• 【数据分析师 Level 1 】10.数据采集方法

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    【数据分析师 Level 1 】3-1.数据采集方法

    数据的来源

    一手数据 VS 二手数据
    • 一手数据（Primary data）
      • 也称为原始数据，顾名思义，是指直接获取，没有经过加工或者第三方传递获得的数据。比如传统调研中的问卷测评、小组访谈、面对面沟通等形式获得的数据，或者是互联网时代用户直接填写的个人信息数据以及平台抓取得行为数据等等
    • 二手数据（Secondary data）
      • 主要是相对于一手数据而言，指的是通过第三方或者是现有的数据资料获取的数据。比如国家统计局数据、知名文献中罗列的数据等等。一手数据的来源渠道，一般比较固定，往往是和自身直接相关。比如搭建的网站、组织的活动，开展的调研等。而二手数据则相对比较多样化，凡是会产出数据相关信息的第三方机构都可以作为来源渠道。
    优劣势分析

    一手数据和二手数据，在实际应用中都是非常重要的。他们不同的优缺点，可以很好地互补，从而帮助企业在效果和效率间找到比较好的平衡

     优点缺点
    一手数据 相关性强 准确度高 理解准确 成本贵 耗时长 清洗工作重
    二手数据 成本低 时间短 清洗工作少 比较普适，相关性弱 准确度不可控制 理解可能存在偏差

    在实际项目中，一般会把两类数据进行结合，总结来看，一手和二手数据的选择，可以参考下图的形式判断

    同时，在一手数据的使用过程中，需要特别注意的是，要对采集回来的数据进行逻辑合理性验证

    而二手数据，因为收集的过程由第三方完成。因此数据的可信性和准确度，就依赖于第三方机构的可信性。

    抽样方法

    如何获取一手数据？

    当我们需要获取一手数据的时候，一种常见的方式就是抽样调查

    抽样调查不止在传统行业中比较常用，在现在的互联网企业中也时常会用到。比如一些优惠活动或者特定客群营销等方案的测试，就需要用到抽样的方式选择测试群体。在做抽样调查时，我们都希望尽可能地减少误差，让抽样的样本能够充分代表整体的特征。那么误差和哪些因素相关呢，抽样误差（Sampling Error）的大小，主要由样本容量的大小和抽样方式来决定。

    一般，我们认为抽样可以分为两类：一类我们叫做概率抽样（Probability Samling），也叫做客观抽样。第二类，我们叫做非概率抽样（Non-probability Sampling），也叫做主观抽样。下面我们介绍两种抽样方法

    概率抽样

    顾名思义，是一种基于概率的抽样方式，因此也被称为客观抽样。从理论的角度来说，概率抽样是符合科学和统计原则的，抽样误差可以估计。也是在可能的情况下，最优先被推荐使用的抽样方法。但是，精确度高的方法，往往操作的复杂度和耗费的成本也会相对偏高。概率抽样，虽然可以避免主观判断带来的谬误，但是它常常受限于项目经费、时间和保密性等原则，从而难以实际使用

    非概率抽样

    和概率抽样相反，非概率抽样是一种简单、易使用的抽样方式。它主要通过抽样者的判断，包括对样本特征的判断和对项目成本的考量，综合特殊的要求或者设定，最终选择合适的样本。因此，这种方法会收到主观因素的影响，不符合统计科学的原则，抽样误差是无法估计和计算的。但是在实际应用中，大量的案例还是证明了非概率误差依然有一定的有效性。在样本量充足的前提下，通过设定简单的配比，以及选择有经验的抽样者，基本上可以保证抽样结果的有效性。而且由于非概率抽样比较容易重复操作，因此用此飞概率抽样反复进行同一试验，结果往往也有趋同性。另外，这一抽样方式，虽然无法衡量抽样误差，但是由于抽样过程可以进行设计和控制，因此可以更简单有效地控制非抽样误差（Non-sampling Error）。

    总结来说，概率抽样和非概率抽样，我们可以通过以下的表格进行区别

     特点优点缺点
    概率抽样 根据科学原则抽取样本 抽样误差可以估计客观 成本贵 耗时长 操作复杂 局限多
    非概率抽样 根据抽样者的主观判断抽取样本 成本低 时间短 操作简单 可行性强 无法衡量抽样误差 存在主管谬误 对抽样者经验要求高
    概率抽样方法

    介绍了概率抽样和非概率抽样之后，我们重点看一下概率抽样方法，常用的概率抽样方法主要有以下4种

    简单随机抽样（Simaple Random Sampling）

    使用简单随机抽样方式进行抽样，总体中的每个样本都有同等的被抽取到的机会。因此，可以用以下的公式，来确定样本量和抽样误差之间的关系

     

     

    其中n表示样本量Z2α​​

    为置信区间，如果没有指定，一般常用取值为1.96（即95%置信区间）α

    为总体标准差E
    为抽样误差范围
    因此根据这个公式，可以实现n和E之间的互相推导

    简单随机抽样中，默认了一个假设，也就是被抽中的机会是均等的，听上去似乎很正常，但是实际上要做到这一点，并不容易。由于改的外观特征和抽样者的心理因素等影响，每个个体被抽到的机会并不是均匀地。因此在实际应用中，通常用抽签或者随机数等形式来进行操作，减少偏差。这样的形式，也决定了在大型调研中简单随机抽样的方式比较难以采用，一般多应用于小型的调研，或者测试客户群体选择等。

    分层抽样（Stratifide Sampling）

    正如之前提到的，简单随机抽样的假设并不总是成立，如果总体可以按照一些特征分成若干层。层与层之间差异明显，每个层内部的个体特征相近，那么我们可以对每个层做简单随机抽样。抽样结果合并的集合，就是我们最终确认的抽样样本。

    在实际操作中，我们可以按照每一层的个体数量来决定抽取数量，是的每个层抽取的比例都相等，这样的抽样我们叫做按比例分层抽样。一般，如果每层重要性差不多，数量差异也不是很大的情况下，我们都是这样操作的。

    而如果有一些层非常重要，或者有些层的个体数非常少，那我们就要采用非按比例分层抽样的方法。

    如果总体中个体间呈现明显的几类，那么使用分层抽样可以更好地反映总体，避免随机抽样可能带来的样本集中或特征缺失的情况。因此，在概率抽样中，分层抽样也是使用最多的一种。我们在对城市，或者是大型的业务线进行研究的时候，都可以采用分层抽样。

    系统抽样（Systematic Sampling）

    除了分层抽样之外，系统抽样也对简单随机抽样，进行了改进。使用系统抽样的时候，仍然需要将个体进行编号，然后根据抽样样本容量决定抽样的间距。因此又叫等距抽样或者机械抽样。这种方法，减少了抽样过程中的人力和时间消耗。不过，系统抽样一般很少作为单独的抽样方法是用，通常是配合其他方法一起进行。

    分段抽样（Multi-stage Sampling）

    前面提到的，都是一次性抽取完成样本的方法，这些方法可以统称为单阶段抽样。然而在有些情况下，我们并不能一次性完成样本的抽取，比如在全国范围内选择一定数量的用户作为试点调查。这个时候我们需要分阶段地去完成抽样过程，这种方法，我们叫做分段抽样。

    分段抽样，我们首先把总体划分成一些大小差不多的群体。在这些群体中随机抽取几个。被抽中的群体，就作为下一步进行随机抽样的“总体”

    因此，在学习过程中，一定要注意区分分段抽样和分层抽样。虽然两者都是对总体进行了一定的划分。但是分层抽样是按照一定特征进行划分，划分的目的是为了避免特征的过分集中和缺失。抽取的过程也是一步完成的，只有在分层之后才会进行随机抽样。而分段抽样则不同，它是由于总体太大，无法直接进行抽取，所以才需要进行多步抽样。每一次对总体的划分都是为了进行随机抽取，而抽取后，下一步的“总体”就会得到一定程度的减小。

