{"id":1047,"date":"2020-06-11T11:00:00","date_gmt":"2020-06-11T02:00:00","guid":{"rendered":"https:\/\/develop-chronos.com\/statistics-top\/statistics\/?p=1047"},"modified":"2020-06-07T09:45:18","modified_gmt":"2020-06-07T00:45:18","slug":"mean-definition","status":"publish","type":"post","link":"https:\/\/develop-chronos.com\/statistics-top\/statistics\/mean-definition","title":{"rendered":"\u671f\u5f85\u5024\u306e\u5b9a\u7fa9\u3010\u671f\u5f85\u5024\u3092\u306f\u3058\u3081\u304b\u3089\u77e5\u308b\u3011"},"content":{"rendered":"\n<p class=\"has-text-align-right\"><span style=\"text-decoration: underline;\">\u5b66\u7fd2\u30ec\u30d9\u30eb\uff1a\u9ad8\u6821\u751f\u3000\u96e3\u6613\u5ea6\uff1a\u2605\u2606\u2606\u2606\u2606<\/span><\/p>\n\n\n\n\n\n\n\n<p>\u671f\u5f85\u5024\u306f\u3001\u78ba\u7387\u5909\u6570\u306e\u5e73\u5747\u3092\u8868\u3057\u307e\u3059\u3002\u3053\u308c\u306f\u78ba\u7387\u5909\u6570\u3092\u5165\u624b\u3057\u305f\u6642\u3001\u6700\u3082\u53d6\u308a\u3046\u308b\u78ba\u7387\u3068\u3057\u3066\u9ad8\u3044\u5024\u3092\u8868\u3057\u307e\u3059\u3002\u78ba\u7387\u5206\u5e03\u306e\u4e2d\u5fc3\u3092\u8868\u3057\u3001\u7d71\u8a08\u7684\u63a8\u5b9a\u3092\u3059\u308b\u4e0a\u3067\u6700\u3082\u91cd\u8981\u306a\u60c5\u5831\u306b\u306a\u308a\u307e\u3059\u3002\u671f\u5f85\u5024\u306b\u306f\u69d8\u3005\u306a\u6027\u8cea\u3001\u5b9a\u7406\u304c\u3042\u308b\u306e\u3067\u4e00\u304b\u3089\u3057\u3063\u304b\u308a\u52c9\u5f37\u3057\u3066\u3044\u304d\u307e\u3057\u3087\u3046\uff01<\/p>\n\n\n\n<div id=\"toc_container\" class=\"toc_light_blue no_bullets\"><p class=\"toc_title\">\u76ee\u6b21<\/p><ul class=\"toc_list\"><li><a href=\"#i\"><span class=\"toc_number toc_depth_1\">1<\/span> \u671f\u5f85\u5024\u306e\u5b9a\u7fa9<\/a><ul><li><a href=\"#i-2\"><span class=\"toc_number toc_depth_2\">1.1<\/span> \u30b5\u30a4\u30b3\u30ed\u306e\u5834\u5408<\/a><\/li><li><a href=\"#i-3\"><span class=\"toc_number toc_depth_2\">1.2<\/span> \u30af\u30b8\u5f15\u304d\u306e\u5834\u5408<\/a><\/li><\/ul><\/li><li><a href=\"#i-4\"><span class=\"toc_number toc_depth_1\">2<\/span> \u671f\u5f85\u5024\u306e\u307e\u3068\u3081<\/a><\/li><li><a href=\"#i-5\"><span class=\"toc_number toc_depth_1\">3<\/span> \u671f\u5f85\u5024\u306e\u95a2\u9023\u8a18\u4e8b<\/a><\/li><\/ul><\/div>\n<h3><span id=\"i\">\u671f\u5f85\u5024\u306e\u5b9a\u7fa9<\/span><\/h3>\n\n\n\n<div style=\"display: inline-block; background: #33cc33; padding: 5px 10px; color: #ffffff; border-radius: 5px 5px 0 0;\"><strong>\u671f\u5f85\u5024(mean)<\/strong><\/div>\n<div style=\"background: #ffffea; padding: 10px; border: 2px solid #33cc33;\">\u78ba\u7387\u5909\u6570\\(X\\)\u306e\u671f\u5f85\u5024\u306f\u8a18\u53f7\\(\\mathrm{E}[X]\\)\u3067\u8868\u3057\u3001\u4e0b\u306e\u3088\u3046\u306b\u5b9a\u7fa9\u3055\u308c\u307e\u3059\u3002\n<div style=\"overflow-x: auto;\">\\begin{align}\n\uff08\u96e2\u6563\u578b\uff09&amp; \\mathrm{E}[X] = \\sum_{i}x_{i}f(x_{i}) \\\\\n\uff08\u9023\u7d9a\u578b\uff09&amp; \\mathrm{E}[X] = \\int_{-\\infty}^{\\infty}xf(x)dx\n\\end{align}<\/div>\n\u3053\u3053\u3067\u3001\\(f(x_{i})\\)\u306f\\(X\\)\u306e\u78ba\u7387\u95a2\u6570\u3092\u8868\u3057\u3001\\(f(x)\\)\u306f\\(X\\)\u306e\u78ba\u7387\u5bc6\u5ea6\u95a2\u6570\u3092\u8868\u3057\u3066\u3044\u307e\u3059\u3002\n<\/div>\n<p>&nbsp;<\/p>\n\n\n\n<div class=\"wp-block-liquid-speech-balloon liquid-speech-balloon-wrap liquid-speech-balloon-00  liquid-speech-balloon-short\"><div class=\"liquid-speech-balloon-avatar\"><\/div><div class=\"liquid-speech-balloon-text\" style=\"border-color:#d6ebf8;background-color:#d6ebf8;color:#000000\"><p>\u5177\u4f53\u4f8b\u3067\u671f\u5f85\u5024\u3092\u6c42\u3081\u3066\u307f\u307e\u3057\u3087\u3046\uff01<\/p><div class=\"liquid-speech-balloon-arrow\" style=\"border-color:transparent #d6ebf8 transparent transparent\"><\/div><\/div><\/div>\n\n\n\n<h4><span id=\"i-2\">\u30b5\u30a4\u30b3\u30ed\u306e\u5834\u5408<\/span><\/h4>\n\n\n\n<p>\u78ba\u7387\u5909\u6570\u3068\u78ba\u7387\u3092\u307e\u3068\u3081\u308b\u3068\u6b21\u306e\u3088\u3046\u306b\u306a\u308a\u307e\u3059\u3002<\/p>\n\n\n\n<figure class=\"wp-block-table aligncenter\"><table><tbody><tr><td>\u78ba\u7387\u5909\u6570\\(X\\)<\/td><td class=\"has-text-align-center\" data-align=\"center\">\\(1\\)<\/td><td class=\"has-text-align-center\" data-align=\"center\">\\(2\\)<\/td><td class=\"has-text-align-center\" data-align=\"center\">\\(3\\)<\/td><td class=\"has-text-align-center\" data-align=\"center\">\\(4\\)<\/td><td class=\"has-text-align-center\" data-align=\"center\">\\(5\\)<\/td><td class=\"has-text-align-center\" data-align=\"center\">\\(6\\)<\/td><\/tr><tr><td>\u78ba\u7387\\(\\mathrm{P}(X)\\)<\/td><td class=\"has-text-align-center\" data-align=\"center\">\\(\\frac{1}{6}\\)<\/td><td class=\"has-text-align-center\" data-align=\"center\">\\(\\frac{1}{6}\\)<\/td><td class=\"has-text-align-center\" data-align=\"center\">\\(\\frac{1}{6}\\)<\/td><td class=\"has-text-align-center\" data-align=\"center\">\\(\\frac{1}{6}\\)<\/td><td class=\"has-text-align-center\" data-align=\"center\">\\(\\frac{1}{6}\\)<\/td><td class=\"has-text-align-center\" data-align=\"center\">\\(\\frac{1}{6}\\)<\/td><\/tr><\/tbody><\/table><\/figure>\n\n\n\n<p>\u3088\u3063\u3066\u671f\u5f85\u5024\\(\\mu\\)\u306f$$\\mu=1\\cdot\\frac{1}{6}+2\\cdot\\frac{1}{6}+\\cdots+6\\cdot\\frac{1}{6}=3.5$$\u3068\u306a\u308a\u307e\u3059\u3002<\/p>\n\n\n\n<h4><span