{"id":133,"date":"2023-08-05T02:21:20","date_gmt":"2023-08-05T02:21:20","guid":{"rendered":"https:\/\/statorials.org\/ja\/%e3%83%81%e3%82%a7%e3%83%92%e3%82%99%e3%82%b7%e3%82%a7%e3%83%95%e3%81%ae%e5%ae%9a%e7%90%86\/"},"modified":"2023-08-05T02:21:20","modified_gmt":"2023-08-05T02:21:20","slug":"%e3%83%81%e3%82%a7%e3%83%92%e3%82%99%e3%82%b7%e3%82%a7%e3%83%95%e3%81%ae%e5%ae%9a%e7%90%86","status":"publish","type":"post","link":"https:\/\/statorials.org\/ja\/%e3%83%81%e3%82%a7%e3%83%92%e3%82%99%e3%82%b7%e3%82%a7%e3%83%95%e3%81%ae%e5%ae%9a%e7%90%86\/","title":{"rendered":"\u30c1\u30a7\u30d3\u30b7\u30a7\u30d5\u306e\u5b9a\u7406"},"content":{"rendered":"<p>\u3053\u306e\u8a18\u4e8b\u3067\u306f\u30c1\u30a7\u30d3\u30b7\u30a7\u30d5\u306e\u5b9a\u7406\u3068\u306f\u4f55\u304b\u306b\u3064\u3044\u3066\u8aac\u660e\u3057\u307e\u3059\u3002\u3053\u3053\u3067\u306f\u3001\u30c1\u30a7\u30d3\u30b7\u30a7\u30d5\u306e\u5b9a\u7406\u306e\u516c\u5f0f\u3001\u89e3\u7b54\u6e08\u307f\u306e\u7df4\u7fd2\u554f\u984c\u3001\u3055\u3089\u306b\u30aa\u30f3\u30e9\u30a4\u30f3\u306e\u30c1\u30a7\u30d3\u30b7\u30a7\u30d5\u306e\u5b9a\u7406\u8a08\u7b97\u30c4\u30fc\u30eb\u3092\u898b\u3064\u3051\u308b\u3053\u3068\u304c\u3067\u304d\u307e\u3059\u3002\u6700\u5f8c\u306b\u3001\u30c1\u30a7\u30d3\u30b7\u30a7\u30d5\u306e\u5b9a\u7406\u3068\u7d4c\u9a13\u5247\u306e\u9055\u3044\u3092\u793a\u3057\u307e\u3059\u3002 <\/p>\n<h2 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"%c2%bfque-es-el-teorema-de-chebyshev\"><\/span>\u30c1\u30a7\u30d3\u30b7\u30a7\u30d5\u306e\u5b9a\u7406\u3068\u306f\u4f55\u3067\u3059\u304b?<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p><strong>\u30c1\u30a7\u30d3\u30b7\u30a7\u30d5\u306e\u5b9a\u7406 \u306f<\/strong>\u3001<strong>\u30c1\u30a7\u30d3\u30b7\u30a7\u30d5\u306e\u4e0d\u7b49\u5f0f<\/strong>\u3068\u3057\u3066\u3082\u77e5\u3089\u308c\u3001\u78ba\u7387\u5909\u6570\u306e\u5024\u304c\u5e73\u5747\u304b\u3089\u4e00\u5b9a\u306e\u8ddd\u96e2\u5185\u306b\u3042\u308b\u78ba\u7387\u3092\u8a08\u7b97\u3059\u308b\u305f\u3081\u306b\u4f7f\u7528\u3055\u308c\u308b\u7d71\u8a08\u898f\u5247\u3067\u3059\u3002<\/p>\n<p>\u8a00\u3044\u63db\u3048\u308c\u3070\u3001\u7d71\u8a08\u5b66\u3067\u306f\u3001\u5024\u304c\u4fe1\u983c\u533a\u9593\u5185\u306b\u3042\u308b\u78ba\u7387\u3092\u6c7a\u5b9a\u3059\u308b\u305f\u3081\u306b\u30c1\u30a7\u30d3\u30b7\u30a7\u30d5\u306e\u5b9a\u7406\u304c\u4f7f\u7528\u3055\u308c\u307e\u3059\u3002<\/p>\n<p>\u3055\u3089\u306b\u3001\u30c1\u30a7\u30d3\u30b7\u30a7\u30d5\u306e\u5b9a\u7406\u306f\u3001\u5927\u6570\u306e\u6cd5\u5247\u306a\u3069\u306e\u4ed6\u306e\u7d71\u8a08\u5b9a\u7406\u3092\u8a3c\u660e\u3059\u308b\u305f\u3081\u306b\u3082\u4f7f\u7528\u3055\u308c\u307e\u3059\u3002<\/p>\n<p>\u30c1\u30a7\u30d3\u30b7\u30a7\u30d5\u306e\u5b9a\u7406\u306f\u30d5\u30e9\u30f3\u30b9\u4eba\u306e\u30a4\u30ec\u30cd\u30fc\uff1d\u30b8\u30e5\u30fc\u30eb\u30fb\u30d3\u30cd\u30e1\u306b\u3088\u3063\u3066\u6700\u521d\u306b\u5b9a\u5f0f\u5316\u3055\u308c\u307e\u3057\u305f\u304c\u3001\u3053\u306e\u5b9a\u7406\u306f 1867 \u5e74\u306b\u30ed\u30b7\u30a2\u306e\u30d1\u30d5\u30cc\u30c6\u30a3\u30fb\u30c1\u30a7\u30d6\u30b7\u30a7\u30d5\u306b\u3088\u3063\u3066\u8003\u6848\u3055\u308c\u305f\u305f\u3081\u3001\u3053\u306e\u3088\u3046\u306b\u540d\u4ed8\u3051\u3089\u308c\u307e\u3057\u305f\u3002<\/p>\n<h2 