    例题精讲

    1.二手数据的特点是（）

    A.数据缺乏可靠性

    B.不适合自己的研究需要

    C.采集数据的成本低，但搜集比较困难

    D.采集数据的成本低，搜集比较容易

    答案：D

    解析：熟悉一手数据和二手数据的特点

    2.与概率抽样相比，非概率抽样的缺点是（）

    A.调查成本比较高

    B.不适合探索性研究

    C.样本统计量的分布是确定的

    D.无法使用样本的结果对总体相应的参数进行推断

    答案：D

    解析：熟悉概率抽样和非概率抽样的异同

    3.为了估计A市愿意坐地铁上下班的人数的比例，在收集数据时，最有可能采用的数据搜集方法是？

    A.普查

    B.实验

    C.随机抽样

    D.公开发表的资料

    答案：C

    解析：在不考虑人力和时间的前提下，上述选项中操作最简单，需要考虑的问题最少的是随机抽样，也能尽可能保证每个个体被抽中的可能性均等

    4.用简单随机重复抽样方法抽取样本单位，如果要使抽样平均误差降低50%，则样本容量需要扩大到原来的（）倍

    A.0.5

    B.不变

    C.2

    D.4

    答案：D

    解析：根据简单随机抽样的样本量确定公式

    n=E2(Z2α​​)2α2​

    得出误差降低50%，样本量需要扩大到原来的4倍

    5.某公司希望估计其生产的某种面向企业用户的产品在市场上的占有率，请问下面哪些抽样方法是不合理的？

    A.从公司客户数据库中随机抽取1000家企业用户进行调研

    B.调研市场上的所有上市公司对于这类产品的使用情况

    C.从市场中的企业中随机抽取调研企业

    D.针对熟悉的企业，排除调研员上门调研

    答案：ABD

    解析：只有C是随机抽样

    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    <html><head>  <title>Evernote Export</title>  <basefont face="微软雅黑" size="2" />  <meta http-equiv="Content-Type" content="text/html;charset=utf-8" />  <meta name="exporter-version" content="YXBJ Windows/600753 (zh-CN, DDL); Windows/10.0.0 (Win64);"/>  <meta name="content-class" content="yinxiang.markdown"/>  <style>    body, td {      font-family: 微软雅黑;      font-size: 10pt;    }  </style></head><body><a name="1875"/>
    <div><span><div style="font-size: 14px; margin: 0; padding: 0; 100%;"><h3 style="line-height: 160%; box-sizing: content-box; font-weight: 700; font-size: 27px; color: #333;">【数据分析师 Level 1 】3-1.数据采集方法</h3><h4 style="line-height: 160%; box-sizing: content-box; font-size: 20px; color: #333;">数据的来源</h4><h5 style="line-height: 160%; box-sizing: content-box; font-weight: 700; font-size: 16px; color: #333;">一手数据 VS 二手数据</h5><ul style="line-height: 160%; box-sizing: content-box; display: block; list-style-type: disc; padding-left: 30px; margin: 6px 0 10px; color: #333;"><li style="line-height: 160%; box-sizing: content-box; position: relative;"><strong style="line-height: 160%; box-sizing: content-box; font-weight: 700;">一手数据（Primary data）</strong><ul style="line-height: 160%; box-sizing: content-box; display: block; list-style-type: disc; padding-left: 30px; margin: 6px 0 10px; color: #333; margin-top: 0; margin-bottom: 0;"><li style="line-height: 160%; box-sizing: content-box; position: relative;">也称为原始数据，顾名思义，是指直接获取，没有经过加工或者第三方传递获得的数据。比如传统调研中的问卷测评、小组访谈、面对面沟通等形式获得的数据，或者是互联网时代用户直接填写的个人信息数据以及平台抓取得行为数据等等</li></ul></li><li style="line-height: 160%; box-sizing: content-box; position: relative;"><strong style="line-height: 160%; box-sizing: content-box; font-weight: 700;">二手数据（Secondary data）</strong><ul style="line-height: 160%; box-sizing: content-box; display: block; list-style-type: disc; padding-left: 30px; margin: 6px 0 10px; color: #333; margin-top: 0; margin-bottom: 0;"><li style="line-height: 160%; box-sizing: content-box; position: relative;">主要是相对于一手数据而言，指的是通过第三方或者是现有的数据资料获取的数据。比如国家统计局数据、知名文献中罗列的数据等等。一手数据的来源渠道，一般比较固定，往往是和自身直接相关。比如搭建的网站、组织的活动，开展的调研等。而二手数据则相对比较多样化，凡是会产出数据相关信息的第三方机构都可以作为来源渠道。</li></ul></li></ul><h5 style="line-height: 160%; box-sizing: content-box; font-weight: 700; font-size: 16px; color: #333;">优劣势分析</h5><p style="line-height: 160%; box-sizing: content-box; margin: 10px 0; color: #333;">一手数据和二手数据，在实际应用中都是非常重要的。他们不同的优缺点，可以很好地互补，从而帮助企业在效果和效率间找到比较好的平衡</p><table style="margin: 2px 0 14px; color: #333; auto; border-collapse: collapse; box-sizing: border-box;"><thead style="line-height: 160%; box-sizing: content-box;"><tr style="line-height: 160%; box-sizing: content-box;"><th style="line-height: 160%; box-sizing: content-box; padding: 5px 14px 5px 12px; border: 1px solid #72777b; border-top: 0; background-color: #7b8184; font-weight: 300; color: #fff; padding-top: 6px;"></th><th style="line-height: 160%; box-sizing: content-box; padding: 5px 14px 5px 12px; border: 1px solid #72777b; border-top: 0; background-color: #7b8184; font-weight: 300; color: #fff; padding-top: 6px;">优点</th><th style="line-height: 160%; box-sizing: content-box; padding: 5px 14px 5px 12px; border: 1px solid #72777b; border-top: 0; background-color: #7b8184; font-weight: 300; color: #fff; padding-top: 6px;">缺点</th></tr></thead><tbody style="line-height: 160%; box-sizing: content-box;"><tr style="line-height: 160%; box-sizing: content-box;"><td style="line-height: 160%; box-sizing: content-box; padding: 5px 14px 5px 12px; border: 1px solid #eaeaea;">一手数据</td><td style="line-height: 160%; box-sizing: content-box; padding: 5px 14px 5px 12px; border: 1px solid #eaeaea;">相关性强 准确度高 理解准确</td><td style="line-height: 160%; box-sizing: content-box; padding: 5px 14px 5px 12px; border: 1px solid #eaeaea;">成本贵 耗时长 清洗工作重</td></tr><tr style="line-height: 160%; box-sizing: content-box;"><td style="line-height: 160%; box-sizing: content-box; padding: 5px 14px 5px 12px; border: 1px solid #eaeaea;">二手数据</td><td style="line-height: 160%; box-sizing: content-box; padding: 5px 14px 5px 12px; border: 1px solid #eaeaea;">成本低 时间短 清洗工作少</td><td style="line-height: 160%; box-sizing: content-box; padding: 5px 14px 5px 12px; border: 1px solid #eaeaea;">比较普适，相关性弱  准确度不可控制  理解可能存在偏差</td></tr></tbody></table><p style="line-height: 160%; box-sizing: content-box; margin: 10px 0; color: #333;">在实际项目中，一般会把两类数据进行结合，总结来看，一手和二手数据的选择，可以参考下图的形式判断</p><p style="line-height: 160%; box-sizing: content-box; margin: 10px 0; color: #333;"><img src="【数据分析师 Level 1 】3-1_files/一手数据和二手数据.png" type="image/png" data-filename="一手数据和二手数据.png"/></p><p style="line-height: 160%; box-sizing: content-box; margin: 10px 0; color: #333;">同时，在一手数据的使用过程中，需要特别注意的是，要对采集回来的数据进行<strong style="line-height: 160%; box-sizing: content-box; font-weight: 700;">逻辑合理性验证</strong></p><p style="line-height: 160%; box-sizing: content-box; margin: 10px 0; color: #333;">而二手数据，因为收集的过程由第三方完成。因此数据的可信性和准确度，就依赖于第三方机构的可信性。</p><h4 style="line-height: 160%; box-sizing: content-box; font-size: 20px; color: #333;">抽样方法</h4><h5 style="line-height: 160%; box-sizing: content-box; font-weight: 700; font-size: 16px; color: #333;">如何获取一手数据？</h5><p style="line-height: 160%; box-sizing: content-box; margin: 10px 0; color: #333;">当我们需要获取一手数据的时候，一种常见的方式就是<strong style="line-height: 160%; box-sizing: content-box; font-weight: 700;">抽样调查</strong></p><p style="line-height: 160%; box-sizing: content-box; margin: 10px 0; color: #333;">抽样调查不止在传统行业中比较常用，在现在的互联网企业中也时常会用到。比如一些优惠活动或者特定客群营销等方案的测试，就需要用到抽样的方式选择测试群体。在做抽样调查时，我们都希望尽可能地减少误差，让抽样的样本能够充分代表整体的特征。那么误差和哪些因素相关呢，抽样误差（Sampling Error）的大小，主要由样本容量的大小和抽样方式来决定。</p><p style="line-height: 160%; box-sizing: content-box; margin: 10px 0; color: #333;">一般，我们认为抽样可以分为两类：一类我们叫做概率抽样（Probability Samling），也叫做客观抽样。第二类，我们叫做非概率抽样（Non-probability Sampling），也叫做主观抽样。下面我们介绍两种抽样方法</p><h5 style="line-height: 160%; box-sizing: content-box; font-weight: 700; font-size: 16px; color: #333;">概率抽样</h5><p style="line-height: 160%; box-sizing: content-box; margin: 10px 0; color: #333;">顾名思义，是一种基于概率的抽样方式，因此也被称为客观抽样。从理论的角度来说，概率抽样是符合科学和统计原则的，抽样误差可以估计。也是在可能的情况下，最优先被推荐使用的抽样方法。但是，精确度高的方法，往往操作的复杂度和耗费的成本也会相对偏高。概率抽样，虽然可以避免主观判断带来的谬误，但是它常常受限于项目经费、时间和保密性等原则，从而难以实际使用</p><h5 style="line-height: 160%; box-sizing: content-box; font-weight: 700; font-size: 16px; color: #333;">非概率抽样</h5><p style="line-height: 160%; box-sizing: content-box; margin: 10px 0; color: #333;">和概率抽样相反，非概率抽样是一种简单、易使用的抽样方式。它主要通过抽样者的判断，包括对样本特征的判断和对项目成本的考量，综合特殊的要求或者设定，最终选择合适的样本。因此，这种方法会收到主观因素的影响，不符合统计科学的原则，抽样误差是无法估计和计算的。