{"id":157,"date":"2023-08-04T20:08:10","date_gmt":"2023-08-04T20:08:10","guid":{"rendered":"https:\/\/statorials.org\/cn\/%e7%9b%b8%e5%af%b9%e9%a2%91%e7%8e%87\/"},"modified":"2023-08-04T20:08:10","modified_gmt":"2023-08-04T20:08:10","slug":"%e7%9b%b8%e5%af%b9%e9%a2%91%e7%8e%87","status":"publish","type":"post","link":"https:\/\/statorials.org\/cn\/%e7%9b%b8%e5%af%b9%e9%a2%91%e7%8e%87\/","title":{"rendered":"\u76f8\u5bf9\u9891\u7387"},"content":{"rendered":"<p>\u5728\u672c\u6587\u4e2d\uff0c\u60a8\u5c06\u4e86\u89e3\u4ec0\u4e48\u662f\u7edf\u8ba1\u5b66\u4e2d\u7684\u76f8\u5bf9\u9891\u7387\u3001\u5982\u4f55\u83b7\u5f97\u76f8\u5bf9\u9891\u7387\u4ee5\u53ca\u4e24\u4e2a\u9010\u6b65\u89e3\u51b3\u76f8\u5bf9\u9891\u7387\u7684\u7ec3\u4e60\u3002 <\/p>\n<h2 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"%c2%bfque-es-la-frecuencia-relativa\"><\/span>\u4ec0\u4e48\u662f\u76f8\u5bf9\u9891\u7387\uff1f<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p>\u5728\u7edf\u8ba1\u5b66\u4e2d\uff0c<strong>\u76f8\u5bf9\u9891\u7387<\/strong>\u662f\u4e00\u79cd\u5ea6\u91cf\uff0c\u4ee5\u6bd4\u4f8b\u6216\u767e\u5206\u6bd4\u7684\u5f62\u5f0f\u6307\u793a\u67d0\u4e2a\u503c\u5728\u6570\u636e\u6837\u672c\u4e2d\u51fa\u73b0\u7684\u6b21\u6570\u3002\u66f4\u51c6\u786e\u5730\u8bf4\uff0c\u76f8\u5bf9\u9891\u7387\u7b49\u4e8e\u7edd\u5bf9\u9891\u7387\u9664\u4ee5\u6570\u636e\u603b\u6570\u3002<\/p>\n<p>\u4f8b\u5982\uff0c\u5982\u679c\u67d0\u4e2a\u503c\u7684\u7edd\u5bf9\u9891\u7387\u4e3a 15\uff0c\u5e76\u4e14\u603b\u5171\u6709 100 \u4e2a\u6570\u636e\u70b9\uff0c\u5219\u8be5\u503c\u7684\u76f8\u5bf9\u9891\u7387\u4e3a 0.15 (15\/100=0.15)\u3002<\/p>\n<p>\u4e00\u822c\u7528\u7b26\u53f7<em><sub>hi<\/sub><\/em>\u6765\u8868\u793a\u76f8\u5bf9\u9891\u7387\u3002\u867d\u7136\u7edf\u8ba1\u754c\u8fd8\u6ca1\u6709\u8fbe\u6210\u5171\u8bc6\uff0c\u6240\u4ee5\u4f60\u53ef\u4ee5\u770b\u5230\u7528\u53e6\u4e00\u4e2a\u7b26\u53f7\u4ee3\u8868\u7684\u76f8\u5bf9\u9891\u7387\u3002 <\/p>\n<h2 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"como-calcular-la-frecuencia-relativa\"><\/span>\u5982\u4f55\u8ba1\u7b97\u76f8\u5bf9\u9891\u7387<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p>\u76f8\u5bf9\u9891\u7387\u7b49\u4e8e\u7edd\u5bf9\u9891\u7387\u9664\u4ee5\u6570\u636e\u603b\u6570\u3002\u56e0\u6b64\uff0c\u8981\u8ba1\u7b97\u76f8\u5bf9\u9891\u7387\uff0c\u5fc5\u987b\u9996\u5148\u627e\u5230\u7edd\u5bf9\u9891\u7387\uff0c\u7136\u540e\u5c06\u5176\u9664\u4ee5\u89c2\u6d4b\u603b\u6570\u3002<\/p>\n<p>\u56e0\u6b64\uff0c<strong>\u76f8\u5bf9\u9891\u7387\u7684\u8ba1\u7b97\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-bd560e31bd770266915cc90afcc43fd2_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"h_i=\\cfrac{f_i}{N}\" title=\"Rendered by QuickLaTeX.com\" height=\"38\" width=\"58\" style=\"vertical-align: -12px;\"><\/p>\n<\/p>\n<p style=\"margin-bottom:5px\">\u91d1\u5b50\uff1a<\/p>\n<ul style=\"color:#FF8A05; font-weight: bold;\">\n<li style=\"margin-bottom:5px\">\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/statorials.org\/wp-content\/ql-cache\/quicklatex.com-ec762950a25d611e8cb122d8b5b223f7_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"h_i\" title=\"Rendered