{"id":1600,"date":"2026-10-30T14:00:00","date_gmt":"2026-10-30T05:00:00","guid":{"rendered":"https:\/\/quantumsea.net\/?p=1600"},"modified":"2026-10-27T14:30:33","modified_gmt":"2026-10-27T05:30:33","slug":"qs-welford-online-variance-20261025","status":"publish","type":"post","link":"https:\/\/quantumsea.net\/?p=1600","title":{"rendered":"Welford\u6cd5\u3001\u6e2c\u5b9a\u5024\u3092\u305f\u3081\u8fbc\u307e\u305a\u306b\u5c0f\u3055\u306a\u3070\u3089\u3064\u304d\u3092\u8a08\u7b97\u3059\u308b"},"content":{"rendered":"<p>\u30bb\u30f3\u30b5\u30fc\u304b\u3089\u6e2c\u5b9a\u5024\u304c\u4e00\u3064\u305a\u3064\u5c4a\u304f\u3068\u304d\u3001\u77e5\u308a\u305f\u3044\u306e\u306f\u5e73\u5747\u3060\u3051\u3068\u306f\u9650\u308a\u307e\u305b\u3093\u3002\u5024\u304c\u3069\u308c\u304f\u3089\u3044\u63fa\u308c\u3066\u3044\u308b\u304b\u3082\u3001\u305d\u306e\u5834\u3067\u8ffd\u3044\u305f\u304f\u306a\u308a\u307e\u3059\u3002\u904e\u53bb\u306e\u6e2c\u5b9a\u5024\u3092\u3059\u3079\u3066\u4fdd\u5b58\u3057\u3066\u6bce\u56de\u8a08\u7b97\u3057\u76f4\u3059\u4ee3\u308f\u308a\u306b\u3001\u4ef6\u6570\u30fb\u5e73\u5747\u30fb\u3070\u3089\u3064\u304d\u306e\u96c6\u8a08\u5024\u3092\u66f4\u65b0\u3057\u3066\u3044\u304f\u65b9\u6cd5\u304c<strong>Welford\u6cd5<\/strong>\u3067\u3059\u3002\u5927\u304d\u306a\u5024\u306e\u307e\u308f\u308a\u306b\u3042\u308b\u5c0f\u3055\u306a\u5909\u5316\u3092\u8a08\u7b97\u3059\u308b\u3068\u304d\u306b\u3082\u3001\u3053\u306e\u66f4\u65b0\u306e\u4ed5\u65b9\u304c\u5f79\u7acb\u3061\u307e\u3059\u3002<\/p>\n<section class=\"influvetor-quick-summary\">\n<p><strong>\u7c21\u5358\u306b\u307e\u3068\u3081\u308b\u3068\uff1f<\/strong><\/p>\n<ul>\n<li>Welford\u6cd5\u306f\u3001\u65b0\u3057\u3044\u5024\u3068\u73fe\u5728\u306e\u5e73\u5747\u3068\u306e\u5dee\u3092\u4f7f\u3044\u3001\u4ef6\u6570\u30fb\u5e73\u5747\u30fb\u504f\u5dee\u5e73\u65b9\u548c\u3092\u4e00\u3064\u305a\u3064\u66f4\u65b0\u3057\u307e\u3059\u3002<\/li>\n<li>\u300c\u4e8c\u4e57\u306e\u5408\u8a08\u300d\u304b\u3089\u5927\u304d\u306a\u6570\u3092\u5f15\u304f\u5f0f\u306f\u3001\u6570\u5b66\u7684\u306b\u306f\u6b63\u3057\u304f\u3066\u3082\u4e38\u3081\u8aa4\u5dee\u3067\u5206\u6563\u3092\u5931\u3046\u3053\u3068\u304c\u3042\u308a\u307e\u3059\u3002<\/li>\n<li>\u96c6\u3081\u305f\u30c7\u30fc\u30bf\u81ea\u4f53\u306e\u5206\u6563\u306a\u3089\u4ef6\u6570\u3067\u5272\u308a\u3001\u6bcd\u96c6\u56