{"id":6171,"date":"2024-06-26T16:09:56","date_gmt":"2024-06-26T08:09:56","guid":{"rendered":"https:\/\/t.n-years.com\/?p=6171"},"modified":"2024-06-26T16:09:58","modified_gmt":"2024-06-26T08:09:58","slug":"%e7%bb%9f%e8%ae%a1%e5%ad%a6%ef%bc%9a%e6%a0%87%e5%87%86%e5%b7%ae%e5%92%8c%e6%96%b9%e5%b7%ae","status":"publish","type":"post","link":"https:\/\/t.n-years.com\/?p=6171","title":{"rendered":"\u7edf\u8ba1\u5b66\uff1a\u6807\u51c6\u5dee\u548c\u65b9\u5dee"},"content":{"rendered":"\n<p class=\"wp-block-paragraph\">\u975e\u539f\u521b\uff0cChatGPT \u751f\u6210\u3002\u6bd5\u4e1a\u592a\u4e45\uff0c\u57fa\u672c\u6982\u5ff5\u90fd\u5fd8\u4e86\u3002<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">\u65b9\u5dee\uff08Variance\uff09\u548c\u6807\u51c6\u5dee\uff08Standard Deviation\uff09\u662f\u7edf\u8ba1\u5b66\u4e2d\u7528\u6765\u8861\u91cf\u6570\u636e\u5206\u6563\u7a0b\u5ea6\u7684\u4e24\u4e2a\u6307\u6807\u3002\u5b83\u4eec\u4e4b\u95f4\u6709\u5bc6\u5207\u7684\u8054\u7cfb\uff0c\u4f46\u8ba1\u7b97\u65b9\u5f0f\u6709\u6240\u4e0d\u540c\u3002\u5177\u4f53\u6765\u8bf4\uff1a<\/p>\n\n\n\n<h3 class=\"wp-block-heading\">\u65b9\u5dee<\/h3>\n\n\n\n<p class=\"wp-block-paragraph\">\u65b9\u5dee\u662f\u6307\u6570\u636e\u4e0e\u5176\u5747\u503c\u4e4b\u95f4\u7684\u5e73\u5747\u5e73\u65b9\u5dee\u3002\u8ba1\u7b97\u516c\u5f0f\u5982\u4e0b\uff1a<\/p>\n\n\n\n<ol class=\"wp-block-list\">\n<li><strong>\u6837\u672c\u65b9\u5dee\uff08Sample Variance\uff09<\/strong>\uff1a<br>[<br>s^2 = \\frac{1}{n-1} \\sum_{i=1}^{n} (x_i - \\bar{x})^2<br>]<br>\u5176\u4e2d\uff1a<\/li>\n<\/ol>\n\n\n\n<ul class=\"wp-block-list\">\n<li>( n ) \u662f\u6837\u672c\u7684\u6570\u91cf\u3002<\/li>\n\n\n\n<li>( x_i ) \u662f\u7b2c ( i ) \u4e2a\u6837\u672c\u6570\u636e\u3002<\/li>\n\n\n\n<li>( \\bar{x} ) \u662f\u6837\u672c\u6570\u636e\u7684\u5747\u503c\u3002<\/li>\n<\/ul>\n\n\n\n<ol class=\"wp-block-list\">\n<li><strong>\u603b\u4f53\u65b9\u5dee\uff08Population Variance\uff09<\/strong>\uff1a<br>[<br>\\sigma^2 = \\frac{1}{N} \\sum_{i=1}^{N} (x_i - \\mu)^2<br>]<br>\u5176\u4e2d\uff1a<\/li>\n<\/ol>\n\n\n\n<ul class=\"wp-block-list\">\n<li>( N ) \u662f\u603b\u4f53\u7684\u6570\u91cf\u3002<\/li>\n\n\n\n<li>( x_i ) \u662f\u7b2c ( i ) \u4e2a\u603b\u4f53\u6570\u636e\u3002<\/li>\n\n\n\n<li>( \\mu ) \u662f\u603b\u4f53\u6570\u636e\u7684\u5747\u503c\u3002<\/li>\n<\/ul>\n\n\n\n<h3 class=\"wp-block-heading\">\u6807\u51c6\u5dee<\/h3>\n\n\n\n<p class=\"wp-block-paragraph\">\u6807\u51c6\u5dee\u662f\u65b9\u5dee\u7684\u5e73\u65b9\u6839\uff0c\u8868\u793a\u6570\u636e\u4e0e\u5747\u503c\u7684\u5e73\u5747\u8ddd\u79bb\u3002\u8ba1\u7b97\u516c\u5f0f\u5982\u4e0b\uff1a<\/p>\n\n\n\n<ol