【數據分析師 Level 1 】10.數據采集方法

 

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【數據分析師 Level 1 】3-1.數據采集方法

數據的來源

一手數據 VS 二手數據

• 一手數據（Primary data）
  • 也稱為原始數據，顧名思義，是指直接獲取，沒有經過加工或者第三方傳遞獲得的數據。比如傳統調研中的問卷測評、小組訪談、面對面溝通等形式獲得的數據，或者是互聯網時代用戶直接填寫的個人信息數據以及平台抓取得行為數據等等
• 二手數據（Secondary data）
  • 主要是相對於一手數據而言，指的是通過第三方或者是現有的數據資料獲取的數據。比如國家統計局數據、知名文獻中羅列的數據等等。一手數據的來源渠道，一般比較固定，往往是和自身直接相關。比如搭建的網站、組織的活動，開展的調研等。而二手數據則相對比較多樣化，凡是會產出數據相關信息的第三方機構都可以作為來源渠道。

優劣勢分析

一手數據和二手數據，在實際應用中都是非常重要的。他們不同的優缺點，可以很好地互補，從而幫助企業在效果和效率間找到比較好的平衡

	優點	缺點
一手數據	相關性強 准確度高 理解准確	成本貴 耗時長 清洗工作重
二手數據	成本低 時間短 清洗工作少	比較普適，相關性弱 准確度不可控制 理解可能存在偏差

在實際項目中，一般會把兩類數據進行結合，總結來看，一手和二手數據的選擇，可以參考下圖的形式判斷

同時，在一手數據的使用過程中，需要特別注意的是，要對采集回來的數據進行邏輯合理性驗證

而二手數據，因為收集的過程由第三方完成。因此數據的可信性和准確度，就依賴於第三方機構的可信性。

抽樣方法

如何獲取一手數據？

當我們需要獲取一手數據的時候，一種常見的方式就是抽樣調查

抽樣調查不止在傳統行業中比較常用，在現在的互聯網企業中也時常會用到。比如一些優惠活動或者特定客群營銷等方案的測試，就需要用到抽樣的方式選擇測試群體。在做抽樣調查時，我們都希望盡可能地減少誤差，讓抽樣的樣本能夠充分代表整體的特征。那么誤差和哪些因素相關呢，抽樣誤差（Sampling Error）的大小，主要由樣本容量的大小和抽樣方式來決定。

一般，我們認為抽樣可以分為兩類：一類我們叫做概率抽樣（Probability Samling），也叫做客觀抽樣。第二類，我們叫做非概率抽樣（Non-probability Sampling），也叫做主觀抽樣。下面我們介紹兩種抽樣方法

概率抽樣

顧名思義，是一種基於概率的抽樣方式，因此也被稱為客觀抽樣。從理論的角度來說，概率抽樣是符合科學和統計原則的，抽樣誤差可以估計。也是在可能的情況下，最優先被推薦使用的抽樣方法。但是，精確度高的方法，往往操作的復雜度和耗費的成本也會相對偏高。概率抽樣，雖然可以避免主觀判斷帶來的謬誤，但是它常常受限於項目經費、時間和保密性等原則，從而難以實際使用

非概率抽樣

和概率抽樣相反，非概率抽樣是一種簡單、易使用的抽樣方式。它主要通過抽樣者的判斷，包括對樣本特征的判斷和對項目成本的考量，綜合特殊的要求或者設定，最終選擇合適的樣本。因此，這種方法會收到主觀因素的影響，不符合統計科學的原則，抽樣誤差是無法估計和計算的。但是在實際應用中，大量的案例還是證明了非概率誤差依然有一定的有效性。在樣本量充足的前提下，通過設定簡單的配比，以及選擇有經驗的抽樣者，基本上可以保證抽樣結果的有效性。而且由於非概率抽樣比較容易重復操作，因此用此飛概率抽樣反復進行同一試驗，結果往往也有趨同性。另外，這一抽樣方式，雖然無法衡量抽樣誤差，但是由於抽樣過程可以進行設計和控制，因此可以更簡單有效地控制非抽樣誤差（Non-sampling Error）。

總結來說，概率抽樣和非概率抽樣，我們可以通過以下的表格進行區別

	特點	優點	缺點
概率抽樣	根據科學原則抽取樣本	抽樣誤差可以估計客觀	成本貴 耗時長 操作復雜 局限多
非概率抽樣	根據抽樣者的主觀判斷抽取樣本	成本低 時間短 操作簡單 可行性強	無法衡量抽樣誤差 存在主管謬誤 對抽樣者經驗要求高

概率抽樣方法

介紹了概率抽樣和非概率抽樣之后，我們重點看一下概率抽樣方法，常用的概率抽樣方法主要有以下4種

簡單隨機抽樣（Simaple Random Sampling）

使用簡單隨機抽樣方式進行抽樣，總體中的每個樣本都有同等的被抽取到的機會。因此，可以用以下的公式，來確定樣本量和抽樣誤差之間的關系

 