但是在实际应用中，大量的案例还是证明了非概率误差依然有一定的有效性。在样本量充足的前提下，通过设定简单的配比，以及选择有经验的抽样者，基本上可以保证抽样结果的有效性。而且由于非概率抽样比较容易重复操作，因此用此飞概率抽样反复进行同一试验，结果往往也有趋同性。另外，这一抽样方式，虽然无法衡量抽样误差，但是由于抽样过程可以进行设计和控制，因此可以更简单有效地控制非抽样误差（Non-sampling Error）。</p><p style="line-height: 160%; box-sizing: content-box; margin: 10px 0; color: #333;"><strong style="line-height: 160%; box-sizing: content-box; font-weight: 700;">总结来说，概率抽样和非概率抽样，我们可以通过以下的表格进行区别</strong></p><table style="margin: 2px 0 14px; color: #333; auto; border-collapse: collapse; box-sizing: border-box;"><thead style="line-height: 160%; box-sizing: content-box;"><tr style="line-height: 160%; box-sizing: content-box;"><th style="line-height: 160%; box-sizing: content-box; padding: 5px 14px 5px 12px; border: 1px solid #72777b; border-top: 0; background-color: #7b8184; font-weight: 300; color: #fff; padding-top: 6px;"></th><th style="line-height: 160%; box-sizing: content-box; padding: 5px 14px 5px 12px; border: 1px solid #72777b; border-top: 0; background-color: #7b8184; font-weight: 300; color: #fff; padding-top: 6px;">特点</th><th style="line-height: 160%; box-sizing: content-box; padding: 5px 14px 5px 12px; border: 1px solid #72777b; border-top: 0; background-color: #7b8184; font-weight: 300; color: #fff; padding-top: 6px;">优点</th><th style="line-height: 160%; box-sizing: content-box; padding: 5px 14px 5px 12px; border: 1px solid #72777b; border-top: 0; background-color: #7b8184; font-weight: 300; color: #fff; padding-top: 6px;">缺点</th></tr></thead><tbody style="line-height: 160%; box-sizing: content-box;"><tr style="line-height: 160%; box-sizing: content-box;"><td style="line-height: 160%; box-sizing: content-box; padding: 5px 14px 5px 12px; border: 1px solid #eaeaea;">概率抽样</td><td style="line-height: 160%; box-sizing: content-box; padding: 5px 14px 5px 12px; border: 1px solid #eaeaea;">根据科学原则抽取样本</td><td style="line-height: 160%; box-sizing: content-box; padding: 5px 14px 5px 12px; border: 1px solid #eaeaea;">抽样误差可以估计客观</td><td style="line-height: 160%; box-sizing: content-box; padding: 5px 14px 5px 12px; border: 1px solid #eaeaea;">成本贵 耗时长 操作复杂 局限多</td></tr><tr style="line-height: 160%; box-sizing: content-box;"><td style="line-height: 160%; box-sizing: content-box; padding: 5px 14px 5px 12px; border: 1px solid #eaeaea;">非概率抽样</td><td style="line-height: 160%; box-sizing: content-box; padding: 5px 14px 5px 12px; border: 1px solid #eaeaea;">根据抽样者的主观判断抽取样本</td><td style="line-height: 160%; box-sizing: content-box; padding: 5px 14px 5px 12px; border: 1px solid #eaeaea;">成本低 时间短 操作简单 可行性强</td><td style="line-height: 160%; box-sizing: content-box; padding: 5px 14px 5px 12px; border: 1px solid #eaeaea;">无法衡量抽样误差  存在主管谬误 对抽样者经验要求高</td></tr></tbody></table><h5 style="line-height: 160%; box-sizing: content-box; font-weight: 700; font-size: 16px; color: #333;">概率抽样方法</h5><p style="line-height: 160%; box-sizing: content-box; margin: 10px 0; color: #333;"><strong style="line-height: 160%; box-sizing: content-box; font-weight: 700;">介绍了概率抽样和非概率抽样之后，我们重点看一下概率抽样方法，常用的概率抽样方法主要有以下4种</strong></p><h6 style="line-height: 160%; box-sizing: content-box; font-size: 13px; color: #333;">简单随机抽样（Simaple Random Sampling）</h6><p style="line-height: 160%; box-sizing: content-box; margin: 10px 0; color: #333;">使用简单随机抽样方式进行抽样，总体中的每个样本都有同等的被抽取到的机会。因此，可以用以下的公式，来确定样本量和抽样误差之间的关系</p><p style="line-height: 160%; box-sizing: content-box; margin: 10px 0; color: #333;"><span style="display: block; margin: 1em 0; text-align: center; line-height: 160%; box-sizing: content-box;"><span style="font: normal 1.21em KaTeX_Main,Times New Roman,serif; white-space: nowrap; text-indent: 0; text-rendering: auto; line-height: 160%; box-sizing: content-box; display: inline-block; text-align: initial;"><span style="line-height: 160%; box-sizing: content-box; clip: 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content-box; display: inline-block; .12em; font-size: 1.42857143em; -ms-high-contrast-adjust: none;"></span><span style="line-height: 160%; box-sizing: content-box; -ms-high-contrast-adjust: none;"><span style="line-height: 160%; box-sizing: content-box; display: inline-table; table-layout: fixed; margin-right: -2px; -ms-high-contrast-adjust: none;"><span style="line-height: 160%; box-sizing: content-box; display: table-row; text-align: center; -ms-high-contrast-adjust: none;"><span style="line-height: 160%; box-sizing: content-box; display: table-cell; vertical-align: bottom; position: relative; height: 0.6915428571428572em; -ms-high-contrast-adjust: none;"><span style="line-height: 160%; box-sizing: content-box; display: block; height: 0; position: relative; top: -2.656em; -ms-high-contrast-adjust: none;"><span style="line-height: 160%; box-sizing: content-box; display: inline-block; overflow: hidden; 0; height: 3em; -ms-high-contrast-adjust: none;"></span><span style="line-height: 160%; box-sizing: content-box; display: inline-block; font-size: .71428571em; -ms-high-contrast-adjust: none;"><span style="line-height: 160%; box-sizing: content-box; -ms-high-contrast-adjust: none;"><span style="line-height: 160%; box-sizing: content-box; -ms-high-contrast-adjust: none;">2</span></span></span></span><span style="line-height: 160%; box-sizing: content-box; display: block; height: 0; position: relative; top: -3.1275em; -ms-high-contrast-adjust: none;"><span style="line-height: 160%; box-sizing: content-box; display: inline-block; overflow: hidden; 0; height: 3em; -ms-high-contrast-adjust: none;"></span><span style="line-height: 160%; box-sizing: content-box; 100%; position: relative; overflow: hidden; display: inline-block; height: 0.245em; -ms-high-contrast-adjust: none;"><img src="data:image/svg+xml;charset=utf8,%3Csvg%20width%3D%22400em%22%20height%3D%220.245em%22%20viewbox%3D%220%200%20400000%20200%22%20preserveaspectratio%3D%22xMinYMin%20slice%22%20style%3D%22display%3A%20block%3B%20position%3A%20absolute%3B%20width%3A%20100%25%3B%20fill%3A%20currentColor%3B%20stroke%3A%20currentColor%3B%20fill-rule%3A%20nonzero%3B%20fill-opacity%3A%201%3B%20stroke-width%3A%201%3B%20stroke-linecap%3A%20butt%3B%20stroke-linejoin%3A%20miter%3B%20stroke-miterlimit%3A%204%3B%20stroke-dasharray%3A%20none%3B%20stroke-dashoffset%3A%200%3B%20stroke-opacity%3A%201%3B%20line-height%3A%20160%25%3B%20box-sizing%3A%20content-box%3B%20-ms-high-contrast-adjust%3A%20none%3B%22%3E%3Cpath%20d%3D%22M0%2080H400000%20v40H0z%20M0%2080H400000%20v40H0z%22%20style%3D%22line-height%3A%20160%25%3B%20box-sizing%3A%20content-box%3B%20stroke%3A%20none%3B%20-ms-high-contrast-adjust%3A%20none%3B%22%2F%3E%3C%2Fsvg%3E" style=" 100%;"></img></span></span><span style="line-height: 160%; box-sizing: content-box; display: block; height: 0; position: relative; top: -3.384em; -ms-high-contrast-adjust: none;"><span style="line-height: 160%; box-sizing: content-box; display: inline-block; overflow: hidden; 0; height: 3em; -ms-high-contrast-adjust: none;"></span><span style="line-height: 160%; box-sizing: content-box; display: inline-block; font-size: .71428571em; -ms-high-contrast-adjust: none;"><span style="line-height: 160%; box-sizing: content-box; -ms-high-contrast-adjust: none;"><span style="line-height: 160%; box-sizing: content-box; font-family: KaTeX_Math; font-style: italic; margin-right: 0.0037em; -ms-high-contrast-adjust: none;">α</span></span></span></span></span><span style="line-height: 160%; box-sizing: content-box; display: table-cell; vertical-align: bottom; font-size: 1px; -ms-high-contrast-adjust: none;">​</span></span><span style="line-height: 160%; box-sizing: content-box; display: table-row; text-align: center; -ms-high-contrast-adjust: none;"><span style="line-height: 160%; box-sizing: content-box; display: table-cell; vertical-align: bottom; position: relative; height: 0.344em; -ms-high-contrast-adjust: none;"></span></span></span></span><span style="line-height: 160%; box-sizing: content-box; display: inline-block; .12em; font-size: 1.42857143em; -ms-high-contrast-adjust: none;"></span></span></span></span></span></span><span style="line-height: 160%; box-sizing: content-box; display: table-cell; vertical-align: bottom; font-size: 1px; -ms-high-contrast-adjust: none;">​</span></span><span style="line-height: 160%; box-sizing: content-box; display: table-row; -ms-high-contrast-adjust: none;"><span style="line-height: 160%; box-sizing: content-box; display: table-cell; vertical-align: bottom; position: relative; height: 0.3907999999999999em; -ms-high-contrast-adjust: none;"></span></span></span></span></span><span style="line-height: 160%; box-sizing: content-box; -ms-high-contrast-adjust: none;"><span style="line-height: 160%; box-sizing: content-box; -ms-high-contrast-adjust: none;">)</span><span style="line-height: 160%; box-sizing: content-box; text-align: left; -ms-high-contrast-adjust: none;"><span style="line-height: 160%; box-sizing: content-box; display: inline-table; table-layout: fixed; -ms-high-contrast-adjust: none;"><span style="line-height: 160%; box-sizing: content-box; display: table-row; -ms-high-contrast-adjust: none;"><span style="line-height: 160%; box-sizing: content-box; display: table-cell; vertical-align: bottom; position: relative; height: 0.8141079999999999em; -ms-high-contrast-adjust: none;"><span style="line-height: 160%; box-sizing: content-box; display: block; height: 0; position: relative; top: -3.063em; margin-right: 0.05em; -ms-high-contrast-adjust: none;"><span style="line-height: 160%; box-sizing: content-box; display: inline-block; overflow: hidden; 0; height: 2.7em; -ms-high-contrast-adjust: none;"></span><span style="line-height: 160%; box-sizing: content-box; display: inline-block; font-size: .7em; -ms-high-contrast-adjust: none;"><span style="line-height: 160%; box-sizing: content-box; -ms-high-contrast-adjust: none;">2</span></span></span></span></span></span></span></span><span style="line-height: 160%; box-sizing: content-box; -ms-high-contrast-adjust: none;"><span style="line-height: 160%; box-sizing: content-box; font-family: KaTeX_Math; font-style: italic; margin-right: 0.0037em; -ms-high-contrast-adjust: none;">α</span><span style="line-height: 160%; box-sizing: content-box; text-align: left; -ms-high-contrast-adjust: none;"><span style="line-height: 160%; box-sizing: content-box; display: inline-table; table-layout: fixed; -ms-high-contrast-adjust: none;"><span style="line-height: 160%; box-sizing: content-box; display: table-row; -ms-high-contrast-adjust: none;"><span style="line-height: 160%; box-sizing: content-box; display: table-cell; vertical-align: bottom; position: relative; height: 0.8141079999999999em; -ms-high-contrast-adjust: none;"><span style="line-height: 160%; box-sizing: content-box; display: block; height: 0; position: relative; top: -3.063em; margin-right: 0.05em; -ms-high-contrast-adjust: none;"><span style="line-height: 160%; box-sizing: content-box; display: inline-block; overflow: hidden; 0; height: 2.7em; -ms-high-contrast-adjust: none;"></span><span style="line-height: 160%; box-sizing: content-box; display: inline-block; font-size: .7em; -ms-high-contrast-adjust: none;"><span style="line-height: 160%; box-sizing: content-box; -ms-high-contrast-adjust: none;">2</span></span></span></span></span></span></span></span></span></span></span><span style="line-height: 160%; box-sizing: content-box; display: table-cell; vertical-align: bottom; font-size: 1px; -ms-high-contrast-adjust: none;">​</span></span><span style="line-height: 160%; box-sizing: content-box; display: table-row; text-align: center; -ms-high-contrast-adjust: none;"><span style="line-height: 160%; box-sizing: content-box; display: table-cell; vertical-align: bottom; position: relative; height: 0.686em; -ms-high-contrast-adjust: none;"></span></span></span></span><span style="line-height: 160%; box-sizing: content-box; display: inline-block; .12em; -ms-high-contrast-adjust: none;"></span></span></span></span></span></span></p><p style="line-height: 160%; box-sizing: content-box; margin: 10px 0; color: #333;">其中n表示样本量<span style="font: normal 1.21em KaTeX_Main,Times New Roman,serif; white-space: nowrap; text-indent: 0; text-rendering: auto; line-height: 160%; box-sizing: content-box;"><span style="line-height: 160%; box-sizing: content-box; clip: rect(1px,1px,1px,1px); padding: 0; border: 0; overflow: hidden; position: fixed; -ms-high-contrast-adjust: none;"></span><span style="line-height: 160%; box-sizing: content-box; display: inline-block; -ms-high-contrast-adjust: none;"><span style="line-height: 160%; box-sizing: content-box; display: inline-block; height: 0.68333em; -ms-high-contrast-adjust: none;"></span><span style="line-height: 160%; box-sizing: content-box; display: inline-block; height: 1.0741299999999998em; vertical-align: -0.3907999999999999em; -ms-high-contrast-adjust: none;"></span><span style="line-height: 160%; box-sizing: content-box; position: relative; display: inline-block; -ms-high-contrast-adjust: none;"><span style="line-height: 160%; box-sizing: content-box; -ms-high-contrast-adjust: none;"><span style="line-height: 160%; box-sizing: content-box; font-family: KaTeX_Math; font-style: italic; margin-right: 0.07153em; -ms-high-contrast-adjust: none;">Z</span><span style="line-height: 160%; box-sizing: content-box; text-align: left; -ms-high-contrast-adjust: none;"><span style="line-height: 160%; box-sizing: content-box; display: inline-table; table-layout: fixed; margin-right: -2px; -ms-high-contrast-adjust: none;"><span style="line-height: 160%; box-sizing: content-box; display: table-row; -ms-high-contrast-adjust: none;"><span style="line-height: 160%; box-sizing: content-box; display: table-cell; vertical-align: bottom; position: relative; height: 0.33408000000000004em; -ms-high-contrast-adjust: none;"><span style="line-height: 160%; box-sizing: content-box; display: block; height: 0; position: relative; top: -2.85em; margin-left: -0.07153em; margin-right: 0.05em; -ms-high-contrast-adjust: none;"><span style="line-height: 160%; box-sizing: content-box; display: inline-block; overflow: hidden; 0; height: 3em; -ms-high-contrast-adjust: none;"></span><span style="line-height: 160%; box-sizing: content-box; display: inline-block; font-size: .7em; -ms-high-contrast-adjust: none;"><span style="line-height: 160%; box-sizing: content-box; -ms-high-contrast-adjust: none;"><span style="line-height: 160%; box-sizing: content-box; -ms-high-contrast-adjust: none;"><span style="line-height: 160%; box-sizing: content-box; display: inline-block; .12em; font-size: 1.42857143em; -ms-high-contrast-adjust: none;"></span><span style="line-height: 160%; box-sizing: content-box; -ms-high-contrast-adjust: none;"><span style="line-height: 160%; box-sizing: content-box; display: inline-table; table-layout: fixed; margin-right: -2px; -ms-high-contrast-adjust: none;"><span