class=\"wp-block-list\">\n<li><strong>\u6837\u672c\u6807\u51c6\u5dee\uff08Sample Standard Deviation\uff09<\/strong>\uff1a<br>[<br>s = \\sqrt{\\frac{1}{n-1} \\sum_{i=1}^{n} (x_i - \\bar{x})^2}<br>]<\/li>\n\n\n\n<li><strong>\u603b\u4f53\u6807\u51c6\u5dee\uff08Population Standard Deviation\uff09<\/strong>\uff1a<br>[<br>\\sigma = \\sqrt{\\frac{1}{N} \\sum_{i=1}^{N} (x_i - \\mu)^2}<br>]<\/li>\n<\/ol>\n\n\n\n<h3 class=\"wp-block-heading\">\u533a\u522b<\/h3>\n\n\n\n<ol class=\"wp-block-list\">\n<li><strong>\u8ba1\u7b97\u65b9\u5f0f<\/strong>\uff1a<\/li>\n<\/ol>\n\n\n\n<ul class=\"wp-block-list\">\n<li>\u65b9\u5dee\u662f\u6570\u636e\u4e0e\u5747\u503c\u4e4b\u95f4\u5dee\u503c\u7684\u5e73\u65b9\u7684\u5e73\u5747\u503c\uff08\u6837\u672c\u65b9\u5dee\u7684\u5206\u6bcd\u4e3a ( n-1 )\uff0c\u603b\u4f53\u65b9\u5dee\u7684\u5206\u6bcd\u4e3a ( N )\uff09\u3002<\/li>\n\n\n\n<li>\u6807\u51c6\u5dee\u662f\u65b9\u5dee\u7684\u5e73\u65b9\u6839\u3002<\/li>\n<\/ul>\n\n\n\n<ol class=\"wp-block-list\">\n<li><strong>\u5355\u4f4d<\/strong>\uff1a<\/li>\n<\/ol>\n\n\n\n<ul class=\"wp-block-list\">\n<li>\u65b9\u5dee\u7684\u5355\u4f4d\u662f\u539f\u59cb\u6570\u636e\u5355\u4f4d\u7684\u5e73\u65b9\u3002<\/li>\n\n\n\n<li>\u6807\u51c6\u5dee\u7684\u5355\u4f4d\u4e0e\u539f\u59cb\u6570\u636e\u7684\u5355\u4f4d\u76f8\u540c\uff0c\u56e0\u800c\u66f4\u76f4\u89c2\u5730\u8868\u793a\u6570\u636e\u7684\u5206\u6563\u7a0b\u5ea6\u3002<\/li>\n<\/ul>\n\n\n\n<h3 class=\"wp-block-heading\">\u8ba1\u7b97\u793a\u4f8b<\/h3>\n\n\n\n<p class=\"wp-block-paragraph\">\u5047\u8bbe\u6709\u5982\u4e0b\u6570\u636e\u96c6\uff1a[1, 2, 3, 4, 5]<\/p>\n\n\n\n<h4 class=\"wp-block-heading\">\u8ba1\u7b97\u5747\u503c\uff1a<\/h4>\n\n\n\n<p class=\"wp-block-paragraph\">[<br>\\bar{x} = \\frac{1+2+3+4+5}{5} = 3<br>]<\/p>\n\n\n\n<h4 class=\"wp-block-heading\">\u8ba1\u7b97\u65b9\u5dee\uff08\u603b\u4f53\uff09\uff1a<\/h4>\n\n\n\n<p class=\"wp-block-paragraph\">[<br>\\sigma^2 = \\frac{(1-3)^2 + (2-3)^2 + (3-3)^2 + (4-3)^2 + (5-3)^2}{5} = \\frac{4+1+0+1+4}{5} = 2<br>]<\/p>\n\n\n\n<h4 class=\"wp-block-heading\">\u8ba1\u7b97\u6807\u51c6\u5dee\uff08\u603b\u4f53\uff09\uff1a<\/h4>\n\n\n\n<p class=\"wp-block-paragraph\">[<br>\\sigma = \\sqrt{2} \\approx 1.41<br>]<\/p>\n\n\n\n<h4 class=\"wp-block-heading\">\u8ba1\u7b97\u65b9\u5dee\uff08\u6837\u672c\uff09\uff1a<\/h4>\n\n\n\n<p class=\"wp-block-paragraph\">[<br>s^2 = \\frac{(1-3)^2 + (2-3)^2 + (3-3)^2 + (4-3)^2 + (5-3)^2}{5-1} = \\frac{4+1+0+1+4}{4} = 2.5<br>]<\/p>\n\n\n\n<h4 