{"id":103,"date":"2023-07-17T04:05:25","date_gmt":"2023-07-17T04:05:25","guid":{"rendered":"https:\/\/mathority.org\/cn\/%e7%ae%97%e6%9c%af%e5%b9%b3%e5%9d%87%e8%ae%a1%e7%ae%97%e5%99%a8\/"},"modified":"2023-07-17T04:05:25","modified_gmt":"2023-07-17T04:05:25","slug":"%e7%ae%97%e6%9c%af%e5%b9%b3%e5%9d%87%e8%ae%a1%e7%ae%97%e5%99%a8","status":"publish","type":"post","link":"https:\/\/mathority.org\/cn\/%e7%ae%97%e6%9c%af%e5%b9%b3%e5%9d%87%e8%ae%a1%e7%ae%97%e5%99%a8\/","title":{"rendered":"\u7b97\u672f\u5e73\u5747\u503c\u8ba1\u7b97\u5668"},"content":{"rendered":"<p>\u4ec0\u4e48\u662f\u7b97\u672f\u5e73\u5747\u503c\u4ee5\u53ca\u5982\u4f55\u8ba1\u7b97\uff1f\u5e73\u5747\u503c\u662f\u901a\u8fc7\u5c06\u7ed9\u5b9a\u7684\u4e00\u7ec4\u6570\u5b57\u76f8\u52a0\u5e76\u5c06\u7ed3\u679c\u9664\u4ee5\u503c\u7684\u6570\u91cf\u800c\u83b7\u5f97\u7684\u6570\u503c\u3002\u4f8b\u5982\uff0c\u5982\u679c\u6211\u4eec\u8981<strong>\u8ba1\u7b97\u6570\u636e2\u30014\u30011\u548c6\u7684\u7b97\u672f\u5e73\u5747\u503c<\/strong>\uff0c\u90a3\u4e48\u6211\u4eec\u9700\u8981\u8fdb\u884c\u4ee5\u4e0b\u8ba1\u7b97\uff1a(2 + 4 + 1 + 5) \/ 4 = 3\u3002\u5728\u672c\u6587\u540e\u9762\u6211\u4eec\u5c06\u5c06\u66f4\u8be6\u7ec6\u5730\u89e3\u91ca\u5982\u4f55\u627e\u5230\u4e00\u7ec4\u6570\u5b57\u7684\u5e73\u5747\u503c\u3002\u6b64\u5916\uff0c\u60a8\u8fd8\u53ef\u4ee5\u4f7f\u7528\u4ee5\u4e0b\u7b97\u672f\u5e73\u5747\u503c\u8ba1\u7b97\u5668\uff0c\u4ee5\u4fbf\u60a8\u53ef\u4ee5\u68c0\u67e5\u7ed3\u679c\u662f\u5426\u6b63\u786e\u3002<\/p>\n<h2 class=\"wp-block-heading\" id=\"calculadora-de-promedio-online\"><span id=\"Calculadora_de_promedio_online\">\u5728\u7ebf\u5e73\u5747\u8ba1\u7b97\u5668<\/span><\/h2>\n<p>\u5982\u679c\u4f60\u60f3\u8ba1\u7b97\u4e00\u7cfb\u5217\u6570\u5b57\u7684\u5e73\u5747\u503c\uff0c\u4f60\u53ef\u4ee5\u4f7f\u7528\u8fd9\u4e2a<strong>\u5728\u7ebf\u7b97\u672f\u5e73\u5747\u8ba1\u7b97\u5668<\/strong>\uff0c\u901a\u8fc7\u5b83\u4f60\u53ef\u4ee5\u68c0\u67e5\u4f60\u7684\u7ec3\u4e60\u7ed3\u679c\u5e76\u77e5\u9053\u4f60\u662f\u5426\u6b63\u786e\u5730\u89e3\u51b3\u4e86\u5b83\u4eec\u3002\u5b83\u7684\u4f7f\u7528\u975e\u5e38\u7b80\u5355\uff0c\u56e0\u4e3a\u60a8\u53ea\u9700\u8f93\u5165\u7ec4\u6210\u8be5\u7ec4\u7684\u6570\u5b57\uff08\u4ee5\u9017\u53f7\u5206\u9694\uff09\uff0c\u7136\u540e\u5355\u51fb\u8ba1\u7b97\u6309\u94ae\u3002\u8bf7\u8bb0\u4f4f\u8f93\u5165\u5e26\u6709\u53e5\u70b9\uff08\u800c\u4e0d\u662f\u9017\u53f7\uff09\u7684<strong>\u5341\u8fdb\u5236\u6570\u5b57<\/strong>\u3002<\/p>\n<p><title>\u7b97\u672f\u5e73\u5747\u503c\u8ba1\u7b97\u5668<\/title><script