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用Excel如何实现不放回随机抽样

  • 2026-04-08 05:58:35
用Excel如何实现不放回随机抽样

所谓随机抽样,简单理解,顾名思义就是从总体中随机抽取几个或几组个体。现实中常见的例子由抽奖、抽查、数据随机分组等。

它又可分为放回随机抽样和不放回随机抽样。不放回随机抽样是指每次随机取个体后不放回总体中,下一次从剩余的个体中再随机取。而放回随机抽样则是在逐个抽取个体时,每次被抽到的个体放回总体中后,再进行下次抽取的抽样方法。

相对而言,放回随机抽样实现较为简单。我们今天分享下如何用Excel实现不放回随机抽样。

举个栗子,如下图所示,A2:A21是EH培训学院的20名……男女。现在需要从中随机抽取3人,授予38妇女红旗手的称号。


解法1:辅助列法

使用辅助列,解决此类问题,应是最简单较快捷的一种解法,基本上老少咸宜,稍有函数公式基础就可以掌握了。

首先将C列作为辅助列,C2输入以下公式,并复制填充至C2:C21区域。

=RAND()

RAND函数生成大于等于0、小于1的随机数。

其次,在E2单元格输入以下公式,复制填充至F2:F4区域即可得到抽奖结果了。

=INDEX(A:A,MATCH(LARGE(C:C,ROW(A1)),C:C,))

LARGE(C:C,ROW(A1)),随着公式向下填充,依次从C列里提取第1、2、3最大的数值;再使用INDEX+MATCH的查询套路得出结果。

结果可能如下:


解法2:一条公式

好伐,打个响指,那能不能只用一条函数公式得出最终结果?

当然也可以,只是稍显复杂。

选取E2:E4单元格区域,使用数组三键(同时按下Ctrl+Shift+Enter)输入以下公式,即可得出结果。

=INDEX(A:A,RIGHT(SMALL(RANDBETWEEN(1^ROW(2:21),99)/1%+ROW(2:21),ROW(1:3)),2))

RANDBETWEEN(1^ROW(2:21),99),随机取得>=1且<99的20个整数,生成一维纵向内存数组,例如:

{3;17;11;40;64;65;75;83;19;37;88;74;76;17;46;39;43;80;38;92}

之后除以1%,将随机值放大百倍,再加上人名所在行的行号(+ROW(2:21)),使用SMALL函数依次从小到大取值,使用RIGHT函数重新取出行号,最后使用INDEX函数得出抽奖结果。

敲黑板!注意这是一条区域数组公式。

公式的计算原理其实是酱紫;我们把20位男女所在的行号,看成是座位号。我们对座位号随机加上不同的权重,然后重新进行排队(升序用small,降序用large),得到一个打乱了的座号排列结果,最后依次将人名取出即可。

公式计算结果可能如下:


解法3:洗牌吧

VBA的解法也有多种,最简单的是字典法,但效率偏差,此处略过不提。嗯,分享下最有效率也最有扩展性的洗牌法。

先讲个故事,憋走开。

假设你是一名人民教师,有一天早晨你想斗地主,目前的情况很明显是一缺三,于是你打算从全班20位同学里随机抽3人。你把他们喊出教室,排成一字纵队。

第一步,你从20人里随机抽取1人。假设抽到的是排在第15位的“随风小妞”。你把她揪出来,拖到第1位去,然后把原本排在第1位的某童鞋安排到第15位去。这样,你就成功抽取了一名……牌友。现在是2缺2。

第二步,你从排在第2位和第20位之间的童鞋里再随机抽取一人——为什么不是从第1位开始抽呢?“随风小妞”举手回答说她已经被抽过了,不能被抽第二次(意思就是她不欠抽了)。假设你这次抽到了排在第6位的“空空”,把她请出来,送到第2位去,再把原本排在第2位的某同学安排到第6位。现在是3缺1了。

第三步,从第3位到第20位之间的童鞋再随机抽取1人,排到第3位去。这样,队伍里的前3名就是你今天的牌友了。恩,加上你,4人刚好,散队,打牌去。

是的,现在,只要我们把上面的故事翻译成VBA代码,之前的示例问题也就解决了。

代码如下:


Sub Myrnd()    Dim r, i&, t, x&    Randomize \\\\\'随机种子初始化    r = [a2:a21] \\\\\'将学生喊出教室,装入数组r    For i = 1 To 3 \\\\\'抽3个人        x = Int(Rnd() * (UBound(r) - i + 1)) + i \\\\\'依次从第1~2……位置起随机抽取学生        t = r(x, 1) \\\\\'被抽中的学生出列        r(x, 1) = r(i, 1) \\\\\'前列的学生去被抽中学生的位置        r(i, 1) = t \\\\\'被抽中的学生站到前排去    Next    [e2].Resize(3, 1) = r \\\\\'将队伍的前3名学生(抽取结果)放入抽奖区End Sub

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  1. CONNECT:[ UseTime:0.000603s ] mysql:host=127.0.0.1;port=3306;dbname=h_sjds;charset=utf8mb4
  2. SHOW FULL COLUMNS FROM `fenlei` [ RunTime:0.000618s ]
  3. SELECT * FROM `fenlei` WHERE `fid` = 0 [ RunTime:0.000260s ]
  4. SELECT * FROM `fenlei` WHERE `fid` = 63 [ RunTime:0.000257s ]
  5. SHOW FULL COLUMNS FROM `set` [ RunTime:0.000461s ]
  6. SELECT * FROM `set` [ RunTime:0.000209s ]
  7. SHOW FULL COLUMNS FROM `article` [ RunTime:0.000638s ]
  8. SELECT * FROM `article` WHERE `id` = 463683 LIMIT 1 [ RunTime:0.000360s ]
  9. UPDATE `article` SET `lasttime` = 1775772983 WHERE `id` = 463683 [ RunTime:0.014923s ]
  10. SELECT * FROM `fenlei` WHERE `id` = 65 LIMIT 1 [ RunTime:0.000234s ]
  11. SELECT * FROM `article` WHERE `id` < 463683 ORDER BY `id` DESC LIMIT 1 [ RunTime:0.000440s ]
  12. SELECT * FROM `article` WHERE `id` > 463683 ORDER BY `id` ASC LIMIT 1 [ RunTime:0.000418s ]
  13. SELECT * FROM `article` WHERE `id` < 463683 ORDER BY `id` DESC LIMIT 10 [ RunTime:0.000913s ]
  14. SELECT * FROM `article` WHERE `id` < 463683 ORDER BY `id` DESC LIMIT 10,10 [ RunTime:0.000669s ]
  15. SELECT * FROM `article` WHERE `id` < 463683 ORDER BY `id` DESC LIMIT 20,10 [ RunTime:0.001002s ]
0.091953s