id=\"i-3\">\u30af\u30b8\u5f15\u304d\u306e\u5834\u5408<\/span><\/h4>\n\n\n\n<p>\u3042\u308b\u30af\u30b8\u5f15\u304d\u306e\u5185\u8a33\u304c\u4ee5\u4e0b\u306e\u3088\u3046\u306b\u306a\u3063\u3066\u3044\u308b\u3068\u3057\u307e\u3059\u3002<\/p>\n\n\n\n<figure class=\"wp-block-table\"><table><tbody><tr><td>\u8cb0\u3048\u308b\u91d1\u984d\uff08\u5186\uff09<\/td><td>20<\/td><td>100<\/td><td>500<\/td><td>1500<\/td><td><\/td><\/tr><tr><td>\u304f\u3058\u306e\u672c\u6570\uff08\u672c\uff09<\/td><td>500<\/td><td>300<\/td><td>150<\/td><td>50<\/td><td>\uff08\u5408\u8a08\uff091000\u672c<\/td><\/tr><\/tbody><\/table><\/figure>\n\n\n\n<p>\u3053\u306e\u30af\u30b8\u5f15\u304d\u306e\u671f\u5f85\u5024\u3092\u6c42\u3081\u3066\u307f\u307e\u3057\u3087\u3046\uff01<br>\u3000\u307e\u305a\u3001\u78ba\u7387\u5909\u6570\u306f\\(x_{1}=20,x_{2}=100,x_{3}=500,x_{4}=1500\\)\u3068\u306a\u308a\u307e\u3059\u3002\u305d\u308c\u305e\u308c\u304c\u5f53\u305f\u308b\u78ba\u7387\u3092\\(p_{1},p_{2},p_{3},p_{4}\\)\u3068\u3059\u308b\u3068\u3001\u304f\u3058\u306e\u672c\u6570\u304b\u3089$$p_{1}=\\frac{10}{20},\\ \\ \\ p_{2}=\\frac{6}{20},\\ \\ \\ p_{3}=\\frac{3}{20},\\ \\ \\ p_{4}=\\frac{1}{20}$$\u3068\u306a\u308a\u307e\u3059\u3002\u3088\u3063\u3066\u3053\u306e\u30af\u30b8\u5f15\u304d\u306e\u671f\u5f85\u5024\\(\\mu\\)\u306f$$\\mu=20\\cdot\\frac{10}{20}+100\\cdot\\frac{6}{20}+500\\cdot\\frac{3}{20}+1500\\cdot\\frac{1}{20}=190\uff08\u5186\uff09$$\u3068\u306a\u308a\u307e\u3059\u3002<\/p>\n\n\n\n<h3><span id=\"i-4\">\u671f\u5f85\u5024\u306e\u307e\u3068\u3081<\/span><\/h3>\n\n\n\n<p>\u671f\u5f85\u5024\u306f\u78ba\u7387\u5909\u6570\u306e\u5e73\u5747\u3092\u8868\u3057\u307e\u3059\u3002\u3082\u3046\u5c11\u3057\u8a73\u3057\u304f\u8aac\u660e\u3059\u308b\u3068\u3001\u671f\u5f85\u5024\u306f\u78ba\u7387\u5909\u6570\u306b\u78ba\u7387\u3067\u91cd\u307f\u3092\u3064\u3051\u305f\u91cd\u307f\u4ed8\u304d\u7b97\u8853\u5e73\u5747\u3068\u306a\u308a\u307e\u3059\u3002\u78ba\u7387\u5206\u5e03\u306e\u4e2d\u5fc3\u3092\u8868\u3059\u6307\u6a19\u306b\u306a\u308b\u306e\u3067\u3001\u7d71\u8a08\u7684\u63a8\u6e2c\u3092\u884c\u3046\u4e0a\u3067\u3001\u3068\u3066\u3082\u91cd\u8981\u306a\u60c5\u5831\u306b\u306a\u308a\u307e\u3059\u3002\u307e\u305f\u78ba\u7387\u5909\u6570\u304c\u96e2\u6563\u578b\u304b\u9023\u7d9a\u578b\u304b\u3067\u3001\u671f\u5f85\u5024\u306e\u6c42\u3081\u65b9\u304c\u548c\u304b\u7a4d\u5206\u304b\u3069\u3046\u304b\u304c\u5909\u308f\u308b\u306e\u3067\u6ce8\u610f\u304c\u5fc5\u8981\u3067\u3059\u3002<\/p>\n\n\n\n<h3><span id=\"i-5\">\u671f\u5f85\u5024\u306e\u95a2\u9023\u8a18\u4e8b<\/span><\/h3>\n\n\n\n<p>\u30fb<a