language=\"javascript\"><\/p>\n<p>function MediaAritmetica (){\n        var numeros = document.getElementById('ValoresEntrada').value.split(',');\n        var suma = 0;\n        for (c in numeros){\n            suma += numeros[c]*1;\n        }\n        return document.getElementById('MediaAritmetica').innerText = suma\/numeros.length;\n    }<\/p>\n<p>function calcularMediaAritmetica() {\n  var input = document.getElementById('ValoresEntrada').value;\n  var numeros = [];\n  var numeroConcreto = 0; <\/p>\n<p>  for(var i = 0; i < input.length; i++) { \n    if (input[i] == ',') { \n      numeros.push(parseInt(input.substring(numeroConcreto,i))); \n      numeroConcreto = i + 1; \n    } else if (i == input.length - 1) { \n      numeros.push(parseInt(input.substring(numeroConcreto))); \n    }\n  }\n  document.getElementById('MediaAritmetica').innerText = 'La media aritm\u00e9tica es: ' + MediaAritmetica.apply(window, numeros);\n  }\n \n<\/script><\/p>\n<form id=\"formMediaAritmetica\" name=\"formMediaAritmetica\" style=\"padding-top: 1rem\"><input type=\"text\" id=\"ValoresEntrada\" name=\"ValoresEntrada\" size=\"30\" placeholder=\"33,5,12\" pattern=\"^\\d+[0-9,]+\\d+$\" required=\"\"><button type=\"button\" onclick=\"calcularMediaAritmetica()\">\u8ba1\u7b97<\/button><\/p>\n<div id=\"MediaAritmetica\"><\/div>\n<\/form>\n<h2 class=\"wp-block-heading\" id=\"como-calcular-la-media-aritmetica\"><span id=\"Como_calcular_la_media_aritmetica\">\u5982\u4f55\u8ba1\u7b97\u7b97\u672f\u5e73\u5747\u503c\uff1f<\/span><\/h2>\n<p>\u6709\u4e00\u4e2a\u7b97\u672f\u5e73\u5747\u503c\u516c\u5f0f\uff0c\u5141\u8bb8\u6211\u4eec\u6839\u636e\u4efb\u4f55\u7cfb\u5217\u6216\u4e00\u7ec4\u6570\u5b57\u6765\u8ba1\u7b97\u5b83\uff1a <\/p>\n<div class=\"wp-block-image\">\n<figure class=\"aligncenter size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"374\" height=\"173\" src=\"https:\/\/mathority.org\/wp-content\/uploads\/2023\/07\/calculatrice-de-moyenne-arithmetique.webp\" data-src=\"\" alt=\"\u7b97\u672f\u5e73\u5747\u503c\u8ba1\u7b97\u5668\" class=\"wp-image-5683 