by QuickLaTeX.com\" height=\"15\" width=\"15\" style=\"vertical-align: -3px;\"><\/p>\n<p>\u662f\u76f8\u5bf9\u9891\u7387\u3002<\/li>\n<li style=\"margin-bottom:5px\">\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/statorials.org\/wp-content\/ql-cache\/quicklatex.com-fcb89ec1b112c79bfb56f1c210f6bb67_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"f_i\" title=\"Rendered by QuickLaTeX.com\" height=\"16\" width=\"14\" style=\"vertical-align: -4px;\"><\/p>\n<p>\u662f\u7edd\u5bf9\u9891\u7387\u3002<\/li>\n<li>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/statorials.org\/wp-content\/ql-cache\/quicklatex.com-7354bae77b50b7d1faed3e8ea7a3511a_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"N\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"16\" style=\"vertical-align: 0px;\"><\/p>\n<p>\u662f\u6570\u636e\u603b\u6570\u3002<\/li>\n<\/ul>\n<p>\u53e6\u4e00\u65b9\u9762\uff0c\u8981\u8ba1\u7b97<strong>\u4ee5\u767e\u5206\u6bd4\u8868\u793a\u7684\u76f8\u5bf9\u9891\u7387<\/strong>\uff0c\u5373\u4ee5\u767e\u5206\u6bd4\u8868\u793a\u7684\u76f8\u5bf9\u9891\u7387\uff0c\u53ea\u9700\u5c06\u524d\u9762\u7684\u516c\u5f0f\u4e58\u4ee5 100\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-3231783a8b050ccb792881ded09ff2ef_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"h_i (\\%)=\\cfrac{f_i}{N}\\cdot 100\" title=\"Rendered by QuickLaTeX.com\" height=\"38\" width=\"126\" style=\"vertical-align: -12px;\"><\/p>\n<\/p>\n<h2 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"ejemplos-de-frecuencia-relativa\"><\/span>\u76f8\u5bf9\u9891\u7387\u7684\u4f8b\u5b50<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p>\u4e00\u65e6\u60a8\u4e86\u89e3\u4e86\u76f8\u5bf9\u9891\u7387\u7684\u5b9a\u4e49\uff0c\u4e0b\u9762\u662f\u4e24\u4e2a\u5b9e\u9645\u793a\u4f8b\uff0c\u60a8\u53ef\u4ee5\u4e86\u89e3\u5982\u4f55\u8ba1\u7b97\u6b64\u7c7b\u9891\u7387\u3002\u5728\u7b2c\u4e00\u4e2a\u793a\u4f8b\u4e2d\uff0c\u786e\u5b9a\u79bb\u6563\u53d8\u91cf\u7684\u76f8\u5bf9\u9891\u7387\uff0c\u5728\u7b2c\u4e8c\u4e2a\u793a\u4f8b\u4e2d\uff0c\u786e\u5b9a\u8fde\u7eed\u53d8\u91cf\u7684\u76f8\u5bf9\u9891\u7387\u3002 <\/p>\n<h3 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"ejemplo-1-variable-discreta\"><\/span>\u793a\u4f8b1\uff1a\u79bb\u6563\u53d8\u91cf<span class=\"ez-toc-section-end\"><\/span><\/h3>\n<ul>\n<li>\u73ed\u7ea7 30 \u540d\u5b66\u751f\u7684\u7edf\u8ba1\u79d1\u76ee\u6210\u7ee9\u5982\u4e0b\u3002\u6bcf\u4e2a\u97f3\u7b26\u7684\u76f8\u5bf9\u9891\u7387\u662f\u591a\u5c11\uff1f <\/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-0b4c2aaf8375eb7531d0723aa5ef006c_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"5\\ 4\\ 7\\ 9\\ 10\\ 6\\ 7\\ 4\\ 8\\ 3\" title=\"Rendered by QuickLaTeX.com\" height=\"13\" width=\"151\" style=\"vertical-align: 0px;\"><\/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-d92283243224cd8cd6067c4452a85f91_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"6\\ 9\\ 8\\ 5\\ 6\\ 4\\ 