class=\"wp-block-heading\">\u8ba1\u7b97\u6807\u51c6\u5dee\uff08\u6837\u672c\uff09\uff1a<\/h4>\n\n\n\n<p class=\"wp-block-paragraph\">[<br>s = \\sqrt{2.5} \\approx 1.58<br>]<\/p>\n\n\n\n<h3 class=\"wp-block-heading\">\u603b\u7ed3<\/h3>\n\n\n\n<ul class=\"wp-block-list\">\n<li>\u65b9\u5dee\u548c\u6807\u51c6\u5dee\u90fd\u662f\u8861\u91cf\u6570\u636e\u5206\u6563\u7a0b\u5ea6\u7684\u6307\u6807\u3002<\/li>\n\n\n\n<li>\u6807\u51c6\u5dee\u662f\u65b9\u5dee\u7684\u5e73\u65b9\u6839\uff0c\u5177\u6709\u4e0e\u539f\u59cb\u6570\u636e\u76f8\u540c\u7684\u5355\u4f4d\uff0c\u56e0\u800c\u66f4\u76f4\u89c2\u3002<\/li>\n\n\n\n<li>\u6837\u672c\u65b9\u5dee\u548c\u6807\u51c6\u5dee\u7684\u8ba1\u7b97\u4f7f\u7528\u4e86 ( n-1 ) \u800c\u4e0d\u662f ( n )\uff0c\u4ee5\u7ea0\u6b63\u6837\u672c\u6570\u636e\u7684\u504f\u5dee\u3002<\/li>\n<\/ul>\n","protected":false},"excerpt":{"rendered":"<p>\u975e\u539f\u521b\uff0cChatGPT \u751f\u6210\u3002\u6bd5\u4e1a\u592a\u4e45\uff0c\u57fa\u672c\u6982\u5ff5\u90fd\u5fd8\u4e86\u3002 \u65b9\u5dee\uff08Variance\uff09\u548c\u6807\u51c6\u5dee\uff08Standard &#8230; <\/p>\n<div class=\"read-more navbutton\"><a href=\"https:\/\/t.n-years.com\/?p=6171\">\u9605\u8bfb\u66f4\u591a<i class=\"fa fa-angle-double-right\"><\/i><\/a><\/div>\n","protected":false},"author":1,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[5],"tags":[],"class_list":["post-6171","post","type-post","status-publish","format-standard","hentry","category-5"],"_links":{"self":[{"href":"https:\/\/t.n-years.com\/index.php?rest_route=\/wp\/v2\/posts\/6171","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/t.n-years.com\/index.php?rest_route=\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/t.n-years.com\/index.php?rest_route=\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/t.n-years.com\/index.php?rest_route=\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/t.n-years.com\/index.php?rest_route=%2Fwp%2Fv2%2Fcomments&post=6171"}],"version-history":[{"count":1,"href":"https:\/\/t.n-years.com\/index.php?rest_route=\/wp\/v2\/posts\/6171\/revisions"}],"predecessor-version":[{"id":6172,"href":"https:\/\/t.n-years.com\/index.php?rest_route=\/wp\/v2\/posts\/6171\/revisions\/6172"}],"wp:attachment":[{"href":"https:\/\/t.n-years.com\/index.php?rest_route=%2Fwp%2Fv2%2Fmedia&parent=6171"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/t.n-years.com\/index.php?rest_route=%2Fwp%2Fv2%2Fcategories&post=6171"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/t.n-years.com\/index.php?rest_route=%2Fwp%2Fv2%2Ftags&post=6171"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}