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"formula-del-teorema-de-chebyshev\"><\/span>\u30c1\u30a7\u30d3\u30b7\u30a7\u30d5\u306e\u5b9a\u7406\u306e\u516c\u5f0f<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p>\u30c1\u30a7\u30d3\u30b7\u30a7\u30d5\u306e\u5b9a\u7406\u306f\u3001\u5024\u304c\u5e73\u5747\u304b\u3089<em>k \u6a19\u6e96\u504f\u5dee\u306b<\/em>\u7b49\u3057\u3044\u78ba\u7387\u306f\u30011 \u304b\u3089 1 \u3092<em>k<\/em>\u306e 2 \u4e57\u3067\u5272\u3063\u305f\u6bd4\u7387\u3092\u5f15\u3044\u305f\u5024\u4ee5\u4e0a\u3067\u3042\u308b\u3068\u8ff0\u3079\u3066\u3044\u307e\u3059\u3002<\/p>\n<p>\u3057\u305f\u304c\u3063\u3066\u3001<strong>\u30c1\u30a7\u30d3\u30b7\u30a7\u30d5\u306e\u5b9a\u7406\u306e\u516c\u5f0f\u306f<\/strong>\u6b21\u306e\u3088\u3046\u306b\u306a\u308a\u307e\u3059\u3002<\/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-f13ff7c0d76ea2442ecd978dbfc457a4_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle P(\\mu-k\\sigma\\leq X \\leq \\mu+k\\sigma)\\geq 1 -\\frac{1}{k^2}\" title=\"Rendered by QuickLaTeX.com\" height=\"36\" width=\"271\" style=\"vertical-align: -12px;\"><\/p>\n<\/p>\n<p>\u91d1<\/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-996ff7036e644e89f8ac379fa58d0cf7_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"X\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"16\" style=\"vertical-align: 0px;\"><\/p>\n<p>\u306f\u78ba\u7387\u5909\u6570\u306e\u5024\u3067\u3059\u3002<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/statorials.org\/wp-content\/ql-cache\/quicklatex.com-05d9eae892416bd34247a25207f8b718_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\mu\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"11\" style=\"vertical-align: -4px;\"><\/p>\n<p>\u5909\u6570\u306e<a href=\"https:\/\/statorials.org\/ja\/\u7b97\u8853\u5e73\u5747\/\">\u7b97\u8853\u5e73\u5747<\/a>\u3001<\/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>\u305d\u306e<a href=\"https:\/\/statorials.org\/ja\/\u6a19\u6e96\u504f\u5dee\u307e\u305f\u306f\u6a19\u6e96\u504f\u5dee\/\">\u6a19\u6e96\u504f\u5dee<\/a>\u3068<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/statorials.org\/wp-content\/ql-cache\/quicklatex.com-d42bc2203d6f76ad01b27ac9acc0bee1_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"k\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"9\" style=\"vertical-align: 0px;\"><\/p>\n<p>\u78ba\u7387\u304c\u8a08\u7b97\u3055\u308c\u308b\u5e73\u5747\u304b\u3089\u306e\u6a19\u6e96\u504f\u5dee\u306e\u6570\u3002<\/p>\n<p>\u3053\u306e\u5f0f\u306f\u3001\u8a08\u7b97\u304c\u5b9f\u884c\u3055\u308c\u308b\u6a19\u6e96\u504f\u5dee\u306e\u6570\u304c 1 \u3088\u308a\u5927\u304d\u3044\u5834\u5408\u3001\u3064\u307e\u308a<em>k<\/em>\u304c 1 \u3088\u308a\u5927\u304d\u3044\u5834\u5408\u306b\u306e\u307f\u4f7f\u7528\u3067\u304d\u308b\u3053\u3068\u306b\u6ce8\u610f\u3057\u3066\u304f\u3060\u3055\u3044\u3002<\/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-76b1d6dbe5ee35b66ff33156e238ad73_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"k>1&#8243; title=&#8221;Rendered by QuickLaTeX.com&#8221; height=&#8221;14&#8243; width=&#8221;41&#8243; style=&#8221;vertical-align: -2px;&#8221;><\/p>\n<\/p>\n<p> \ud83d\udc49<u style=\"text-decoration-color:#FF8A05;\">\u4ee5\u4e0b\u306e\u30aa\u30f3\u30e9\u30a4\u30f3\u306e\u30c1\u30a7\u30d3\u30b7\u30a7\u30d5\u306e\u5b9a\u7406\u8a08\u7b97\u30c4\u30fc\u30eb\u3092\u4f7f\u7528\u3057\u3066\u78ba\u7387\u3092\u8a08\u7b97\u3067\u304d\u307e\u3059\u3002<\/u><\/p>\n<h2 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"ejemplo-del-teorema-de-chebyshev\"><\/span>\u30c1\u30a7\u30d3\u30b7\u30a7\u30d5\u306e\u5b9a\u7406\u306e\u4f8b<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p>\u30c1\u30a7\u30d3\u30b7\u30a7\u30d5\u306e\u5b9a\u7406\u306e\u5b9a\u7fa9\u3068\u305d\u306e\u516c\u5f0f\u304c\u4f55\u3067\u3042\u308b\u304b\u3092\u7406\u89e3\u3057\u305f\u3089\u3001\u6982\u5ff5\u3092\u3088\u308a\u3088\u304f\u7406\u89e3\u3059\u308b\u305f\u3081\u306b\u3053\u306e\u7d71\u8a08\u5b9a\u7406\u306e\u89e3\u6c7a\u4f8b\u3092\u793a\u3057\u307e\u3059\u3002<\/p>\n<ul>\n<li>\u5927\u5b66\u306e\u30b3\u30fc\u30b9\u7d71\u8a08\u3067\u7372\u5f97\u3057\u305f\u6210\u7e3e\u304c\u5e73\u5747 65\u3001\u6a19\u6e96\u504f\u5dee 10 \u306e\u5206\u5e03\u3067\u5b9a\u7fa9\u3055\u308c\u3066\u3044\u308b\u5834\u5408\u300150 \uff5e 80 \u306e\u6210\u7e3e\u3092\u7372\u5f97\u3057\u305f\u5b66\u751f\u306e\u5272\u5408\u306f\u4f55\u30d1\u30fc\u30bb\u30f3\u30c8\u3067\u3057\u3087\u3046\u304b?<\/li>\n<\/ul>\n<p>\u3053\u306e\u554f\u984c\u3092\u89e3\u6c7a\u3059\u308b\u306b\u306f\u3001\u30c1\u30a7\u30d3\u30b7\u30a7\u30d5\u306e\u5b9a\u7406\u306e\u516c\u5f0f\u3092\u9069\u7528\u3059\u308b\u5fc5\u8981\u304c\u3042\u308a\u307e\u3059\u3002\u305f\u3060\u3057\u3001\u5024 50 \u3068 80 \u304c\u5909\u6570\u306e\u5e73\u5747\u304b\u3089\u3069\u308c\u3060\u3051\u306e\u6a19\u6e96\u504f\u5dee\u304c\u3042\u308b\u304b\u3092\u6700\u521d\u306b\u6c7a\u5b9a\u3059\u308b\u5fc5\u8981\u304c\u3042\u308a\u307e\u3059\u3002\u3053\u308c\u3092\u884c\u3046\u306b\u306f\u3001\u6b21\u306e\u8a08\u7b97\u3092\u884c\u3046\u3060\u3051\u3067\u3059\u3002 <\/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-23a555d6493c0a0be742097fe319932d_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"k=\\cfrac{\\text{valor}-\\text{media}}{\\text{desviaci\\'on t\\'ipica}}\" title=\"Rendered by QuickLaTeX.com\" height=\"42\" width=\"165\" 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-edee4613c11e3eebd7e1158ad7f7b5c4_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"k=\\cfrac{50-65}{10}=-1,5\" title=\"Rendered by QuickLaTeX.com\" height=\"39\" width=\"155\" 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-7668ffc75752b84a5fdfe4de807efe0d_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"k=\\cfrac{80-65}{10}=1,5\" title=\"Rendered by QuickLaTeX.com\" height=\"39\" width=\"141\" style=\"vertical-align: -12px;\"><\/p>\n<\/p>\n<p>\u3057\u305f\u304c\u3063\u3066\u3001\u5024 50 \u3068 80 \u306f\u3001\u305d\u308c\u305e\u308c\u4e0b\u4f4d\u5e73\u5747\u3068\u4e0a\u4f4d\u5e73\u5747\u304b\u3089\u306e 1.5 \u6a19\u6e96\u504f\u5dee\u306b\u5bfe\u5fdc\u3057\u307e\u3059\u3002\u3057\u305f\u304c\u3063\u3066\u3001k=1.5 \u306e\u30c1\u30a7\u30d3\u30b7\u30a7\u30d0\u306e\u5b9a\u7406\u306e\u5f0f\u3092\u4f7f\u7528\u3057\u307e\u3059\u3002 <\/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-6dede501857215fec033905b64a01431_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle P(\\mu-k\\sigma\\leq X \\leq \\mu+k\\sigma)\\leq 1 -\\frac{1}{k^2}\" title=\"Rendered by QuickLaTeX.com\" height=\"36\" width=\"271\" 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-ace95ab1310d82dc6a6275b123556c07_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle P(\\mu-1,5\\sigma\\leq X \\leq \\mu+1,5\\sigma)\\leq 1 -\\frac{1}{1,5^2}\" title=\"Rendered by QuickLaTeX.com\" height=\"40\" width=\"319\" 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-aa011250591257ffebf651292398d016_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle P(50\\leq X \\leq 80)\\leq 0,5556\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"203\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<p>\u3057\u305f\u304c\u3063\u3066\u3001\u5c11\u306a\u304f\u3068\u3082 55.56% \u306e\u5b66\u751f\u304c 50 \u304b\u3089 80 \u306e\u9593\u306e\u6210\u7e3e\u3092\u7372\u5f97\u3057\u307e\u3057\u305f\u3002 <\/p>\n<h2 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"calculadora-del-teorema-de-chebyshev\"><\/span>\u30c1\u30a7\u30d3\u30b7\u30a7\u30d5\u306e\u5b9a\u7406\u8a08\u7b97\u6a5f<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p>\u554f\u984c\u306e\u5024\u3068\u5e73\u5747\u5024\u306e\u9593\u306e\u6a19\u6e96\u504f\u5dee\u306e\u6570<em>(k)<\/em>\u3092\u5165\u529b\u3057\u3001\u300c\u8a08\u7b97\u300d\u3092\u30af\u30ea\u30c3\u30af\u3057\u307e\u3059\u3002\u8a08\u7b97\u6a5f\u306f\u4fe1\u983c\u533a\u9593\u306e\u6700\u5c0f\u78ba\u7387\u3092\u8fd4\u3057\u307e\u3059\u3002<\/p>\n<p>\u6a19\u6e96\u504f\u5dee\u306e\u6570\u306f\u3001\u5c0f\u6570\u70b9\u533a\u5207\u308a\u6587\u5b57\u3068\u3057\u3066\u30c9\u30c3\u30c8\u3092\u4f7f\u7528\u3057\u3066\u5165\u529b\u3059\u308b\u5fc5\u8981\u304c\u3042\u308a\u307e\u3059\u3002 <\/p>\n<form action=\"\" method=\"post\">\n<ul style=\"color:#1C2C92;\">\n<li style=\"margin-bottom:15px\"><span style=\"color:#101010;font-weight: normal;\">\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/statorials.org\/wp-content\/ql-cache\/quicklatex.com-f4c08f6419fa469da3aa1c832f5c6b2b_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"k = \" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"28\" style=\"vertical-align: 0px;\"><\/p>\n<p><input name=\"datos\" style=\"border:1.5px solid #1C2C92; border-radius:5px;  padding:7px; color:#000000; background-color:#EBF5FB; width:60px\" placeholder=\"1.5\" required=\"\" oninvalid=\"this.setCustomValidity('Introduce el n\u00famero total de datos aqu\u00ed')\" oninput=\"this.setCustomValidity('')\"><\/span><\/li>\n<\/ul>\n<div style=\"text-align:center\"><input align=\"center\" style=\"font-size:105%; border-radius:30px; margin: 20px\" type=\"submit\" name=\"submit\" value=\"\u8a08\u7b97\u3059\u308b\"><\/div>\n<\/form>\n<h2 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"el-teorema-de-chebyshev-y-la-regla-empirica\"><\/span>\u30c1\u30a7\u30d3\u30b7\u30a7\u30d5\u306e\u5b9a\u7406\u3068\u7d4c\u9a13\u5247<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p>\u7d71\u8a08\u5b66\u306b\u304a\u3051\u308b 2 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