6\\ 2\\ 4\\ 7\" title=\"Rendered by QuickLaTeX.com\" height=\"13\" width=\"142\" style=\"vertical-align: 0px;\"><\/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-e48f65ca1a0f947935791d6ca68469c9_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"8\\ 9\\ 10\\ 5\\ 4\\ 3\\ 6\\ 8\\ 7\\ 5\" title=\"Rendered by QuickLaTeX.com\" height=\"13\" width=\"150\" style=\"vertical-align: 0px;\"><\/p>\n<\/p>\n<p>\u672c\u7ec3\u4e60\u4e2d\u7684\u53d8\u91cf\u662f\u79bb\u6563\u7684\uff0c\u56e0\u4e3a\u6570\u636e\u53ea\u80fd\u662f\u6574\u6570\uff1b\u56e0\u6b64\uff0c\u65e0\u9700\u5c06\u6570\u636e\u5206\u7ec4\u3002<\/p>\n<p>\u4e3a\u4e86\u627e\u5230\u76f8\u5bf9\u9891\u7387\uff0c\u6211\u4eec\u5fc5\u987b\u9996\u5148\u786e\u5b9a\u7edd\u5bf9\u9891\u7387\u3002\u56e0\u6b64\uff0c\u6211\u4eec\u6784\u5efa\u4e00\u4e2a\u9891\u7387\u8868\u5e76\u8ba1\u7b97\u6bcf\u4e2a\u4e0d\u540c\u503c\u7684\u7edd\u5bf9\u9891\u7387\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\/tableau-de-frequence-absolue.png\" alt=\"\u7edd\u5bf9\u9891\u7387\" class=\"wp-image-3232\" width=\"208\" height=\"403\" srcset=\"\" sizes=\"auto, \"><\/figure>\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\/\u7edd\u5bf9\u9891\u73871\/\">\u5982\u4f55\u8ba1\u7b97\u7edd\u5bf9\u9891\u7387<\/a><\/div>\n<p>\u73b0\u5728\u6211\u4eec\u5df2\u7ecf\u8ba1\u7b97\u4e86\u7edd\u5bf9\u9891\u7387\uff0c\u6211\u4eec\u53ef\u4ee5\u8ba1\u7b97\u76f8\u5bf9\u9891\u7387\u3002\u4e3a\u6b64\uff0c\u53ea\u9700\u5c06\u6bcf\u4e2a\u7edd\u5bf9\u9891\u7387\u9664\u4ee5\u6570\u636e\u603b\u6570 (30)\uff1a <\/p>\n<figure class=\"wp-block-image aligncenter size-large is-resized\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/statorials.org\/wp-content\/uploads\/2023\/08\/calcul-de-frequence-relative.png\" alt=\"\u76f8\u5bf9\u9891\u7387\u8ba1\u7b97\" class=\"wp-image-3307\" width=\"318\" height=\"521\" srcset=\"\" sizes=\"auto, \"><\/figure>\n<p>\u90a3\u4e48\uff0c\u7edd\u5bf9\u9891\u7387\u548c\u76f8\u5bf9\u9891\u7387\u95ee\u9898\u7684\u9891\u7387\u8868\u5982\u4e0b\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\/frequence-relative.png\" alt=\"\u76f8\u5bf9\u9891\u7387\" class=\"wp-image-3308\" width=\"318\" height=\"403\" srcset=\"\" sizes=\"auto, \"><\/figure>\n<p>\u8bf7\u6ce8\u610f\uff0c\u6240\u6709\u76f8\u5bf9\u9891\u7387\u7684\u603b\u548c\u59cb\u7ec8\u4e3a 1\uff0c\u5426\u5219\u8fd9\u610f\u5473\u7740\u67d0\u4e9b\u8ba1\u7b97\u662f\u9519\u8bef\u7684\u3002 <\/p>\n<h3 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"ejemplo-2-variable-continua\"><\/span>\u793a\u4f8b 2\uff1a\u8fde\u7eed\u53d8\u91cf<span class=\"ez-toc-section-end\"><\/span><\/h3>\n<ul>\n<li>\u6d4b\u91cf\u4e86 20 \u4e2a\u4eba\u7684\u8eab\u9ad8\uff0c\u5f97\u5230\u5982\u4e0b\u7ed3\u679c\u3002\u5c06\u6570\u636e\u5206\u6210\u591a\u4e2a\u533a\u95f4\u5e76\u627e\u51fa\u6bcf\u4e2a\u533a\u95f4\u7684\u76f8\u5bf9\u9891\u7387\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-dabf08a3cde1b12a0a9ded21b1de245c_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"1,84\\ 1,71\\ 1,75\\ 1,92\\ 1,57\\ 1,67\\ 1,94\\ 1,83\\ 1,79\\ 