href=\"https:\/\/develop-chronos.com\/statistics-top\/statistics\/conditional-mean\">\u6761\u4ef6\u4ed8\u304d\u671f\u5f85\u5024<\/a>\uff1a\u6761\u4ef6\u4ed8\u304d\u78ba\u7387\u5909\u6570\u306e\u671f\u5f85\u5024\u306e\u6c42\u3081\u65b9\u3092\u7d39\u4ecb\u3057\u3066\u3044\u307e\u3059\u3002<\/p>\n\n\n\n<p>\u30fb<a href=\"https:\/\/develop-chronos.com\/statistics-top\/statistics\/mean-nature\">\u671f\u5f85\u5024\u306e\u6027\u8cea<\/a>\uff1a\u671f\u5f85\u5024\u306e\u6301\u3064\u6027\u8cea\u3092\u307e\u3068\u3081\u3066\u3044\u307e\u3059\u3002<\/p>\n","protected":false},"excerpt":{"rendered":"<p>\u5b66\u7fd2\u30ec\u30d9\u30eb\uff1a\u9ad8\u6821\u751f\u3000\u96e3\u6613\u5ea6\uff1a\u2605\u2606\u2606\u2606\u2606 \u671f\u5f85\u5024\u306f\u3001\u78ba\u7387\u5909\u6570\u306e\u5e73\u5747\u3092\u8868\u3057\u307e\u3059\u3002\u3053\u308c\u306f\u78ba\u7387\u5909\u6570\u3092\u5165\u624b\u3057\u305f\u6642\u3001\u6700\u3082\u53d6\u308a\u3046\u308b\u78ba\u7387\u3068\u3057\u3066\u9ad8\u3044\u5024\u3092\u8868\u3057\u307e &#8230; <\/p>\n","protected":false},"author":1,"featured_media":829,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"spay_email":""},"categories":[72],"tags":[73],"jetpack_featured_media_url":"https:\/\/develop-chronos.com\/statistics-top\/statistics\/wp-content\/uploads\/2020\/05\/135-money-images.jpg","_links":{"self":[{"href":"https:\/\/develop-chronos.com\/statistics-top\/statistics\/wp-json\/wp\/v2\/posts\/1047"}],"collection":[{"href":"https:\/\/develop-chronos.com\/statistics-top\/statistics\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/develop-chronos.com\/statistics-top\/statistics\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/develop-chronos.com\/statistics-top\/statistics\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/develop-chronos.com\/statistics-top\/statistics\/wp-json\/wp\/v2\/comments?post=1047"}],"version-history":[{"count":11,"href":"https:\/\/develop-chronos.com\/statistics-top\/statistics\/wp-json\/wp\/v2\/posts\/1047\/revisions"}],"predecessor-version":[{"id":1101,"href":"https:\/\/develop-chronos.com\/statistics-top\/statistics\/wp-json\/wp\/v2\/posts\/1047\/revisions\/1101"}],"wp:featuredmedia":[{"embeddable":true,"href":"https:\/\/develop-chronos.com\/statistics-top\/statistics\/wp-json\/wp\/v2\/media\/829"}],"wp:attachment":[{"href":"https:\/\/develop-chronos.com\/statistics-top\/statistics\/wp-json\/wp\/v2\/media?parent=1047"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/develop-chronos.com\/statistics-top\/statistics\/wp-json\/wp\/v2\/categories?post=1047"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/develop-chronos.com\/statistics-top\/statistics\/wp-json\/wp\/v2\/tags?post=1047"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}