{"id":258,"date":"2023-08-03T12:41:07","date_gmt":"2023-08-03T12:41:07","guid":{"rendered":"https:\/\/statorials.org\/cn\/z%e5%88%86%e6%95%b0\/"},"modified":"2023-08-03T12:41:07","modified_gmt":"2023-08-03T12:41:07","slug":"z%e5%88%86%e6%95%b0","status":"publish","type":"post","link":"https:\/\/statorials.org\/cn\/z%e5%88%86%e6%95%b0\/","title":{"rendered":"Z \u5206\u6570"},"content":{"rendered":"<p>\u672c\u6587\u89e3\u91ca\u4e86\u7edf\u8ba1\u5b66\u4e2d\u7684 Z \u5206\u6570\u3002\u60a8\u8fd8\u5c06\u4e86\u89e3\u5982\u4f55\u8ba1\u7b97\u80a1\u7968\u7684 Z \u5206\u6570\u3001\u8ba1\u7b97\u65b9\u6cd5\u7684\u793a\u4f8b\u4ee5\u53ca Z \u5206\u6570\u7684\u7279\u5f81\u3002 <\/p>\n<h2 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"%c2%bfque-es-la-puntuacion-z\"><\/span>\u4ec0\u4e48\u662fZ\u5206\u6570\uff1f<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p> <strong>Z-score<\/strong>\u6216<strong>Z-score<\/strong>\u662f\u4e00\u79cd\u7edf\u8ba1\u5206\u6570\uff0c\u6307\u793a\u67d0\u4e2a\u503c\u4e0e\u5e73\u5747\u503c\u7684\u6807\u51c6\u5dee\u6709\u591a\u5c11\u3002\u8981\u8ba1\u7b97\u67d0\u4e2a\u503c\u7684 Z \u5206\u6570\uff0c\u8bf7\u4ece\u8be5\u503c\u4e2d\u51cf\u53bb\u5e73\u5747\u503c\uff0c\u7136\u540e\u9664\u4ee5\u6570\u636e\u6837\u672c\u7684\u6807\u51c6\u5dee\u3002<\/p>\n<p>\u4f8b\u5982\uff0c\u5982\u679c\u67d0\u4e2a\u503c\u6bd4\u6570\u636e\u96c6\u7684\u7b97\u672f\u5e73\u5747\u503c\u5c0f\u4e24\u4e2a\u6807\u51c6\u5dee\uff0c\u5219\u8be5\u503c\u7684 Z \u5206\u6570\u4e3a -2\u3002<\/p>\n<p>\u8be5\u7edf\u8ba1\u672f\u8bed\u4e5f\u79f0\u4e3a<strong>\u6807\u51c6\u5206\u6570<\/strong>\u3001 <strong>Z \u7edf\u8ba1\u91cf<\/strong>\u6216<strong>Z \u503c\u3002<\/strong><\/p>\n<p>\u503c\u7684 Z \u5206\u6570\u5728\u5047\u8bbe\u68c0\u9a8c\u4e2d\u975e\u5e38\u6709\u7528\uff0c\u53ef\u8ba1\u7b97\u7f6e\u4fe1\u533a\u95f4\u7684\u9650\u5236\uff0c\u4ece\u800c\u8ba1\u7b97\u62d2\u7edd\u539f\u5047\u8bbe\u7684\u533a\u57df\u3002 <\/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\/\u7f6e\u4fe1\u533a\u95f4\/\">\u7edf\u8ba1\u4e2d\u7684\u7f6e\u4fe1\u533a\u95f4\u662f\u4ec0\u4e48\uff1f<\/a> <\/div>\n<h2 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"formula-de-la-puntuacion-z\"><\/span> Z\u5206\u6570\u516c\u5f0f<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p><strong>Z \u5206\u6570\u7b49\u4e8e\u6570\u636e\u96c6\u7684\u503c\u4e0e\u5e73\u5747\u503c\u4e4b\u95f4\u7684\u5dee\u9664\u4ee5\u6807\u51c6\u5dee\u3002<\/strong>\u56e0\u6b64\uff0c\u8981\u627e\u5230 Z \u5206\u6570\uff0c\u5fc5\u987b\u9996\u5148\u4ece\u503c\u4e2d\u51cf\u53bb\u5e73\u5747\u503c\uff0c\u7136\u540e\u5c06\u7ed3\u679c\u9664\u4ee5\u6807\u51c6\u5dee\u3002<\/p>\n<p>\u7b80\u800c\u8a00\u4e4b\uff0c <strong>Z-score \u516c\u5f0f<\/strong>\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-d95c28d27f77d977ff6c9b7fcb1b8480_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"Z=\\cfrac{X-\\overline{X}}{\\sigma}\" title=\"Rendered by QuickLaTeX.com\" height=\"41\" width=\"93\" 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-0be116875001706f29a24434bd0d91c9_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"Z\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"12\" style=\"vertical-align: 0px;\"><\/p>\n<p>\u662f Z \u5206\u6570\uff0c<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/statorials.org\/wp-content\/ql-cache\/quicklatex.com-a84020904813123dc75b89c701025ecd_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"X_i\" title=\"Rendered by QuickLaTeX.com\" height=\"15\" width=\"20\" style=\"vertical-align: -3px;\"><\/p>\n<p>\u662f\u8ba1\u7b97 Z \u5206\u6570\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-5b485d4231dfeb4b50ddf271c3abb0b3_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\overline{X}\" title=\"Rendered by QuickLaTeX.com\" height=\"15\" width=\"17\" style=\"vertical-align: 0px;\"><\/p>\n<p>\u662f\u7b97\u672f\u5e73\u5747\u503c\u5e76\u4e14<\/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>\u662f\u6807\u51c6\u504f\u5dee\u6216\u5178\u578b\u504f\u5dee\u3002<\/p>\n<p> Z \u5206\u6570\u503c\u7684\u89e3\u91ca\u5f88\u7b80\u5355\uff1aZ \u5206\u6570\u503c\u8868\u793a\u503c\u4e0e\u5e73\u5747\u503c\u4e4b\u95f4\u7684\u6807\u51c6\u5dee\u6570\u3002\u56e0\u6b64\uff0cZ \u5206\u6570\u7684\u7edd\u5bf9\u503c\u8d8a\u5927\uff0c\u8be5\u503c\u4e0e\u5e73\u5747\u503c\u7684\u504f\u5dee\u5c31\u8d8a\u5927\u3002 <\/p>\n<h2 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"ejemplos-de-puntuaciones-z\"><\/span> Z \u5206\u6570\u793a\u4f8b<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p>\u4e00\u65e6\u6211\u4eec\u4e86\u89e3\u4e86 Z \u5206\u6570\u7684\u5b9a\u4e49\uff0c\u4ee5\u4fbf\u60a8\u66f4\u597d\u5730\u7406\u89e3\u5176\u542b\u4e49\uff0c\u5728\u672c\u8282\u4e2d\u6211\u4eec\u5c06\u7ee7\u7eed\u89e3\u51b3\u4e00\u4e2a\u8ba1\u7b97\u591a\u4e2a Z \u5206\u6570\u7684\u793a\u4f8b\u3002<\/p>\n<ul>\n<li>\u8ba1\u7b97\u4ee5\u4e0b\u6240\u6709\u6570\u636e\u7684 Z \u5206\u6570\uff1a7\u30012\u30014\u30019\u30013<\/li>\n<\/ul>\n<p>\u9996\u5148\uff0c\u6211\u4eec\u9700\u8981\u6c42\u6837\u672c\u6570\u636e\u7684\u7b97\u672f\u5e73\u5747\u503c\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-58669a07e461a9747b39102cc4775733_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\overline{X}=\\cfrac{7+2+4+9+3}{5}=5\" title=\"Rendered by QuickLaTeX.com\" height=\"39\" width=\"204\" style=\"vertical-align: -12px;\"><\/p>\n<\/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\/\u7b97\u672f\u5e73\u5747\u6570\/\">\u7b97\u672f\u5e73\u5747\u503c\u662f\u5982\u4f55\u8ba1\u7b97\u7684\uff1f<\/a><\/div>\n<p class=\"has-text-align-left\">\u5176\u6b21\uff0c\u6211\u4eec\u8ba1\u7b97\u6570\u636e\u7cfb\u5217\u7684\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-bdd7b3d503cf74ee9d40e048c42f4310_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\sigma=2,61\" title=\"Rendered by QuickLaTeX.com\" height=\"16\" width=\"68\" style=\"vertical-align: -4px;\"><\/p>\n<\/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\/\u6807\u51c6\u5dee\u6216\u6807\u51c6\u5dee\/\">\u6807\u51c6\u5dee\u8ba1\u7b97\u5668<\/a><\/div>\n<p>\u6700\u540e\uff0c\u6211\u4eec\u5bf9\u6bcf\u4e2a\u6570\u636e\u5e94\u7528 Z \u5206\u6570\u516c\u5f0f\u5e76\u8ba1\u7b97\u6240\u6709 Z \u5206\u6570\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-d95c28d27f77d977ff6c9b7fcb1b8480_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"Z=\\cfrac{X-\\overline{X}}{\\sigma}\" title=\"Rendered by QuickLaTeX.com\" height=\"41\" width=\"93\" 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-9cc8368486f111e58b19371371764247_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"Z_1=\\cfrac{7-5}{2,61}=0,77\" title=\"Rendered by