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1.当总体中一部分个体与另一部分个体有明显的差异且易于区别时,常将相近的个体归成一组,然后按照各部分所占的比例进行抽样,这种抽样称为分层抽样,其中所分成的各部分称为层,分层抽样时,每一个个体被抽到的概率都是相等的,分层抽仿世样适用于总体由差别明显的几部分组成的情况;在每一层抽样时,采用简单随机抽样或系统抽样。分层抽样是等概率抽样,它也是公平的,用分层抽样从个体数为N的总体中抽取一个容量为n的样本时,在整个抽样过程中每个个体被抽到的概率相等,都等于 。
2.分层抽样的步骤:
第一步:分层
第二步:按比例确定每层抽取的个体的个数;
第三步:各层抽样;

第四步:综合每层抽样,抽取样本。
拓展资料
分层抽样法也叫类型抽样法。它是从一个可以分成不同子总体(或称为层)的总体中,按规定的比例从不顷大仔同层中随机抽取样品(个体)的方法。这种方法的优点是,样本的代表性雀汪比较好,抽样误差比较小。缺点是抽样手续较简单随机抽样还要繁杂些。定量调查中的分层抽样是一种卓越的概率抽样方式,在调查中经常被使用。
系统抽样:
第一步:编号。给样本的200个数据随机编号,编号为001,002,003,……,200;
第二步:确定组距。N=200÷20=10,即分成10组,然后在每一组随机选取一个数字(采用随机抽样抽灶好取),假设选取到的是a(1≤a≤10);
第三步:在每一组中各抽取一个数字,分别为a,10+a,20+a,……,90+a;
第四步:对应的号码即为所要抽取的样本。
分层抽样:
第一步:确定在每一层抽取的个数,根据比例可知,应该在一等品中抽取10个,在二等品中抽取6个,在三等品中抽取4个;
第二步:对一等品、二等品、三等品进行随机编隐闹铅号,一等品的编号为001,002,003,……,100,二等品的编号为101,102,……,160,三等品的编号为161,162,……,200;
第三步:采用简单弯袜随机抽样从一等品、二等品、三等品中分别抽取10个、6个、4个,对应的号码即为我们所要抽取的样本。
(1)系统抽样的步骤为:
①采取随机方式将总体中的个体编号。
②将整个的编号均衡地分段,确定分段间隔k。大野含 是整脊陪数时, ; 不是整数时,从N中剔除一些个体,使得其为整数为止。
③第一段用简单随机抽样确定起始号码 。
④按照规则抽取样本: ; +k; +2k;…… +(n-1)k;
(2)课本中指出,当总体中的个体数不能被样本容量整除时,可先用简单随机抽样从总体中剔除几个个体,使剩下的个体数能被样本容量整除,然后再按系统滚笑抽样进行。这时在整个抽样过程中每个个体被抽取的可能性仍然相等。
所以一等品:10个。二等品:3。三等品:2.
分层抽样最主要的就是比例:[(100+60+40)/100]*20=10
[(100+60+40)/60]*20=3
[(100+60+40)/40]*20=3
分层抽样又称类型抽样,是一种较为常用的抽样方法。在样本大小不变的情况下,总体的一致性越高,抽样误差就越小。分层抽样是先将总体中的所有单位按某种特征或属性(如性别、年龄、职业或地域等)划分成若干类型或层次,然后再在各个类型或层次中采用简单随机抽样或系统抽样的办法抽取一个子样本,最后将这些子样本合起来构成总体的样本。
分层抽样的基本步骤是:总体分层—层中抽样—子样本集合。例如,在一所大学抽取学生进行调查时,可以先把总体分为男生和女生两大类;然后采用简单随机抽样或系统抽样的方法,分别从男生斗扮和女生中各抽取100名空宏灶学生。这样,由这200名学生所构成的就是一个由分绝橘层抽样所得到的样本。
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