style="line-height: 160%; box-sizing: content-box; display: table-row; text-align: center; -ms-high-contrast-adjust: none;"><span style="line-height: 160%; box-sizing: content-box; display: table-cell; vertical-align: bottom; position: relative; height: 0.6915428571428572em; -ms-high-contrast-adjust: none;"><span style="line-height: 160%; box-sizing: content-box; display: block; height: 0; position: relative; top: -2.656em; -ms-high-contrast-adjust: none;"><span style="line-height: 160%; box-sizing: content-box; display: inline-block; overflow: hidden; 0; height: 3em; -ms-high-contrast-adjust: none;"></span><span style="line-height: 160%; box-sizing: content-box; display: inline-block; font-size: .71428571em; -ms-high-contrast-adjust: none;"><span style="line-height: 160%; box-sizing: content-box; -ms-high-contrast-adjust: none;"><span style="line-height: 160%; box-sizing: content-box; -ms-high-contrast-adjust: none;">2</span></span></span></span><span style="line-height: 160%; box-sizing: content-box; display: block; height: 0; position: relative; top: -3.1275em; -ms-high-contrast-adjust: none;"><span style="line-height: 160%; box-sizing: content-box; display: inline-block; overflow: hidden; 0; height: 3em; -ms-high-contrast-adjust: none;"></span><span style="line-height: 160%; box-sizing: content-box; 100%; position: relative; overflow: hidden; display: inline-block; height: 0.245em; -ms-high-contrast-adjust: none;"><img src="data:image/svg+xml;charset=utf8,%3Csvg%20width%3D%22400em%22%20height%3D%220.245em%22%20viewbox%3D%220%200%20400000%20200%22%20preserveaspectratio%3D%22xMinYMin%20slice%22%20style%3D%22display%3A%20block%3B%20position%3A%20absolute%3B%20width%3A%20100%25%3B%20fill%3A%20currentColor%3B%20stroke%3A%20currentColor%3B%20fill-rule%3A%20nonzero%3B%20fill-opacity%3A%201%3B%20stroke-width%3A%201%3B%20stroke-linecap%3A%20butt%3B%20stroke-linejoin%3A%20miter%3B%20stroke-miterlimit%3A%204%3B%20stroke-dasharray%3A%20none%3B%20stroke-dashoffset%3A%200%3B%20stroke-opacity%3A%201%3B%20line-height%3A%20160%25%3B%20box-sizing%3A%20content-box%3B%20-ms-high-contrast-adjust%3A%20none%3B%22%3E%3Cpath%20d%3D%22M0%2080H400000%20v40H0z%20M0%2080H400000%20v40H0z%22%20style%3D%22line-height%3A%20160%25%3B%20box-sizing%3A%20content-box%3B%20stroke%3A%20none%3B%20-ms-high-contrast-adjust%3A%20none%3B%22%2F%3E%3C%2Fsvg%3E" style=" 100%;"></img></span></span><span style="line-height: 160%; box-sizing: content-box; display: block; height: 0; position: relative; top: -3.384em; -ms-high-contrast-adjust: none;"><span style="line-height: 160%; box-sizing: content-box; display: inline-block; overflow: hidden; 0; height: 3em; -ms-high-contrast-adjust: none;"></span><span style="line-height: 160%; box-sizing: content-box; display: inline-block; font-size: .71428571em; -ms-high-contrast-adjust: none;"><span style="line-height: 160%; box-sizing: content-box; -ms-high-contrast-adjust: none;"><span style="line-height: 160%; box-sizing: content-box; font-family: KaTeX_Math; font-style: italic; margin-right: 0.0037em; -ms-high-contrast-adjust: none;">α</span></span></span></span></span><span style="line-height: 160%; box-sizing: content-box; display: table-cell; vertical-align: bottom; font-size: 1px; -ms-high-contrast-adjust: none;">​</span></span><span style="line-height: 160%; box-sizing: content-box; display: table-row; text-align: center; -ms-high-contrast-adjust: none;"><span style="line-height: 160%; box-sizing: content-box; display: table-cell; vertical-align: bottom; position: relative; height: 0.344em; -ms-high-contrast-adjust: none;"></span></span></span></span><span style="line-height: 160%; box-sizing: content-box; display: inline-block; .12em; font-size: 1.42857143em; -ms-high-contrast-adjust: none;"></span></span></span></span></span></span><span style="line-height: 160%; box-sizing: content-box; display: table-cell; vertical-align: bottom; font-size: 1px; -ms-high-contrast-adjust: none;">​</span></span><span style="line-height: 160%; box-sizing: content-box; display: table-row; -ms-high-contrast-adjust: none;"><span style="line-height: 160%; box-sizing: content-box; display: table-cell; vertical-align: bottom; position: relative; height: 0.3907999999999999em; -ms-high-contrast-adjust: none;"></span></span></span></span></span></span></span></span></p><p style="line-height: 160%; box-sizing: content-box; margin: 10px 0; color: #333;">为置信区间，如果没有指定，一般常用取值为1.96（即95%置信区间）<span style="font: normal 1.21em KaTeX_Main,Times New Roman,serif; white-space: nowrap; text-indent: 0; text-rendering: auto; line-height: 160%; box-sizing: content-box;"><span style="line-height: 160%; box-sizing: content-box; clip: rect(1px,1px,1px,1px); padding: 0; border: 0; overflow: hidden; position: fixed; -ms-high-contrast-adjust: none;"></span><span style="line-height: 160%; box-sizing: content-box; display: inline-block; -ms-high-contrast-adjust: none;"><span style="line-height: 160%; box-sizing: content-box; display: inline-block; height: 0.43056em; -ms-high-contrast-adjust: none;"></span><span style="line-height: 160%; box-sizing: content-box; display: inline-block; height: 0.43056em; vertical-align: 0em; -ms-high-contrast-adjust: none;"></span><span style="line-height: 160%; box-sizing: content-box; position: relative; display: inline-block; -ms-high-contrast-adjust: none;"><span style="line-height: 160%; box-sizing: content-box; font-family: KaTeX_Math; font-style: italic; margin-right: 0.0037em; -ms-high-contrast-adjust: none;">α</span></span></span></span></p><p style="line-height: 160%; box-sizing: content-box; margin: 10px 0; color: #333;">为总体标准差<span style="font: normal 1.21em KaTeX_Main,Times New Roman,serif; white-space: nowrap; text-indent: 0; text-rendering: auto; line-height: 160%; box-sizing: content-box;"><span style="line-height: 160%; box-sizing: content-box; clip: rect(1px,1px,1px,1px); padding: 0; border: 0; overflow: hidden; position: fixed; -ms-high-contrast-adjust: none;"></span><span style="line-height: 160%; box-sizing: content-box; display: inline-block; -ms-high-contrast-adjust: none;"><span style="line-height: 160%; box-sizing: content-box; display: inline-block; height: 0.68333em; -ms-high-contrast-adjust: none;"></span><span style="line-height: 160%; box-sizing: content-box; display: inline-block; height: 0.68333em; vertical-align: 0em; -ms-high-contrast-adjust: none;"></span><span style="line-height: 160%; box-sizing: content-box; position: relative; display: inline-block; -ms-high-contrast-adjust: none;"><span style="line-height: 160%; box-sizing: content-box; font-family: KaTeX_Math; font-style: italic; margin-right: 0.05764em; -ms-high-contrast-adjust: none;">E</span></span></span></span><br/>为抽样误差范围<br/>因此根据这个公式，可以实现n和E之间的互相推导</p><p style="line-height: 160%; box-sizing: content-box; margin: 10px 0; color: #333;">简单随机抽样中，默认了一个假设，也就是被抽中的机会是均等的，听上去似乎很正常，但是实际上要做到这一点，并不容易。由于改的外观特征和抽样者的心理因素等影响，每个个体被抽到的机会并不是均匀地。因此在实际应用中，通常用抽签或者随机数等形式来进行操作，减少偏差。这样的形式，也决定了在大型调研中简单随机抽样的方式比较难以采用，一般多应用于小型的调研，或者测试客户群体选择等。</p><h6 style="line-height: 160%; box-sizing: content-box; font-size: 13px; color: #333;">分层抽样（Stratifide Sampling）</h6><p style="line-height: 160%; box-sizing: content-box; margin: 10px 0; color: #333;">正如之前提到的，简单随机抽样的假设并不总是成立，如果总体可以按照一些特征分成若干层。层与层之间差异明显，每个层内部的个体特征相近，那么我们可以对每个层做简单随机抽样。抽样结果合并的集合，就是我们最终确认的抽样样本。</p><p style="line-height: 160%; box-sizing: content-box; margin: 10px 0; color: #333;">在实际操作中，我们可以按照每一层的个体数量来决定抽取数量，是的每个层抽取的比例都相等，这样的抽样我们叫做按比例分层抽样。