e3\u306e\u5206\u6563\u3092\u4e0d\u504f\u63a8\u5b9a\u3059\u308b\u306a\u3089\u3001\u6761\u4ef6\u3092\u6e80\u305f\u3059\u6a19\u672c\u306b\u3064\u3044\u3066\u4ef6\u6570\u304b\u30891\u3092\u5f15\u3044\u305f\u6570\u3067\u5272\u308a\u307e\u3059\u3002<\/li>\n<\/ul>\n<\/section>\n<h2>\u5e73\u5747\u306e\u8fd1\u304f\u306b\u3042\u308b\u3001\u308f\u305a\u304b\u306a\u9055\u3044\u3092\u6e2c\u308b<\/h2>\n<p>\u5206\u6563\u306f\u3001\u5024\u304c\u5e73\u5747\u304b\u3089\u3069\u308c\u3060\u3051\u96e2\u308c\u3066\u3044\u308b\u304b\u3092\u8868\u3059\u91cf\u3067\u3059\u3002\u305d\u308c\u305e\u308c\u306e\u5024\u304b\u3089\u5e73\u5747\u3092\u5f15\u304d\u3001\u305d\u306e\u5dee\u3092\u4e8c\u4e57\u3057\u3066\u8db3\u3057\u305f\u3082\u306e\u3092<strong>\u504f\u5dee\u5e73\u65b9\u548c<\/strong>\u3068\u547c\u3073\u307e\u3059\u3002\u3053\u3053\u3067\u306f\u3001\u3053\u306e\u5408\u8a08\u3092 <em>M2<\/em> \u3068\u66f8\u304d\u307e\u3059\u3002\u6e2c\u5b9a\u5024\u306e\u5358\u4f4d\u304c\u79d2\u306a\u3089\u3001M2\u3084\u5206\u6563\u306e\u5358\u4f4d\u306f\u79d2\u306e\u4e8c\u4e57\u3067\u3059\u3002\u5e73\u65b9\u6839\u3092\u53d6\u3063\u305f\u6a19\u6e96\u504f\u5dee\u306f\u3001\u5143\u3068\u540c\u3058\u79d2\u3067\u8aad\u3081\u307e\u3059\u3002<\/p>\n<p>\u305f\u3068\u3048\u3070\u3001\u8aac\u660e\u7528\u306e3\u70b9\u3092 100000001\u3001100000002\u3001100000003 \u3068\u3057\u307e\u3059\u3002\u5e73\u5747\u306f 100000002 \u3067\u3001\u5e73\u5747\u3068\u306e\u5dee\u306f \u22121\u30010\u30011\u3002\u3057\u305f\u304c\u3063\u3066 M2 \u306f 1\uff0b0\uff0b1\uff1d2 \u3067\u3059\u3002\u5168\u4f53\u306b\u5927\u304d\u306a\u4e00\u5b9a\u5024\u304c\u52a0\u308f\u3063\u3066\u3044\u3066\u3082\u3001\u3053\u306e3\u70b9\u306e\u9593\u306e\u5e83\u304c\u308a\u306f\u5909\u308f\u308a\u307e\u305b\u3093\u3002<\/p>\n<p>\u3053\u306e3\u70b9\u305d\u306e\u3082\u306e\u306e\u5206\u6563\u306f M2\/3\uff1d2\/3 \u3067\u3059\u3002\u4e00\u65b9\u3001\u72ec\u7acb\u306b\u540c\u3058\u5206\u5e03\u304b\u3089\u5f97\u305f\u6a19\u672c\u3092\u4f7f\u3063\u3066\u3001\u6709\u9650\u306a\u6bcd\u5206\u6563\u3092\u4e0d\u504f\u63a8\u5b9a\u3059\u308b\u5834\u5408\u306f M2\/(3\u22121)\uff1d1 \u3092\u4f7f\u3044\u307e\u3059\u3002\u300c\u5206\u6563\u304c2\/3\u304b1\u304b\u300d\u3068\u3044\u3046\u9055\u3044\u306f\u3001\u3053\u3053\u3067\u306f\u8a08\u7b97\u306e\u5931\u6557\u3067\u306f\u306a\u304f\u3001\u4f55\u3092\u6c42\u3081\u308b\u304b\u306b\u3088\u308b\u5206\u6bcd\u306e\u9055\u3044\u3067\u3059\u3002<\/p>\n<h2>\u540c\u3058\u5f0f\u306e\u306f\u305a\u306a\u306e\u306b\u3001\u7b54\u3048\u304c0\u306b\u306a\u308b<\/h2>\n<p>M2\u306f\u3001\u5404\u5024\u306e\u4e8c\u4e57\u3092\u8db3\u3057\u305f\u5f8c\u3001\u300c\u5024\u306e\u5408\u8a08\u306e\u4e8c\u4e57\u3092\u4ef6\u6570\u3067\u5272\u3063\u305f\u3082\u306e\u300d\u3092\u5f15\u3044\u3066\u3082\u6c42\u3081\u3089\u308c\u307e\u3059\u3002<\/p>\n<p><code style=\"white-space:normal;overflow-wrap:anywhere\">M2 = \u03a3x\u00b2 \u2212 (\u03a3x)\u00b2\/n<\/code><\/p>\n<p>\u3053\u306e\u5f62\u306a\u3089\u5408\u8a08\u3068\u4e8c\u4e57\u306e\u5408\u8a08\u3092\u899a\u3048\u3066\u304a\u304f\u3060\u3051\u3067\u6e08\u307f\u307e\u3059\u3002\u305f\u3060\u3057\u3001\u4f8b\u306e\u3088\u3046\u306b\u5e73\u5747\u304c\u5927\u304d\u304f\u3001\u3070\u3089\u3064\u304d\u304c\u5c0f\u3055\u3044\u30c7\u30fc\u30bf\u3067\u306f\u3001\u4e8c\u3064\u306e\u5927\u304d\u306a\u6570\u3092\u5f15\u3044\u3066\u5c0f\u3055\u306a\u5dee\u3092\u53d6\u308a\u51fa\u3059\u8a08\u7b97\u306b\u306a\u308a\u307e\u3059\u3002\u30b3\u30f3\u30d4\u30e5\u30fc\u30bf\u30fc\u304c\u9014\u4e2d\u306e\u5024\u3092\u6709\u9650\u306e\u6841\u6570\u3078\u4e38\u3081\u308b\u3068\u3001\u6b8b\u3057\u305f\u3044\u5dee\u306b\u5bfe\u3057\u3066\u8aa4\u5dee\u304c\u5927\u304d\u304f\u306a\u308b\u3053\u3068\u304c\u3042\u308a\u307e\u3059\u3002Chan\u30fbGolub\u30fbLeVeque\u306e\u8ad6\u6587\u306f\u3001\u3053\u306e\u8a08\u7b97\u65b9\u6cd5\u306e\u554f\u984c\u3068\u4ee3\u308f\u308a\u306e\u65b9\u6cd5\u3092\u6bd4\u8f03\u3057\u3066\u3044\u307e\u3059\u3002<sup class=\"source-note\">[1]<\/sup><\/p>\n<p>\u4e0a\u306e3\u70b9\u3092Python\u306ebinary64\u6d6e\u52d5\u5c0f\u6570\u70b9\u3067\u9806\u306b\u8db3\u3057\u3066\u8a08\u7b97\u3057\u305f\u72ec\u81ea\u4f8b\u3067\u306f\u3001\u3053\u306e\u5f0f\u306eM2\u306f0\u306b\u306a\u308a\u307e\u3057\u305f\u3002\u5165\u529b\u3057\u305f\u6574\u6570\u81ea\u4f53\u306f\u6b63\u78ba\u306b\u8868\u305b\u3066\u3044\u3066\u3082\u3001\u4e8c\u4e57\u3068\u5408\u8a08\u306e\u6bb5\u968e\u3067\u4e38\u3081\u304c\u751f\u3058\u307e\u3059\u3002\u540c\u3058\u30c7\u30fc\u30bf\u3067\u3001\u5e73\u5747\u3068\u306e\u5dee\u3092\u4e8c\u4e57\u3057\u3066\u8db3\u3059\u65b9\u6cd5\u3068Welford\u6cd5\u3067\u306fM2\uff1d2\u304c\u5f97\u3089\u308c\u307e\u3057\u305f\u3002\u3053\u308c\u306f\u3053\u306e\u5165\u529b\u3068\u8a08\u7b97\u9806\u3067\u306e\u7d50\u679c\u3067\u3001\u3042\u3089\u3086\u308b\u30c7\u30fc\u30bf\u3067\u540c\u3058\u8aa4\u5dee\u306b\u306a\u308b\u3068\u3044\u3046\u610f\u5473\u3067\u306f\u3042\u308a\u307e\u305b\u3093\u3002<\/p>\n<figure><img