lazyload\" srcset=\"\" sizes=\"auto, \"><figcaption class=\"wp-element-caption\">\u7b97\u672f\u5e73\u5747\u516c\u5f0f<\/figcaption><\/figure>\n<\/div>\n<p>\u4f8b\u5982\uff0c\u5982\u679c\u60a8\u60f3\u8ba1\u7b97\u4e00\u7ec4\u6570\u5b57 [1, 4, 7, 2, 5, 10] \u7684\u5e73\u5747\u503c\uff0c\u53ea\u9700\u5c06\u5b83\u4eec\u52a0\u5728\u4e00\u8d77\uff0c\u7136\u540e\u5c06\u7ed3\u679c\u9664\u4ee5\u60a8\u4e4b\u524d\u6dfb\u52a0\u7684\u503c\u7684\u6570\u91cf\uff1a( 1 + 4 + 7 + 3 + 5 + 10) \/ 6 = 5\u3002\u867d\u7136\u6709\u65f6\u6211\u4eec\u4f1a\u9700\u8981\u8ba1\u7b97<a href=\"https:\/\/mathority.org\/cn\/\u9891\u7387\u8868\/\" target=\"_blank\" rel=\"noreferrer noopener\">\u9891\u6570\u8868<\/a>\u4e2d\u6570\u503c\u7684\u7b97\u672f\u5e73\u5747\u503c\u3002\u5728\u8fd9\u4e9b\u60c5\u51b5\u4e0b\uff0c\u6211\u4eec\u5fc5\u987b\u5e94\u7528\u76f8\u540c\u7684\u516c\u5f0f\uff0c\u4f46\u5c06\u6bcf\u4e2a\u6570\u5b57\u4e58\u4ee5\u5b83\u51fa\u73b0\u7684\u6b21\u6570\uff08\u5176<a href=\"https:\/\/mathority.org\/cn\/\u7edd\u5bf9\u9891\u7387\/\" target=\"_blank\" rel=\"noreferrer noopener\">\u7edd\u5bf9\u9891\u7387<\/a>\uff09\uff0c\u5e76\u4f7f N \u7b49\u4e8e\u7edd\u5bf9\u9891\u7387\u7684\u603b\u548c\u3002\u4f8b\u5982\uff0c(1 x 4 + 3 x 2 + 5 x 4) \/ (4 + 2 + 4) = 3\u3002<\/p>\n<p>\u6211\u4eec\u8fd8\u53ef\u4ee5\u5c06\u8be5\u516c\u5f0f\u8868\u793a\u4e3a N \u4e0e\u57fa\u6570 i \u4e4b\u548c (\u03a3 <sub>i<\/sub> <sup>N<\/sup> )\uff0c\u7136\u540e\u9664\u4ee5 N\u3002\u6700\u540e\u4e00\u4e2a\u8868\u8fbe\u5f0f\u662f\u4e0e\u4e0a\u56fe\u4e2d\u76f8\u540c\u7684\u5185\u5bb9\u7684\u53e6\u4e00\u79cd\u8868\u8fbe\u65b9\u5f0f\u3002\u5c3d\u7ba1\u8fd9\u901a\u5e38\u5728\u6570\u5b66\u6559\u79d1\u4e66\u4e2d\u51fa\u73b0\u5f97\u66f4\u591a\uff0c\u4f46\u8fd9\u5c31\u662f\u4e3a\u4ec0\u4e48\u4e86\u89e3\u8fd9\u4e00\u70b9\u5f88\u91cd\u8981\u3002<\/p>\n<h2 class=\"wp-block-heading\" id=\"propiedades-de-la-media-aritmetica\"><span id=\"Propiedades_de_la_media_aritmetica\">\u7b97\u672f\u5e73\u5747\u503c\u7684\u6027\u8d28<\/span><\/h2>\n<ul>\n<li><strong>\u504f\u5dee\u4e4b\u548c\uff1a<\/strong>\u6240\u6709\u6570\u636e\u4e0e\u6574\u4f53\u5747\u503c\u7684\u504f\u5dee\u4e4b\u548c\u7b49\u4e8e0\uff0c\u7531\u8fd9\u4e2a\u6027\u8d28\u6211\u4eec\u53ef\u4ee5\u63a8\u5bfc\u51fa\u4e0b\u9762\u7684\u516c\u5f0f\u03a3(X <sub>i<\/sub> - x\u0304) = 0\u3002<\/li>\n<li><strong>\u504f\u5dee\u5e73\u65b9\u548c\uff1a<\/strong>\u5f53\u6211\u4eec\u5c06\u6240\u6709\u6570\u636e\u7684\u7b97\u672f\u5e73\u5747\u503c\u7684\u504f\u5dee\u5e73\u65b9\u76f8\u52a0\u65f6\uff0c\u6211\u4eec\u5f97\u5230\u4e00\u4e2a\u6700\u5c0f\u6570\u503c\u3002\u5219 \u03a3(X <sub>i<\/sub> - x\u0304) <sup>2<\/sup> \u2264 \u03a3(X <sub>i<\/sub> - a) <sup>2<\/sup> , a \u2208 \u211d\u3002<\/li>\n<li><strong>\u7b49\u4ef7\u7b97\u672f\u5e73\u5747\u503c\uff1a<\/strong>\u5982\u679c\u6211\u4eec\u5c06\u4e00\u4e2a\u503c x \u6dfb\u52a0\u5230\u6784\u6210\u6570\u503c\u96c6\u7684\u6240\u6709\u503c\u4e2d\uff0c\u90a3\u4e48\u8fd9\u4e9b\u6570\u5b57\u7684\u5e73\u5747\u503c\u5c06\u7b49\u4e8e\u4e4b\u524d\u7684\u7b97\u672f\u5e73\u5747\u503c\u4e0e\u88ab\u6dfb\u52a0\u7684\u6570\u5b57\u4e4b\u548c\uff1ax\u0304 = x\u0304 <sub>0+<\/sub>\u6709\u3002\u8fd9\u79cd\u60c5\u51b5\u4e5f\u53d1\u751f\u5728\u4ea7\u54c1\u4e0a\u3002<\/li>\n<\/ul>\n<h2 class=\"wp-block-heading\" id=\"aplicaciones-del-promedio\"><span id=\"Aplicaciones_del_promedio\">\u5e73\u5747\u5e94\u7528\u7a0b\u5e8f<\/span><\/h2>\n<p>\u4e00\u822c\u6765\u8bf4\uff0c\u6211\u4eec\u4f7f\u7528\u8fd9\u4e2a\u6570\u5b66\u8d44\u6e90\u6765\u8ba1\u7b97<strong>\u6211\u4eec\u7684\u96c6\u5408\u7684\u4ee3\u8868\u503c<\/strong>\uff0c\u901a\u8fc7\u5b83\u6211\u4eec\u53ef\u4ee5\u4ee5\u7b80\u5316\u7684\u65b9\u5f0f\u7406\u89e3\u6570\u503c\u7ec4\u7684\u884c\u4e3a\u3002\u4e00\u4e2a\u4f8b\u5b50\u662f\u8ba1\u7b97\u73ed\u7ea7\u7684\u5e73\u5747\u6210\u7ee9\uff0c\u8fd9\u6837\u6211\u4eec\u5c31\u53ef\u4ee5\u77e5\u9053\u4ee3\u8868\u5b66\u751f\u603b\u6570\u7684\u5206\u6570\u3002\u6211\u4eec\u901a\u5e38\u8fd8\u5728\u79d1\u5b66\u5b9e\u9a8c\u4e2d\u4f7f\u7528\u5e73\u5747\uff0c\u56e0\u4e3a\u6211\u4eec\u7ecf\u5e38\u9700\u8981\u6536\u96c6\u591a\u4e2a\u7ed3\u679c\u5e76\u5bf9\u5b83\u4eec\u8fdb\u884c\u5e73\u5747\u4ee5\u83b7\u5f97\u66f4\u51c6\u786e\u7684\u7ed3\u679c\u3002<\/p>\n<h2 class=\"wp-block-heading\" id=\"ejercicios-resueltos-de-la-media-aritmetica\"><span