QuickLaTeX.com\" height=\"43\" width=\"142\" 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-1a83d919634eb30117f8486f2aeb353e_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"Z_2=\\cfrac{7-2}{2,61}=1,92\" title=\"Rendered by QuickLaTeX.com\" height=\"43\" width=\"141\" 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-2b97295bd9d968df0fc0f94f5591cd52_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"Z_3=\\cfrac{7-4}{2,61}=1,15\" title=\"Rendered by QuickLaTeX.com\" height=\"43\" width=\"141\" 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-bc52b9731711b52ca7053a4dff1f5859_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"Z_4=\\cfrac{7-9}{2,61}=-0,77\" title=\"Rendered by QuickLaTeX.com\" height=\"43\" width=\"156\" 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-95a1a2a8d573a0da47be3dbb719dc9f7_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"Z_5=\\cfrac{7-3}{2,61}=1,53\" title=\"Rendered by QuickLaTeX.com\" height=\"43\" width=\"142\" style=\"vertical-align: -16px;\"><\/p>\n<\/p>\n<h2 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"la-puntuacion-z-y-la-regla-empirica\"><\/span> Z \u5206\u6570\u548c\u7ecf\u9a8c\u6cd5\u5219<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p><span style=\"text-decoration: underline;\">\u5728\u6837\u672c\u5206\u5e03\u4e3a\u6b63\u6001\u5206\u5e03\u7684\u60c5\u51b5\u4e0b<\/span>\uff0c\u5f97\u76ca\u4e8e\u7ecf\u9a8c\u6cd5\u5219\uff0c\u6211\u4eec\u53ef\u4ee5\u901a\u8fc7\u8ba1\u7b97\u67d0\u4e2a\u503c\u7684Z\u5206\u6570\uff0c\u5feb\u901f\u77e5\u9053\u8be5\u503c\u5bf9\u5e94\u4e8e\u591a\u5c11\u767e\u5206\u6bd4\u7684\u503c\u3002 <\/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\/\u6b63\u6001\u5206\u5e03\/\">\u4ec0\u4e48\u662f\u6b63\u6001\u5206\u5e03\uff1f<\/a><\/div>\n<p>\u56e0\u6b64\uff0c\u7ecf\u9a8c\u6cd5\u5219\u8868\u660e\uff0c\u5728\u4efb\u4f55\u6b63\u6001\u5206\u5e03\u4e2d\uff0c\u4ee5\u4e0b\u60c5\u51b5\u5747\u6210\u7acb\uff1a<\/p>\n<ul>\n<li> 68% \u7684\u503c\u5728\u5e73\u5747\u503c\u7684\u4e00\u4e2a\u6807\u51c6\u5dee\u4e4b\u5185\u3002<\/li>\n<li> 95% \u7684\u503c\u5728\u5e73\u5747\u503c\u7684\u4e24\u4e2a\u6807\u51c6\u5dee\u4e4b\u5185\u3002<\/li>\n<li> 99.7% \u7684\u503c\u5728\u5e73\u5747\u503c\u7684\u4e09\u4e2a\u6807\u51c6\u5dee\u4e4b\u5185\u3002<\/li>\n<\/ul>\n<p>\u56e0\u6b64\uff0c\u5982\u679c\u8fd9\u662f\u6b63\u6001\u5206\u5e03\uff0c\u6211\u4eec\u53ef\u4ee5\u6839\u636e\u7ecf\u9a8c\u6cd5\u5219\u63a8\u51fa\u4ee5\u4e0b\u5185\u5bb9\uff1a<\/p>\n<ul>\n<li>\u5982\u679c Z \u5206\u6570\u5c0f\u4e8e 1\uff0c\u5219\u8be5\u503c\u4f4d\u4e8e\u524d 68% \u7684\u503c\u4e2d\u3002<\/li>\n<li>\u5982\u679c Z \u5206\u6570\u5927\u4e8e 1 \u4f46\u5c0f\u4e8e 2\uff0c\u5219\u8be5\u503c\u4f4d\u4e8e\u524d 95% \u7684\u503c\u4e2d\u3002<\/li>\n<li>\u5982\u679cZ\u5206\u6570\u5927\u4e8e2\u4f46\u5c0f\u4e8e3\uff0c\u5219\u8be5\u503c\u572899.7%\u7684\u503c\u4e4b\u5185\u3002<\/li>\n<\/ul>\n<p>\u60a8\u53ef\u4ee5\u5728\u4e0b\u8868\u4e2d\u770b\u5230\u66f4\u591a\u7ecf\u9a8c\u6cd5\u5219\u503c\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\/\">\u7ecf\u9a8c\u503c\u89c4\u5219\u8868<\/a><\/div>\n<h2 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"propiedades-de-las-puntuaciones-z\"><\/span> Z \u5206\u6570\u5c5e\u6027<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p>Z 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