decoding=\"async\" src=\"https:\/\/quantumsea.net\/wp-content\/uploads\/2026\/10\/qs-welford-online-variance-20261025-figure-01373fc1cabe.png\" alt=\"100000001\u3001100000002\u3001100000003\u306e3\u70b9\u3092\u6bd4\u8f03\u3002\u5927\u304d\u306a\u4e8c\u4e57\u548c\u540c\u58eb\u3092\u5f15\u304f\u8a08\u7b97\u3067\u306f\u3001\u3053\u306ebinary64\u5b9f\u884c\u4f8b\u306eM2\u306f0\u3002Welford\u6cd5\u3067\u306f\u3001\u70b9\u3092\u52a0\u3048\u308b\u305f\u3073\u306bM2\u304c0\u30010.5\u30012\u3068\u66f4\u65b0\u3055\u308c\u308b\u3002\" style=\"max-width:100%;height:auto\"><figcaption>\u56f31\u3000\u540c\u30583\u70b9\u3092\u4f7f\u3063\u305f\u72ec\u81ea\u306e\u8a08\u7b97\u4f8b\u3002M2\u306f\u5206\u6563\u306b\u5272\u308a\u7b97\u3059\u308b\u524d\u306e\u504f\u5dee\u5e73\u65b9\u548c\u3067\u3059\u3002\u6b63\u78ba\u306a\u5024\u306f2\u3067\u3001\u5206\u6bcd\u3092n\u22121\u3068\u3059\u308b\u5206\u6563\u306f1\u306b\u306a\u308a\u307e\u3059\u3002<\/figcaption><\/figure>\n<h2>\u65b0\u3057\u3044\u5024\u304c\u6765\u305f\u3089\u3001\u5e73\u5747\u3068\u5e83\u304c\u308a\u3092\u4e00\u7dd2\u306b\u76f4\u3059<\/h2>\n<p>Welford\u6cd5\u3067\u6301\u3061\u7d9a\u3051\u308b\u306e\u306f\u3001\u4ef6\u6570 <em>n<\/em>\u3001\u5e73\u5747 <em>m<\/em>\u3001\u504f\u5dee\u5e73\u65b9\u548c <em>M2<\/em> \u3067\u3059\u3002\u6b21\u306e\u5024 <em>x<\/em> \u3092\u53d7\u3051\u53d6\u3063\u305f\u3089\u3001\u307e\u305a\u300c\u3044\u307e\u306e\u5e73\u5747\u304b\u3089\u3069\u308c\u3060\u3051\u96e2\u308c\u3066\u3044\u308b\u304b\u300d\u3092 \u03b4\uff1dx\u2212m \u3068\u7f6e\u304d\u307e\u3059\u3002\u4ef6\u6570\u30921\u5897\u3084\u3057\u3066\u3001\u65b0\u3057\u3044\u5e73\u5747\u3092 m\u2032\uff1dm\uff0b\u03b4\/(n\uff0b1) \u306b\u3057\u307e\u3059\u3002<\/p>\n<p>\u6b21\u306b\u3001M2\u3078 <strong>\u03b4\u00d7(x\u2212m\u2032)<\/strong> \u3092\u52a0\u3048\u307e\u3059\u3002\u6700\u521d\u306e\u5dee\u03b4\u306f\u66f4\u65b0\u524d\u306e\u5e73\u5747\u304b\u3089\u6e2c\u308a\u3001\u5f8c\u306e\u5dee\u306f\u66f4\u65b0\u5f8c\u306e\u5e73\u5747\u304b\u3089\u6e2c\u308b\u3068\u3053\u308d\u304c\u30dd\u30a4\u30f3\u30c8\u3067\u3059\u3002\u5e73\u5747\u304c\u52d5\u304f\u3068\u3001\u904e\u53bb\u306e\u70b9\u304c\u65b0\u3057\u3044\u5e73\u5747\u304b\u3089\u3069\u308c\u3060\u3051\u96e2\u308c\u3066\u3044\u308b\u304b\u3082\u5909\u308f\u308a\u307e\u3059\u3002\u3053\u306e\u88dc\u6b63\u307e\u3067\u542b\u3081\u305f\u5408\u8a08\u3092\u3001\u904e\u53bb\u306e\u70b9\u3092\u8aad\u307f\u76f4\u3055\u305a\u306b\u66f4\u65b0\u3067\u304d\u307e\u3059\u3002<sup class=\"source-note\">[1, 3]<\/sup><\/p>\n<p>\u6700\u521d\u306e\u70b9\u3060\u3051\u306a\u3089\u5e73\u5747\u306f\u305d\u306e\u5024\u3001M2\u306f0\u3067\u3059\u3002\u4f8b\u306e2\u70b9\u76ee\u3067\u306f\u3001\u53e4\u3044\u5e73\u5747\u3068\u306e\u5dee\u304c1\u3001\u65b0\u3057\u3044\u5e73\u5747\u3068\u306e\u5dee\u304c0.5\u306a\u306e\u3067\u3001M2\u30780.5\u3092\u52a0\u3048\u307e\u3059\u30023\u70b9\u76ee\u3067\u306f\u5dee\u304c1.5\u30681\u306b\u306a\u308a\u3001\u3055\u3089\u306b1.5\u3092\u52a0\u3048\u3066M2\uff1d2\u3002\u5e73\u5747\u3068\u5c0f\u3055\u306a\u5dee\u3092\u4e2d\u5fc3\u306b\u8a08\u7b97\u3059\u308b\u305f\u3081\u3001\u5148\u307b\u3069\u306e\u5de8\u5927\u306a\u4e8c\u4e57\u548c\u540c\u58eb\u306e\u5f15\u304d\u7b97\u3092\u907f\u3051\u3089\u308c\u307e\u3059\u3002<\/p>\n<p>3\u70b9\u3092\u51e6\u7406\u3057\u7d42\u3048\u305f\u72b6\u614b\u306f\u3001n\uff1d3\u3001m\uff1d100000002\u3001M2\uff1d2\u3067\u3059\u3002\u6b21\u306e\u6e2c\u5b9a\u5024\u304c\u5c4a\u3044\u3066\u3082\u3001\u3053\u306e\u4e09\u3064\u304b\u3089\u66f4\u65b0\u3092\u7d9a\u3051\u3089\u308c\u307e\u3059\u3002GNU Scientific Library\u306eRunning Statistics\u3082\u3001\u4e00\u5ea6\u306b\u4e00\u3064\u306e\u5024\u3092\u52a0\u3048\u3066\u7d71\u8a08\u91cf\u3092\u66f4\u65b0\u3059\u308b\u6a5f\u80fd\u3092\u63d0\u4f9b\u3057\u3066\u3044\u307e\u3059\u3002GSL 2.8\u306e\u5b9f\u88c5\u3067\u306f\u3001\u540c\u3058\u504f\u5dee\u5e73\u65b9\u548c\u306e\u66f4\u65b0\u3092\u4ee3\u6570\u7684\u306b\u7b49\u4fa1\u306a\u5f62\u3067\u8a08\u7b97\u3057\u3001\u5206\u6563\u306fM2\/(n\u22121)\u3067\u8fd4\u3057\u307e\u3059\u3002<sup class=\"source-note\">[2, 