id=\"Ejercicios_resueltos_de_la_media_aritmetica\">\u7b97\u672f\u5e73\u5747\u6570\u89e3\u51b3\u7684\u95ee\u9898<\/span><\/h2>\n<p>\u63a5\u4e0b\u6765\uff0c\u6211\u4eec\u5c06\u4e3a\u60a8\u63d0\u4f9b\u4e00\u4e9b\u5173\u4e8e\u4e09\u79cd\u4e3b\u8981\u7b97\u672f\u5e73\u5747\u7c7b\u578b\u7684\u7ec3\u4e60\uff0c\u8bf7\u8bb0\u4f4f\u5b83\u4eec\u90fd\u662f<strong>\u7528\u672c\u6587\u4e2d\u89e3\u91ca\u7684\u65b9\u6cd5<\/strong>\u89e3\u51b3\u7684\u3002\u5982\u679c\u60a8\u613f\u610f\uff0c\u60a8\u53ef\u4ee5\u4f7f\u7528\u4e0a\u9762\u7684\u8ba1\u7b97\u5668\u548c\u6211\u4eec\u7684<a href=\"https:\/\/mathority.org\/cn\/\u5728\u7ebf\u79d1\u5b66\u8ba1\u7b97\u5668\/\" target=\"_blank\" rel=\"noreferrer noopener\">\u5728\u7ebf\u8ba1\u7b97\u5668<\/a>\u8fdb\u884c\u6570\u5b57\u90e8\u5206\uff08\u8ba1\u7b97\uff09\u3002\u4e5f\u5c31\u662f\u8bf4\uff0c\u6211\u4eec\u8ba9\u4f60\u7ec3\u4e60\uff1a<\/p>\n<h3 class=\"wp-block-heading\" id=\"media-aritmetica-basica\">\u57fa\u672c\u7b97\u672f\u5e73\u5747\u6570<\/h3>\n<p><strong>\u8ba1\u7b97\u4ee5\u4e0b\u6570\u636e\u96c6 [2, 5, 3, 7, 6, 1] \u7684\u7b97\u672f\u5e73\u5747\u503c\u3002\u5b8c\u6210\u6b64\u64cd\u4f5c\u540e\uff0c\u60a8\u9700\u8981\u8ba1\u7b97\u540c\u4e00\u7ec4\u6570\u5b57\u7684\u5e73\u5747\u503c\uff0c\u4f46\u5168\u90e8\u4e58\u4ee5 2\uff1a<\/strong><\/p>\n<p>\u8981\u89e3\u51b3\u7b2c\u4e00\u90e8\u5206\uff0c\u6211\u4eec\u53ea\u9700\u4f7f\u7528\u4e0a\u9762\u8bc4\u8bba\u8fc7\u7684\u516c\u5f0f\uff1a <span style=\"font-size: inherit;\">x\u0304 =<\/span> (2 + 5 + 3 + 7 + 6 + 1) \/ 6 = 4\u3002\u8981\u8ba1\u7b97\u7b2c\u4e8c\u90e8\u5206\u7684\u5e73\u5747\u503c\uff0c\u6211\u4eec\u5fc5\u987b\u8fdb\u884c\u76f8\u540c\u7684\u8ba1\u7b97\uff0c\u4f46\u5c06\u6bcf\u4e2a\u6570\u5b57\u4e58\u4ee5 2\uff1a(2 x 2 + 5 x 2 + 3 x 2 + 7 x 2 + 6 x 2 + 1 x 2) \/ 6 = 8\u3002\u6b63\u5982\u6211\u4eec\u6240\u89c1\uff0c\u5728\u7b2c\u4e8c\u79cd\u60c5\u51b5\u4e0b\uff0c\u5e73\u5747\u503c\u7684\u7ed3\u679c\u662f\u4e24\u500d\uff0c\u8fd9\u662f\u53ef\u4ee5\u9884\u89c1\u7684\uff0c\u56e0\u4e3a\u7b49\u6548\u4ea7\u54c1\u7684\u5c5e\u6027\u5f97\u5230\u4e86\u9a8c\u8bc1\u3002<\/p>\n<h3 class=\"wp-block-heading\" id=\"media-aritmetica-para-datos-agrupados\">\u5206\u7ec4\u6570\u636e\u7684\u7b97\u672f\u5e73\u5747\u503c<\/h3>\n<p><strong>\u5341\u4e94\u540d\u5b66\u751f\u7684\u6570\u5b66\u6210\u7ee9\u4e3a\uff1a 5, 8, 7, 4, 9, 3, 6, 8, 7, 8, 9, 7, 5, 8, 