一般，如果每层重要性差不多，数量差异也不是很大的情况下，我们都是这样操作的。</p><p style="line-height: 160%; box-sizing: content-box; margin: 10px 0; color: #333;">而如果有一些层非常重要，或者有些层的个体数非常少，那我们就要采用非按比例分层抽样的方法。</p><p style="line-height: 160%; box-sizing: content-box; margin: 10px 0; color: #333;">如果总体中个体间呈现明显的几类，那么使用分层抽样可以更好地反映总体，避免随机抽样可能带来的样本集中或特征缺失的情况。因此，在概率抽样中，分层抽样也是使用最多的一种。我们在对城市，或者是大型的业务线进行研究的时候，都可以采用分层抽样。</p><h6 style="line-height: 160%; box-sizing: content-box; font-size: 13px; color: #333;">系统抽样（Systematic Sampling）</h6><p style="line-height: 160%; box-sizing: content-box; margin: 10px 0; color: #333;">除了分层抽样之外，系统抽样也对简单随机抽样，进行了改进。使用系统抽样的时候，仍然需要将个体进行编号，然后根据抽样样本容量决定抽样的间距。因此又叫等距抽样或者机械抽样。这种方法，减少了抽样过程中的人力和时间消耗。不过，系统抽样一般很少作为单独的抽样方法是用，通常是配合其他方法一起进行。</p><h6 style="line-height: 160%; box-sizing: content-box; font-size: 13px; color: #333;">分段抽样（Multi-stage Sampling）</h6><p style="line-height: 160%; box-sizing: content-box; margin: 10px 0; color: #333;">前面提到的，都是一次性抽取完成样本的方法，这些方法可以统称为单阶段抽样。然而在有些情况下，我们并不能一次性完成样本的抽取，比如在全国范围内选择一定数量的用户作为试点调查。这个时候我们需要分阶段地去完成抽样过程，这种方法，我们叫做分段抽样。</p><p style="line-height: 160%; box-sizing: content-box; margin: 10px 0; color: #333;">分段抽样，我们首先把总体划分成一些大小差不多的群体。在这些群体中随机抽取几个。被抽中的群体，就作为下一步进行随机抽样的“总体”</p><p style="line-height: 160%; box-sizing: content-box; margin: 10px 0; color: #333;">因此，在学习过程中，一定要注意区分分段抽样和分层抽样。虽然两者都是对总体进行了一定的划分。但是分层抽样是按照一定特征进行划分，划分的目的是为了避免特征的过分集中和缺失。抽取的过程也是一步完成的，只有在分层之后才会进行随机抽样。而分段抽样则不同，它是由于总体太大，无法直接进行抽取，所以才需要进行多步抽样。每一次对总体的划分都是为了进行随机抽取，而抽取后，下一步的“总体”就会得到一定程度的减小。</p><p style="line-height: 160%; box-sizing: content-box; margin: 10px 0; color: #333;"><img src="【数据分析师 Level 1 】3-1_files/选择抽样方法.png" type="image/png" data-filename="选择抽样方法.png"/></p><h4 style="line-height: 160%; box-sizing: content-box; font-size: 20px; color: #333;">例题精讲</h4><p style="line-height: 160%; box-sizing: content-box; margin: 10px 0; color: #333;"><strong style="line-height: 160%; box-sizing: content-box; font-weight: 700;">1.二手数据的特点是（）</strong></p><p style="line-height: 160%; box-sizing: content-box; margin: 10px 0; color: #333;">A.数据缺乏可靠性</p><p style="line-height: 160%; box-sizing: content-box; margin: 10px 0; color: #333;">B.不适合自己的研究需要</p><p style="line-height: 160%; box-sizing: content-box; margin: 10px 0; color: #333;">C.采集数据的成本低，但搜集比较困难</p><p style="line-height: 160%; box-sizing: content-box; margin: 10px 0; color: #333;">D.采集数据的成本低，搜集比较容易</p><p style="line-height: 160%; box-sizing: content-box; margin: 10px 0; color: #333;">答案：D</p><p style="line-height: 160%; box-sizing: content-box; margin: 10px 0; color: #333;">解析：熟悉一手数据和二手数据的特点</p><p style="line-height: 160%; box-sizing: content-box; margin: 10px 0; color: #333;"><strong style="line-height: 160%; box-sizing: content-box; font-weight: 700;">2.与概率抽样相比，非概率抽样的缺点是（）</strong></p><p style="line-height: 160%; box-sizing: content-box; margin: 10px 0; color: #333;">A.调查成本比较高</p><p style="line-height: 160%; box-sizing: content-box; margin: 10px 0; color: #333;">B.不适合探索性研究</p><p style="line-height: 160%; box-sizing: content-box; margin: 10px 0; color: #333;">C.样本统计量的分布是确定的</p><p style="line-height: 160%; box-sizing: content-box; margin: 10px 0; color: #333;">D.无法使用样本的结果对总体相应的参数进行推断</p><p style="line-height: 160%; box-sizing: content-box; margin: 10px 0; color: #333;">答案：D</p><p style="line-height: 160%; box-sizing: content-box; margin: 10px 0; color: #333;">解析：熟悉概率抽样和非概率抽样的异同</p><p style="line-height: 160%; box-sizing: content-box; margin: 10px 0; color: #333;"><strong style="line-height: 160%; box-sizing: content-box; font-weight: 700;">3.为了估计A市愿意坐地铁上下班的人数的比例，在收集数据时，最有可能采用的数据搜集方法是？</strong></p><p style="line-height: 160%; box-sizing: content-box; margin: 10px 0; color: #333;">A.普查</p><p style="line-height: 160%; box-sizing: content-box; margin: 10px 0; color: #333;">B.实验</p><p style="line-height: 160%; box-sizing: content-box; margin: 10px 0; color: #333;">C.随机抽样</p><p style="line-height: 160%; box-sizing: content-box; margin: 10px 0; color: #333;">D.公开发表的资料</p><p style="line-height: 160%; box-sizing: content-box; margin: 10px 0; color: #333;">答案：C</p><p style="line-height: 160%; box-sizing: content-box; margin: 10px 0; color: #333;">解析：在不考虑人力和时间的前提下，上述选项中操作最简单，需要考虑的问题最少的是随机抽样，也能尽可能保证每个个体被抽中的可能性均等</p><p style="line-height: 160%; box-sizing: content-box; margin: 10px 0; color: #333;"><strong style="line-height: 160%; box-sizing: content-box; font-weight: 700;">4.用简单随机重复抽样方法抽取样本单位，如果要使抽样平均误差降低50%，则样本容量需要扩大到原来的（）倍</strong></p><p style="line-height: 160%; box-sizing: content-box; margin: 10px 0; color: #333;">A.0.5</p><p style="line-height: 160%; box-sizing: content-box; margin: 10px 0; color: #333;">B.不变</p><p style="line-height: 160%; box-sizing: content-box; margin: 10px 0; color: #333;">C.2</p><p style="line-height: 160%; box-sizing: content-box; margin: 10px 0; color: #333;">D.4</p><p style="line-height: 160%; box-sizing: content-box; margin: 10px 0; color: #333;">答案：D</p><p style="line-height: 160%; box-sizing: content-box; margin: 10px 0; color: #333;">解析：根据简单随机抽样的样本量确定公式</p><p style="line-height: 160%; box-sizing: content-box; margin: 10px 0; color: #333;"><span style="display: block; margin: 1em 0; text-align: center; line-height: 160%; box-sizing: content-box;"><span style="font: normal 1.21em KaTeX_Main,Times New Roman,serif; white-space: nowrap; text-indent: 0; text-rendering: auto; line-height: 160%; box-sizing: content-box; display: inline-block; text-align: initial;"><span style="line-height: 160%; box-sizing: content-box; clip: rect(1px,1px,1px,1px); padding: 0; border: 0; overflow: hidden; position: fixed; -ms-high-contrast-adjust: none;"></span><span style="line-height: 160%; box-sizing: content-box; display: inline-block; -ms-high-contrast-adjust: none;"><span style="line-height: 160%; box-sizing: content-box; display: inline-block; height: 1.5949079999999998em; -ms-high-contrast-adjust: none;"></span><span style="line-height: 160%; box-sizing: content-box; display: inline-block; height: 2.2809079999999997em; vertical-align: -0.686em; -ms-high-contrast-adjust: none;"></span><span style="line-height: 160%; box-sizing: content-box; position: relative; display: inline-block; -ms-high-contrast-adjust: none;"><span style="line-height: 160%; box-sizing: content-box; font-family: KaTeX_Math; font-style: italic; -ms-high-contrast-adjust: none;">n</span><span style="line-height: 160%; box-sizing: content-box; display: inline-block; border: 0 solid; position: relative; margin-right: 0.2777777777777778em; -ms-high-contrast-adjust: none;"></span><span style="line-height: 160%; box-sizing: content-box; -ms-high-contrast-adjust: none;">=</span><span style="line-height: 160%; box-sizing: content-box; display: inline-block; border: 0 solid; position: relative; margin-right: 0.2777777777777778em; -ms-high-contrast-adjust: none;"></span><span style="line-height: 160%; box-sizing: content-box; -ms-high-contrast-adjust: none;"><span style="line-height: 160%; box-sizing: content-box; display: inline-block; .12em; -ms-high-contrast-adjust: none;"></span><span style="line-height: 160%; box-sizing: content-box; -ms-high-contrast-adjust: none;"><span style="line-height: 160%; box-sizing: content-box; display: inline-table; table-layout: fixed; margin-right: -2px; -ms-high-contrast-adjust: none;"><span style="line-height: 160%; box-sizing: content-box; display: table-row; text-align: center; -ms-high-contrast-adjust: none;"><span style="line-height: 160%; box-sizing: content-box; display: table-cell; vertical-align: bottom; position: relative; height: 1.5949079999999998em; -ms-high-contrast-adjust: none;"><span style="line-height: 160%; box-sizing: content-box; display: block; height: 0; position: relative; top: -2.314em; -ms-high-contrast-adjust: none;"><span style="line-height: 160%; box-sizing: content-box; display: inline-block; overflow: hidden; 0; height: 3em; -ms-high-contrast-adjust: none;"></span><span style="line-height: 160%; box-sizing: content-box; display: inline-block; -ms-high-contrast-adjust: none;"><span style="line-height: 160%; box-sizing: content-box; -ms-high-contrast-adjust: none;"><span style="line-height: 160%; box-sizing: content-box; font-family: KaTeX_Math; font-style: italic; margin-right: 0.05764em; -ms-high-contrast-adjust: none;">E</span><span style="line-height: 160%; box-sizing: content-box; text-align: left; -ms-high-contrast-adjust: none;"><span style="line-height: 160%; box-sizing: content-box; display: inline-table; table-layout: fixed; -ms-high-contrast-adjust: none;"><span style="line-height: 160%; box-sizing: content-box; display: table-row; -ms-high-contrast-adjust: none;"><span style="line-height: 160%; box-sizing: content-box; display: table-cell; vertical-align: bottom; position: relative; height: 0.740108em; -ms-high-contrast-adjust: none;"><span style="line-height: 160%; box-sizing: content-box; display: block; height: 0; position: relative; top: -2.9890000000000003em; margin-right: 0.05em; -ms-high-contrast-adjust: none;"><span style="line-height: 160%; box-sizing: content-box; display: inline-block; overflow: hidden; 0; height: 2.7em; -ms-high-contrast-adjust: none;"></span><span style="line-height: 160%; box-sizing: content-box; display: inline-block; font-size: .7em; -ms-high-contrast-adjust: none;"><span style="line-height: 160%; box-sizing: content-box; -ms-high-contrast-adjust: none;">2</span></span></span></span></span></span></span></span></span></span><span style="line-height: 160%; box-sizing: content-box; display: block; height: 0; position: relative; top: -3.15em; -ms-high-contrast-adjust: none;"><span style="line-height: 160%; box-sizing: content-box; display: inline-block; overflow: hidden; 0; height: 3em; -ms-high-contrast-adjust: none;"></span><span style="line-height: 160%; box-sizing: content-box; 100%; position: relative; overflow: hidden; display: inline-block; height: 0.2em; -ms-high-contrast-adjust: none;"><img src="data:image/svg+xml;charset=utf8,%3Csvg%20width%3D%22400em%22%20height%3D%220.2em%22%20viewbox%3D%220%200%20400000%20200%22%20preserveaspectratio%3D%22xMinYMin%20slice%22%20style%3D%22display%3A%20block%3B%20position%3A%20absolute%3B%20width%3A%20100%25%3B%20fill%3A%20currentColor%3B%20stroke%3A%20currentColor%3B%20fill-rule%3A%20nonzero%3B%20fill-opacity%3A%201%3B%20stroke-width%3A%201%3B%20stroke-linecap%3A%20butt%3B%20stroke-linejoin%3A%20miter%3B%20stroke-miterlimit%3A%204%3B%20stroke-dasharray%3A%20none%3B%20stroke-dashoffset%3A%200%3B%20stroke-opacity%3A%201%3B%20line-height%3A%20160%25%3B%20box-sizing%3A%20content-box%3B%20-ms-high-contrast-adjust%3A%20none%3B%22%3E%3Cpath%20d%3D%22M0%2080H400000%20v40H0z%20M0%2080H400000%20v40H0z%22%20style%3D%22line-height%3A%20160%25%3B%20box-sizing%3A%20content-box%3B%20stroke%3A%20none%3B%20-ms-high-contrast-adjust%3A%20none%3B%22%2F%3E%3C%2Fsvg%3E" style=" 100%;"></img></span></span><span style="line-height: 160%; box-sizing: content-box; display: block; height: 0; position: relative; top: -3.7808em; -ms-high-contrast-adjust: none;"><span style="line-height: 160%; box-sizing: content-box; display: inline-block; overflow: hidden; 0; height: 3em; -ms-high-contrast-adjust: none;"></span><span style="line-height: 160%; box-sizing: content-box; display: inline-block; -ms-high-contrast-adjust: none;"><span style="line-height: 160%; box-sizing: content-box; -ms-high-contrast-adjust: none;">(</span><span style="line-height: 160%; box-sizing: content-box; -ms-high-contrast-adjust: none;"><span style="line-height: 160%; box-sizing: content-box; font-family: KaTeX_Math; font-style: italic; margin-right: 0.07153em; -ms-high-contrast-adjust: none;">Z</span><span style="line-height: 160%; box-sizing: content-box; text-align: left; -ms-high-contrast-adjust: none;"><span style="line-height: 160%; box-sizing: content-box; display: inline-table; table-layout: fixed; margin-right: -2px; -ms-high-contrast-adjust: none;"><span style="line-height: 160%; box-sizing: content-box; display: table-row; -ms-high-contrast-adjust: none;"><span style="line-height: 160%; box-sizing: content-box; display: table-cell; vertical-align: bottom; position: relative; height: 0.33408000000000004em; -ms-high-contrast-adjust: none;"><span style="line-height: 160%; box-sizing: content-box; display: block; height: 0; position: relative; top: -2.85em; margin-left: -0.07153em; margin-right: 0.05em; -ms-high-contrast-adjust: none;"><span style="line-height: 160%; box-sizing: content-box; display: inline-block; overflow: hidden; 0; height: 3em; -ms-high-contrast-adjust: none;"></span><span style="line-height: 160%; box-sizing: content-box; display: inline-block; font-size: .7em; -ms-high-contrast-adjust: none;"><span style="line-height: 160%; box-sizing: content-box; -ms-high-contrast-adjust: none;"><span style="line-height: 160%; box-sizing: content-box; -ms-high-contrast-adjust: none;"><span style="line-height: 160%; box-sizing: content-box; display: inline-block; .12em; font-size: 1.42857143em; -ms-high-contrast-adjust: none;"></span><span style="line-height: 160%; box-sizing: content-box; -ms-high-contrast-adjust: none;"><span style="line-height: 160%; box-sizing: content-box; display: inline-table; table-layout: fixed; margin-right: -2px; -ms-high-contrast-adjust: none;"><span style="line-height: 160%; box-sizing: content-box; display: table-row; text-align: center; -ms-high-contrast-adjust: none;"><span style="line-height: 160%; box-sizing: content-box; display: table-cell; vertical-align: bottom; position: relative; height: 0.6915428571428572em; -ms-high-contrast-adjust: none;"><span style="line-height: 160%; box-sizing: content-box; display: block; height: 0; position: relative; top: -2.656em; -ms-high-contrast-adjust: none;"><span style="line-height: 160%; box-sizing: content-box; display: inline-block; overflow: hidden; 0; height: 3em; -ms-high-contrast-adjust: none;"></span><span style="line-height: 160%; box-sizing: content-box; display: inline-block; font-size: .71428571em; -ms-high-contrast-adjust: none;"><span style="line-height: 160%; box-sizing: content-box; -ms-high-contrast-adjust: none;"><span style="line-height: 160%; box-sizing: content-box; -ms-high-contrast-adjust: none;">2</span></span></span></span><span style="line-height: 160%; box-sizing: content-box; display: block; height: 0; position: relative; top: -3.1275em; -ms-high-contrast-adjust: none;"><span style="line-height: 160%; box-sizing: content-box; display: inline-block; overflow: hidden; 0; height: 3em; -ms-high-contrast-adjust: none;"></span><span style="line-height: 160%; box-sizing: content-box; 100%; position: relative; overflow: hidden; display: inline-block; height: 0.245em; -ms-high-contrast-adjust: none;"><img