1,68\" title=\"Rendered by QuickLaTeX.com\" height=\"17\" width=\"397\" style=\"vertical-align: -4px;\"><\/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-7c22571f0ef18923fbfb50586e3b6c29_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"1,54\\ 1,61\\ 1,78\\ 1,62\\ 1,89\\ 1,80\\ 1,99\\ 1,77\\ 1,70\\ 1,63\" title=\"Rendered by QuickLaTeX.com\" height=\"17\" width=\"397\" style=\"vertical-align: -4px;\"><\/p>\n<\/p>\n<p>\u8be5\u7edf\u8ba1\u6837\u672c\u4e2d\u7684\u6570\u636e\u5c5e\u4e8e\u8fde\u7eed\u53d8\u91cf\uff0c\u56e0\u4e3a\u5b83\u4eec\u662f\u5341\u8fdb\u5236\u7684\uff0c\u56e0\u6b64\u53d8\u91cf\u53ef\u4ee5\u53d6\u4efb\u4f55\u503c\u3002\u56e0\u6b64\uff0c\u5728\u8fdb\u884c\u9891\u7387\u8ba1\u7b97\u4e4b\u524d\uff0c\u6211\u4eec\u9996\u5148\u5c06\u6570\u636e\u5206\u7ec4\u4e3a\u5e45\u5ea6\u4e3a\u5341\u5206\u4e4b\u5341\u7684\u533a\u95f4\u3002<\/p>\n<p>\u63a5\u4e0b\u6765\uff0c\u6211\u4eec\u5236\u4f5c\u4e00\u4e2a\u9891\u7387\u8868\uff0c\u5176\u4e2d\u5305\u542b\u6bcf\u4e2a\u533a\u95f4\u7684\u7edd\u5bf9\u9891\u7387\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\/donnees-du-tableau-de-frequence-absolue-regroupees-en-intervalles.png\" alt=\"\u5206\u7ec4\u4e3a\u533a\u95f4\u7684\u6570\u636e\u7684\u7edd\u5bf9\u9891\u7387\" class=\"wp-image-3233\" width=\"244\" height=\"264\" srcset=\"\" sizes=\"auto, \"><\/figure>\n<p>\u4e00\u65e6\u6211\u4eec\u627e\u5230\u4e86\u7edd\u5bf9\u9891\u7387\uff0c\u6211\u4eec\u5c31\u53ef\u4ee5\u901a\u8fc7\u5c06\u6bcf\u4e2a\u533a\u95f4\u7684\u7edd\u5bf9\u9891\u7387\u9664\u4ee5\u6570\u636e\u603b\u6570\uff0820\uff09\u6765\u5f97\u5230\u6bcf\u4e2a\u533a\u95f4\u7684\u76f8\u5bf9\u9891\u7387\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\/frequence-relative-pour-les-donnees-regroupees-dans-les-intervalles.png\" alt=\"\u5206\u7ec4\u4e3a\u533a\u95f4\u7684\u6570\u636e\u7684\u76f8\u5bf9\u9891\u7387\" class=\"wp-image-3310\" width=\"348\" height=\"264\" srcset=\"\" sizes=\"auto, \"><\/figure>\n<h2 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"frecuencia-relativa-acumulada\"><\/span>\u7d2f\u79ef\u76f8\u5bf9\u9891\u7387<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p>\u987e\u540d\u601d\u4e49\uff0c\u7d2f\u79ef\u76f8\u5bf9\u9891\u7387\u662f\u7edf\u8ba1\u4e2d\u4f7f\u7528\u7684\u53e6\u4e00\u79cd\u9891\u7387\uff0c\u6839\u636e\u76f8\u5bf9\u9891\u7387\u8ba1\u7b97\u5f97\u51fa\u3002<\/p>\n<p>\u66f4\u51c6\u786e\u5730\u8bf4\uff0c\u67d0\u4e2a\u503c\u7684<strong>\u7d2f\u79ef\u76f8\u5bf9\u9891\u7387<\/strong>\u7b49\u4e8e\u8be5\u503c\u672c\u8eab\u7684\u76f8\u5bf9\u9891\u7387\u52a0\u4e0a\u6240\u6709\u8f83\u5c0f\u503c\u7684\u76f8\u5bf9\u9891\u7387\u4e4b\u548c\u3002<\/p>\n<p>\u4e3a\u4e86\u8ba9\u60a8\u4e86\u89e3\u5982\u4f55\u83b7\u5f97\u7d2f\u79ef\u76f8\u5bf9\u9891\u7387\uff0c\u7b2c\u4e00\u4e2a\u793a\u4f8b\u4e2d\u7684\u6570\u636e\u96c6\u7684\u7d2f\u79ef\u76f8\u5bf9\u9891\u7387\u5df2\u8ba1\u7b97\u5982\u4e0b\uff1a <\/p>\n<figure class=\"wp-block-image aligncenter size-full is-resized\"><img decoding=\"async\" loading=\"lazy\" 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