8\u3002\u8ba1\u7b97\u73ed\u7ea7\u5e73\u5747\u5206\uff1a<\/strong><\/p>\n<p>\u5728\u8fd9\u79cd\u60c5\u51b5\u4e0b\uff0c\u6211\u4eec\u5fc5\u987b\u8ba1\u7b97\u6bcf\u4e2a\u6570\u5b57\u5728\u5217\u8868\u4e2d\u51fa\u73b0\u7684\u6b21\u6570\uff0c\u7136\u540e\u6211\u4eec\u5c06\u4f7f\u7528\u5e94\u7528\u4e8e\u5206\u7ec4\u6570\u636e\u7684\u7b97\u672f\u5e73\u5747\u503c\u516c\u5f0f\uff08\u5176\u4e2d\u7edd\u5bf9\u9891\u7387\u4ecb\u5165\u7684\u516c\u5f0f\uff09\u6765\u89e3\u51b3\u8ba1\u7b97\uff1a <span style=\"font-size: inherit;\">x\u0304 =<\/span> (3 x 1 + 4x1 + 5x2 + 6x1 + 7x3 + 8x5 + 9x2) \/ 15 = 6.8\u3002\u603b\u4e4b\uff0c\u6211\u4eec\u53ef\u4ee5\u770b\u5230\uff0c\u5c3d\u7ba1\u6709\u4e00\u4e9b\u9ad8\u5206\uff0c\u4f46\u4f4e\u503c\u5bf9\u6574\u4f53\u5e73\u5747\u503c\u6709\u975e\u5e38\u8d1f\u9762\u7684\u5f71\u54cd\u3002<\/p>\n<h3 class=\"wp-block-heading\" id=\"calculo-a-partir-de-una-media-conocida\">\u6839\u636e\u5df2\u77e5\u5e73\u5747\u503c\u8ba1\u7b97<\/h3>\n<p><strong>\u5982\u679c\u6211\u4eec\u77e5\u9053\u4e24\u4e2a\u6570\u5b57\u7684\u5e73\u5747\u503c\u662f 9.25\uff0c\u5176\u4e2d\u4e00\u4e2a\u6570\u5b57\u662f 6\uff0c\u90a3\u4e48\u7b2c\u4e8c\u4e2a\u6570\u5b57\u662f\u591a\u5c11\uff1f<\/strong><\/p>\n<p>\u4e3a\u4e86\u8ba1\u7b97\u7b2c\u4e8c\u4e2a\u503c\uff0c\u6211\u4eec\u9700\u8981\u6839\u636e\u6211\u4eec\u5728\u7ec3\u4e60\u4e2d\u4e00\u76f4\u4f7f\u7528\u7684\u516c\u5f0f\u5efa\u7acb\u4e00\u4e2a\u65b9\u7a0b\uff1a(6 + x) \/ 2 = 9.25\u3002\u6700\u540e\u6211\u4eec\u5c06x\u5206\u79bb\u51fa\u6765\uff0c\u6211\u4eec\u5c31\u5f97\u5230\u5b83\u7684\u6570\u503c\uff0c\u5b83\u76f8\u5f53\u4e8e\u7b2c\u4e8c\u4e2a\u6570\u7684\u6570\u503c\u3002\u5728\u672c\u4f8b\u4e2d x = 12.5\u3002<\/p>\n","protected":false},"excerpt":{"rendered":"<p>\u4ec0\u4e48\u662f\u7b97\u672f\u5e73\u5747\u503c\u4ee5\u53ca\u5982\u4f55\u8ba1\u7b97\uff1f\u5e73\u5747\u503c\u662f\u901a\u8fc7\u5c06\u7ed9\u5b9a\u7684\u4e00\u7ec4\u6570\u5b57\u76f8\u52a0\u5e76\u5c06\u7ed3\u679c\u9664\u4ee5\u503c\u7684\u6570\u91cf\u800c\u83b7\u5f97\u7684\u6570\u503c\u3002\u4f8b\u5982\uff0c\u5982\u679c\u6211\u4eec &hellip;<\/p>\n<p class=\"read-more\"> <a class=\"\" href=\"https:\/\/mathority.org\/cn\/%e7%ae%97%e6%9c%af%e5%b9%b3%e5%9d%87%e8%ae%a1%e7%ae%97%e5%99%a8\/\"> <span class=\"screen-reader-text\">\u7b97\u672f\u5e73\u5747\u503c\u8ba1\u7b97\u5668<\/span> \u67e5\u770b\u5168\u6587 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