src="data:image/svg+xml;charset=utf8,%3Csvg%20width%3D%22400em%22%20height%3D%220.245em%22%20viewbox%3D%220%200%20400000%20200%22%20preserveaspectratio%3D%22xMinYMin%20slice%22%20style%3D%22display%3A%20block%3B%20position%3A%20absolute%3B%20width%3A%20100%25%3B%20fill%3A%20currentColor%3B%20stroke%3A%20currentColor%3B%20fill-rule%3A%20nonzero%3B%20fill-opacity%3A%201%3B%20stroke-width%3A%201%3B%20stroke-linecap%3A%20butt%3B%20stroke-linejoin%3A%20miter%3B%20stroke-miterlimit%3A%204%3B%20stroke-dasharray%3A%20none%3B%20stroke-dashoffset%3A%200%3B%20stroke-opacity%3A%201%3B%20line-height%3A%20160%25%3B%20box-sizing%3A%20content-box%3B%20-ms-high-contrast-adjust%3A%20none%3B%22%3E%3Cpath%20d%3D%22M0%2080H400000%20v40H0z%20M0%2080H400000%20v40H0z%22%20style%3D%22line-height%3A%20160%25%3B%20box-sizing%3A%20content-box%3B%20stroke%3A%20none%3B%20-ms-high-contrast-adjust%3A%20none%3B%22%2F%3E%3C%2Fsvg%3E" style=" 100%;"></img></span></span><span style="line-height: 160%; box-sizing: content-box; display: block; height: 0; position: relative; top: -3.384em; -ms-high-contrast-adjust: none;"><span style="line-height: 160%; box-sizing: content-box; display: inline-block; overflow: hidden; 0; height: 3em; -ms-high-contrast-adjust: none;"></span><span style="line-height: 160%; box-sizing: content-box; display: inline-block; font-size: .71428571em; -ms-high-contrast-adjust: none;"><span style="line-height: 160%; box-sizing: content-box; -ms-high-contrast-adjust: none;"><span style="line-height: 160%; box-sizing: content-box; font-family: KaTeX_Math; font-style: italic; margin-right: 0.0037em; -ms-high-contrast-adjust: none;">α</span></span></span></span></span><span style="line-height: 160%; box-sizing: content-box; display: table-cell; vertical-align: bottom; font-size: 1px; -ms-high-contrast-adjust: none;">​</span></span><span style="line-height: 160%; box-sizing: content-box; display: table-row; text-align: center; -ms-high-contrast-adjust: none;"><span style="line-height: 160%; box-sizing: content-box; display: table-cell; vertical-align: bottom; position: relative; height: 0.344em; -ms-high-contrast-adjust: none;"></span></span></span></span><span style="line-height: 160%; box-sizing: content-box; display: inline-block; .12em; font-size: 1.42857143em; -ms-high-contrast-adjust: none;"></span></span></span></span></span></span><span style="line-height: 160%; box-sizing: content-box; display: table-cell; vertical-align: bottom; font-size: 1px; -ms-high-contrast-adjust: none;">​</span></span><span style="line-height: 160%; box-sizing: content-box; display: table-row; -ms-high-contrast-adjust: none;"><span style="line-height: 160%; box-sizing: content-box; display: table-cell; vertical-align: bottom; position: relative; height: 0.3907999999999999em; -ms-high-contrast-adjust: none;"></span></span></span></span></span><span style="line-height: 160%; box-sizing: content-box; -ms-high-contrast-adjust: none;"><span style="line-height: 160%; box-sizing: content-box; -ms-high-contrast-adjust: none;">)</span><span style="line-height: 160%; box-sizing: content-box; text-align: left; -ms-high-contrast-adjust: none;"><span style="line-height: 160%; box-sizing: content-box; display: inline-table; table-layout: fixed; -ms-high-contrast-adjust: none;"><span style="line-height: 160%; box-sizing: content-box; display: table-row; -ms-high-contrast-adjust: none;"><span style="line-height: 160%; box-sizing: content-box; display: table-cell; vertical-align: bottom; position: relative; height: 0.8141079999999999em; -ms-high-contrast-adjust: none;"><span style="line-height: 160%; box-sizing: content-box; display: block; height: 0; position: relative; top: -3.063em; margin-right: 0.05em; -ms-high-contrast-adjust: none;"><span style="line-height: 160%; box-sizing: content-box; display: inline-block; overflow: hidden; 0; height: 2.7em; -ms-high-contrast-adjust: none;"></span><span style="line-height: 160%; box-sizing: content-box; display: inline-block; font-size: .7em; -ms-high-contrast-adjust: none;"><span style="line-height: 160%; box-sizing: content-box; -ms-high-contrast-adjust: none;">2</span></span></span></span></span></span></span></span><span style="line-height: 160%; box-sizing: content-box; -ms-high-contrast-adjust: none;"><span style="line-height: 160%; box-sizing: content-box; font-family: KaTeX_Math; font-style: italic; margin-right: 0.0037em; -ms-high-contrast-adjust: none;">α</span><span style="line-height: 160%; box-sizing: content-box; text-align: left; -ms-high-contrast-adjust: none;"><span style="line-height: 160%; box-sizing: content-box; display: inline-table; table-layout: fixed; -ms-high-contrast-adjust: none;"><span style="line-height: 160%; box-sizing: content-box; display: table-row; -ms-high-contrast-adjust: none;"><span style="line-height: 160%; box-sizing: content-box; display: table-cell; vertical-align: bottom; position: relative; height: 0.8141079999999999em; -ms-high-contrast-adjust: none;"><span style="line-height: 160%; box-sizing: content-box; display: block; height: 0; position: relative; top: -3.063em; margin-right: 0.05em; -ms-high-contrast-adjust: none;"><span style="line-height: 160%; box-sizing: content-box; display: inline-block; overflow: hidden; 0; height: 2.7em; -ms-high-contrast-adjust: none;"></span><span style="line-height: 160%; box-sizing: content-box; display: inline-block; font-size: .7em; -ms-high-contrast-adjust: none;"><span style="line-height: 160%; box-sizing: content-box; -ms-high-contrast-adjust: none;">2</span></span></span></span></span></span></span></span></span></span></span><span style="line-height: 160%; box-sizing: content-box; display: table-cell; vertical-align: bottom; font-size: 1px; -ms-high-contrast-adjust: none;">​</span></span><span style="line-height: 160%; box-sizing: content-box; display: table-row; text-align: center; -ms-high-contrast-adjust: none;"><span style="line-height: 160%; box-sizing: content-box; display: table-cell; vertical-align: bottom; position: relative; height: 0.686em; -ms-high-contrast-adjust: none;"></span></span></span></span><span style="line-height: 160%; box-sizing: content-box; display: inline-block; .12em; -ms-high-contrast-adjust: none;"></span></span></span></span></span></span></p><p style="line-height: 160%; box-sizing: content-box; margin: 10px 0; color: #333;">得出误差降低50%，样本量需要扩大到原来的4倍</p><p style="line-height: 160%; box-sizing: content-box; margin: 10px 0; color: #333;"><strong style="line-height: 160%; box-sizing: content-box; font-weight: 700;">5.某公司希望估计其生产的某种面向企业用户的产品在市场上的占有率，请问下面哪些抽样方法是不合理的？</strong></p><p style="line-height: 160%; box-sizing: content-box; margin: 10px 0; color: #333;">A.从公司客户数据库中随机抽取1000家企业用户进行调研</p><p style="line-height: 160%; box-sizing: content-box; margin: 10px 0; color: #333;">B.调研市场上的所有上市公司对于这类产品的使用情况</p><p style="line-height: 160%; box-sizing: content-box; margin: 10px 0; color: #333;">C.从市场中的企业中随机抽取调研企业</p><p style="line-height: 160%; box-sizing: content-box; margin: 10px 0; color: #333;">D.针对熟悉的企业，排除调研员上门调研</p><p style="line-height: 160%; box-sizing: content-box; margin: 10px 0; color: #333;">答案：ABD</p><p style="line-height: 160%; box-sizing: content-box; margin: 10px 0; color: #333;">解析：只有C是随机抽样</p></div><center style="display:none !important;visibility:collapse !important;height:0 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  • 原文地址：https://www.cnblogs.com/pandaboy1123/p/14196667.html
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