3]<\/sup><\/p>\n<h2>\u4fdd\u5b58\u3059\u308b\u91cf\u3092\u6e1b\u3089\u3057\u3066\u3082\u3001\u5931\u308f\u308c\u305f\u7cbe\u5ea6\u307e\u3067\u306f\u623b\u305b\u306a\u3044<\/h2>\n<p>Welford\u6cd5\u306f\u3001\u5230\u7740\u3059\u308b\u30c7\u30fc\u30bf\u5168\u4f53\u306e\u5e73\u5747\u3068\u5206\u6563\u3092\u66f4\u65b0\u3057\u305f\u3044\u5834\u9762\u306b\u5411\u304d\u307e\u3059\u3002\u4ef6\u6570\u306b\u6bd4\u4f8b\u3059\u308b\u914d\u5217\u3092\u6301\u305f\u305a\u3001\u4e00\u5b9a\u91cf\u306e\u96c6\u8a08\u7528\u30e1\u30e2\u30ea\u30fc\u3067\u7d9a\u3051\u3089\u308c\u308b\u305f\u3081\u3067\u3059\u3002\u305f\u3060\u3057\u3001\u6b8b\u308b\u306e\u306f\u96c6\u8a08\u5024\u306a\u306e\u3067\u3001\u5f8c\u304b\u3089\u300c\u6628\u65e5\u306e3\u756a\u76ee\u306e\u6e2c\u5b9a\u5024\u300d\u3092\u53d6\u308a\u51fa\u3059\u3053\u3068\u306f\u3067\u304d\u307e\u305b\u3093\u3002\u5143\u30c7\u30fc\u30bf\u306e\u8ffd\u8de1\u304c\u5fc5\u8981\u306a\u3089\u3001\u4fdd\u5b58\u306e\u4ed5\u7d44\u307f\u306f\u5225\u306b\u7528\u610f\u3057\u307e\u3059\u3002<\/p>\n<p>\u307e\u305f\u3001\u3053\u308c\u306f\u5168\u30c7\u30fc\u30bf\u3092\u540c\u3058\u91cd\u307f\u3067\u96c6\u8a08\u3059\u308b\u66f4\u65b0\u3067\u3059\u3002\u300c\u76f4\u8fd1100\u70b9\u3060\u3051\u300d\u3084\u300c\u6700\u8fd1\u306e\u5024\u307b\u3069\u91cd\u304f\u3059\u308b\u300d\u3068\u3044\u3046\u8981\u6c42\u306b\u306f\u3001\u305d\u306e\u7bc4\u56f2\u3084\u91cd\u307f\u306b\u5bfe\u5fdc\u3059\u308b\u5225\u306e\u66f4\u65b0\u5247\u304c\u5fc5\u8981\u3067\u3059\u3002\u30c7\u30fc\u30bf\u304c2\u70b9\u672a\u6e80\u306a\u3089\u3001n\u22121\u3067\u5272\u308b\u6a19\u672c\u5206\u6563\u3082\u5b9a\u7fa9\u3067\u304d\u307e\u305b\u3093\u3002\u30e9\u30a4\u30d6\u30e9\u30ea\u304c\u8fd4\u30590\u306a\u3069\u306e\u898f\u7d04\u3068\u3001\u6e2c\u5b9a\u306e\u3070\u3089\u3064\u304d\u304c0\u3060\u3063\u305f\u3068\u3044\u3046\u610f\u5473\u306f\u5206\u3051\u3066\u6271\u3044\u307e\u3059\u3002<\/p>\n<p>\u4e38\u3081\u8aa4\u5dee\u304c\u306a\u304f\u306a\u308b\u308f\u3051\u3067\u3082\u3042\u308a\u307e\u305b\u3093\u3002\u51e6\u7406\u9806\u3084\u6570\u5024\u306e\u5927\u304d\u3055\u306b\u3088\u3063\u3066\u7d50\u679c\u306f\u5909\u308f\u308a\u5f97\u307e\u3059\u3057\u3001\u5165\u529b\u6642\u70b9\u3067\u5225\u306e\u6e2c\u5b9a\u5024\u304c\u540c\u3058\u6d6e\u52d5\u5c0f\u6570\u70b9\u6570\u3078\u4e38\u3081\u3089\u308c\u3066\u3044\u308c\u3070\u3001\u66f4\u65b0\u5f0f\u3060\u3051\u3067\u306f\u5143\u306e\u5dee\u3092\u5fa9\u5143\u3067\u304d\u307e\u305b\u3093\u3002\u4fdd\u5b58\u6e08\u307f\u306e\u5168\u30c7\u30fc\u30bf\u3092\u8aad\u307f\u76f4\u305b\u308b\u306a\u3089\u3001\u5e73\u5747\u3092\u6c42\u3081\u3066\u304b\u3089\u504f\u5dee\u3092