\u91cf\u4e4b\u95f4\u7684\u6700\u4f73\u62df\u5408\u7ebf\u6027\u5173\u7cfb\u3002\u56de\u5f52\u5206\u6790\u6700\u540e\u4f1a\u5f97\u5230\u4e00\u4e2a\u56de\u5f52\u65b9\u7a0b\uff0c\\[y = a + bx\\]\uff0cy\u662f\u56e0\u53d8\u91cf\uff0cx\u662f\u89e3\u91ca\u53d8\u91cf\uff0ca\u662f\u622a\u8ddd\uff0cb\u662f\u56de\u5f52\u7cfb\u6570\u3002\u5bf9\u4e8e\u56de\u5f52\u7cfb\u6570\uff0c\u6211\u4eec\u9700\u8981\u5173\u5fc3\u7684\u67093\u4ef6\u4e8b\uff1a\u6b63\u8d1f\uff0c\u5373\u89e3\u91ca\u53d8\u91cf\u4e0e\u56e0\u53d8\u91cf\u4e4b\u95f4\u7684\u76f8\u5173\u5173\u7cfb\u7684\u65b9\u5411\uff1b\u5927\u5c0f\uff0c\u89e3\u91ca\u53d8\u91cf\u5bf9\u56e0\u53d8\u91cf\u5f71\u54cd\u7684\u7a0b\u5ea6\uff1b\u542b\u4e49\uff0c\u6837\u672c\u662f\u5426\u80fd\u591f\u53cd\u6620\u6574\u4e2a\u7fa4\u4f53\u666e\u904d\u7684\u6709\u610f\u4e49\u7684\u76f8\u5173\u5173\u7cfb\u3002\u524d\u4e24\u4e2a\u5f88\u5bb9\u6613\u7406\u89e3\uff0c\u6700\u540e\u4e00\u4e2a\u542b\u4e49\u95ee\u9898\uff0c\u5176\u5b9e\u5c31\u662f\u524d\u9762\u51e0\u7ae0\u4e00\u76f4\u5728\u8bb2\u7684\u7f6e\u4fe1\u533a\u95f4\u3002\u6211\u4eec\u53ef\u4ee5\u7528\u76f8\u540c\u7684\u65b9\u6cd5\u6765\u5224\u65ad\u8fd9\u4e00\u6837\u672c\u7684\u56de\u5f52\u7cfb\u6570\u662f\u5426\u5728\u6807\u51c6\u8bef\u5dee\u7684\u5408\u7406\u533a\u95f4\u5185\u3002\u8981\u6ce8\u610f\u7684\u662f\uff0c\u5bf9\u4e8e\u5c0f\u578b\u6837\u672c\u6570\u636e\uff0c\u56de\u5f52\u7cfb\u6570\u7684\u5e73\u5747\u503c\u4e0d\u4f1a\u5448\u73b0\u6b63\u6001\u5206\u5e03\uff0c\u800c\u662ft\u5206\u5e03\u3002<\/p>\n<p>\u524d\u9762\u7b2c4\u7ae0\u8bb2\u4e86\u76f8\u5173\u5173\u7cfb\uff0c\u90fd\u662f\u7528\u6765\u63cf\u8ff0\u4e24\u4e2a\u91cf\u4e4b\u95f4\u76f8\u5173\u6027\u7684\u7cfb\u6570\uff0c\u76f8\u5173\u7cfb\u6570\u548c\u56de\u5f52\u7cfb\u6570\u6709\u4ec0\u4e48\u8054\u7cfb\u5462\uff1f\u5176\u5b9e\u5f88\u7b80\u5355\uff0c\\[b = r \\times \\frac{{{\\sigma _y}}}{{{\\sigma _x}}}\\]\uff0cb\u662f\u56de\u5f52\u7cfb\u6570\uff0cr\u662f\u76f8\u5173\u7cfb\u6570\uff0c\u662fy\u7684\u6807\u51c6\u5dee\uff0c\u662fx\u7684\u6807\u51c6\u5dee\u3002\u76f4\u89c9\u4e0a\u601d\u8003\u4e00\u4e0b\u4e5f\u53ef\u4ee5\u7406\u89e3\uff0c\u6807\u51c6\u5dee\u5927\u5c0f\u8868\u793a\u4e24\u4e2a\u91cf\u7684\u53d8\u5316\u7a0b\u5ea6\uff0c\u6bd4\u503c\u5c31\u662f\u4e00\u4e2a\u968f\u53e6\u4e00\u4e2a\u7684\u53d8\u5316\u7a0b\u5ea6\u4e86\uff0c\u518d\u4e58\u4ee5\u8868\u793a\u7d27\u5bc6\u7a0b\u5ea6\u7684\u76f8\u5173\u6027\u7cfb\u6570\u5c31\u662f\u56de\u5f52\u7cfb\u6570\u4e86\u3002<\/p>\n<p><strong>\u7b2c13\u7ae0 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