\u8a08\u7b97\u3059\u308b\u4e8c\u6bb5\u968e\u306e\u65b9\u6cd5\u3082\u9078\u629e\u80a2\u3067\u3059\u3002\u307e\u305a\u3001\u9010\u6b21\u51e6\u7406\u304c\u5fc5\u8981\u306a\u306e\u304b\u3001\u3069\u306e\u5206\u6bcd\u306e\u5206\u6563\u304c\u6b32\u3057\u3044\u306e\u304b\u3001\u5165\u529b\u306b\u5fc5\u8981\u306a\u7cbe\u5ea6\u304c\u6b8b\u3063\u3066\u3044\u308b\u304b\u3002\u3053\u306e\u4e09\u70b9\u3092\u305d\u308d\u3048\u308b\u3068\u3001\u3070\u3089\u3064\u304d\u306e\u5024\u3092\u8aad\u307f\u9055\u3048\u306b\u304f\u304f\u306a\u308a\u307e\u3059\u3002<\/p>\n<h2>\u53c2\u8003\u8cc7\u6599<\/h2>\n<ol>\n<li>Tony F. Chan, Gene H. Golub, Randall J. LeVeque, <a href=\"https:\/\/www.math.pku.edu.cn\/teachers\/litj\/notes\/numer_anal\/AmerStat_37_242_Chan_Variance.pdf\">Algorithms for Computing the Sample Variance: Analysis and Recommendations<\/a>, The American Statistician 37(3), 242\u2013247, 1983\u3002\u5f0f(1.1)\u301c(1.3)\u3001\u8a08\u7b97\u8aa4\u5dee\u3068\u65b9\u6cd5\u306e\u6bd4\u8f03\u3002<\/li>\n<li>GNU Scientific Library 2.8, <a href=\"https:\/\/www.gnu.org\/software\/gsl\/doc\/html\/rstat.html\">Running Statistics<\/a>\u3002\u9010\u6b21\u7d71\u8a08\u91cf\u306eAPI\u3068\u5206\u6563\u306e\u5b9a\u7fa9\u3002<\/li>\n<li>GNU Scientific Library, <a href=\"https:\/\/git.savannah.gnu.org\/cgit\/gsl.git\/plain\/rstat\/rstat.c?h=release-2-8\">rstat\/rstat.c \u2014 release-2-8<\/a>\u3002gsl_rstat_add\u3068gsl_rstat_variance\u306e\u5b9f\u88c5\u3002\u539f\u8cc7\u6599\u30fb\u516c\u958b\u5b9f\u88c5\u306e\u78ba\u8a8d\u65e5\uff1a2026\u5e7410\u670825\u65e5\u3002<\/li>\n<\/ol>\n","protected":false},"excerpt":{"rendered":"<p>\u30bb\u30f3\u30b5\u30fc\u304b\u3089\u6e2c\u5b9a\u5024\u304c\u4e00\u3064\u305a\u3064\u5c4a\u304f\u3068\u304d\u3001\u77e5\u308a\u305f\u3044\u306e\u306f\u5e73\u5747\u3060\u3051\u3068\u306f\u9650\u308a\u307e\u305b\u3093\u3002\u5024\u304c\u3069\u308c\u304f\u3089\u3044\u63fa\u308c\u3066\u3044\u308b\u304b\u3082\u3001\u305d\u306e\u5834\u3067\u8ffd\u3044\u305f\u304f\u306a\u308a\u307e\u3059\u3002\u904e\u53bb\u306e\u6e2c\u5b9a\u5024\u3092\u3059\u3079\u3066\u4fdd\u5b58\u3057\u3066\u6bce\u56de\u8a08\u7b97\u3057\u76f4\u3059\u4ee3\u308f\u308a\u306b\u3001\u4ef6\u6570\u30fb\u5e73\u5747\u30fb\u3070\u3089\u3064\u304d\u306e\u96c6\u8a08\u5024\u3092\u66f4\u65b0\u3057\u3066 [&hellip;]<\/p>\n","protected":false},"author":3,"featured_media":1598,"comment_status":"closed","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":{"_jetpack_newsletter_access":"","_jetpack_dont_email_post_to_subs":true,"_jetpack_newsletter_tier_id":0,"_jetpack_memberships_contains_paywalled_content":false,"_jetpack_feature_clip_id":0,"_jetpack_memberships_contains_paid_content":false,"footnotes":"","jetpack_publicize_message":"","jetpack_publicize_feature_enabled":false,"jetpack_social_post_already_shared":true,"jetpack_social_options":{"image_generator_settings":{"template":"highway","default_image_id":0,"font":"","enabled":false},"version":2},"jetpack_post_was_ever_published":false},"categories":[30],"tags":[324],"class_list":["post-1600","post","type-post","status-publish","format-standard","has-post-thumbnail","hentry","category-computing","tag-welford-algorithm"],"jetpack_publicize_connections":[],"jetpack_sharing_enabled":true,"jetpack_featured_media_url":"https:\/\/quantumsea.net\/wp-content\/uploads\/2026\/10\/qs-welford-online-variance-20261025-featured-b51da1fbe6ef.png","_links":{"self":[{"href":"https:\/\/quantumsea.net\/index.php?rest_route=\/wp\/v2\/posts\/1600","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/quantumsea.net\/index.php?rest_route=\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/quantumsea.net\/index.php?rest_route=\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/quantumsea.net\/index.php?rest_route=\/wp\/v2\/users\/3"}],"replies":[{"embeddable":true,"href":"https:\/\/quantumsea.net\/index.php?rest_route=%2Fwp%2Fv2%2Fcomments&post=1600"}],"version-history":[{"count":1,"href":"https:\/\/quantumsea.net\/index.php?rest_route=\/wp\/v2\/posts\/1600\/revisions"}],"predecessor-version":[{"id":1601,"href":"https:\/\/quantumsea.net\/index.php?rest_route=\/wp\/v2\/posts\/1600\/revisions\/1601"}],"wp:featuredmedia":[{"embeddable":true,"href":"https:\/\/quantumsea.net\/index.php?rest_route=\/wp\/v2\/media\/1598"}],"wp:attachment":[{"href":"https:\/\/quantumsea.net\/index.php?rest_route=%2Fwp%2Fv2%2Fmedia&parent=1600"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/quantumsea.net\/index.php?rest_route=%2Fwp%2Fv2%2Fcategories&post=1600"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/quantumsea.net\/index.php?rest_route=%2Fwp%2Fv2%2Ftags&post=1600"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}