 

其中n表示樣本量Z2α​​

為置信區間，如果沒有指定，一般常用取值為1.96（即95%置信區間）α

為總體標准差E
為抽樣誤差范圍
因此根據這個公式，可以實現n和E之間的互相推導

簡單隨機抽樣中，默認了一個假設，也就是被抽中的機會是均等的，聽上去似乎很正常，但是實際上要做到這一點，並不容易。由於改的外觀特征和抽樣者的心理因素等影響，每個個體被抽到的機會並不是均勻地。因此在實際應用中，通常用抽簽或者隨機數等形式來進行操作，減少偏差。這樣的形式，也決定了在大型調研中簡單隨機抽樣的方式比較難以采用，一般多應用於小型的調研，或者測試客戶群體選擇等。

分層抽樣（Stratifide Sampling）

正如之前提到的，簡單隨機抽樣的假設並不總是成立，如果總體可以按照一些特征分成若干層。層與層之間差異明顯，每個層內部的個體特征相近，那么我們可以對每個層做簡單隨機抽樣。抽樣結果合並的集合，就是我們最終確認的抽樣樣本。

在實際操作中，我們可以按照每一層的個體數量來決定抽取數量，是的每個層抽取的比例都相等，這樣的抽樣我們叫做按比例分層抽樣。一般，如果每層重要性差不多，數量差異也不是很大的情況下，我們都是這樣操作的。

而如果有一些層非常重要，或者有些層的個體數非常少，那我們就要采用非按比例分層抽樣的方法。

如果總體中個體間呈現明顯的幾類，那么使用分層抽樣可以更好地反映總體，避免隨機抽樣可能帶來的樣本集中或特征缺失的情況。因此，在概率抽樣中，分層抽樣也是使用最多的一種。我們在對城市，或者是大型的業務線進行研究的時候，都可以采用分層抽樣。

系統抽樣（Systematic Sampling）

除了分層抽樣之外，系統抽樣也對簡單隨機抽樣，進行了改進。使用系統抽樣的時候，仍然需要將個體進行編號，然后根據抽樣樣本容量決定抽樣的間距。因此又叫等距抽樣或者機械抽樣。這種方法，減少了抽樣過程中的人力和時間消耗。不過，系統抽樣一般很少作為單獨的抽樣方法是用，通常是配合其他方法一起進行。

分段抽樣（Multi-stage Sampling）

前面提到的，都是一次性抽取完成樣本的方法，這些方法可以統稱為單階段抽樣。然而在有些情況下，我們並不能一次性完成樣本的抽取，比如在全國范圍內選擇一定數量的用戶作為試點調查。這個時候我們需要分階段地去完成抽樣過程，這種方法，我們叫做分段抽樣。

分段抽樣，我們首先把總體划分成一些大小差不多的群體。在這些群體中隨機抽取幾個。被抽中的群體，就作為下一步進行隨機抽樣的“總體”

因此，在學習過程中，一定要注意區分分段抽樣和分層抽樣。雖然兩者都是對總體進行了一定的划分。但是分層抽樣是按照一定特征進行划分，划分的目的是為了避免特征的過分集中和缺失。抽取的過程也是一步完成的，只有在分層之后才會進行隨機抽樣。而分段抽樣則不同，它是由於總體太大，無法直接進行抽取，所以才需要進行多步抽樣。每一次對總體的划分都是為了進行隨機抽取，而抽取后，下一步的“總體”就會得到一定程度的減小。

例題精講

1.二手數據的特點是（）

A.數據缺乏可靠性

B.不適合自己的研究需要

C.采集數據的成本低，但搜集比較困難

D.采集數據的成本低，搜集比較容易

答案：D

解析：熟悉一手數據和二手數據的特點

2.與概率抽樣相比，非概率抽樣的缺點是（）

A.調查成本比較高

B.不適合探索性研究

C.樣本統計量的分布是確定的

D.無法使用樣本的結果對總體相應的參數進行推斷

答案：D

解析：熟悉概率抽樣和非概率抽樣的異同

3.為了估計A市願意坐地鐵上下班的人數的比例，在收集數據時，最有可能采用的數據搜集方法是？

A.普查

B.實驗

C.隨機抽樣

D.公開發表的資料

答案：C

解析：在不考慮人力和時間的前提下，上述選項中操作最簡單，需要考慮的問題最少的是隨機抽樣，也能盡可能保證每個個體被抽中的可能性均等

4.用簡單隨機重復抽樣方法抽取樣本單位，如果要使抽樣平均誤差降低50%，則樣本容量需要擴大到原來的（）倍

A.0.5

B.不變

C.2

D.4

答案：D

解析：根據簡單隨機抽樣的樣本量確定公式

n=E2(Z2α​​)2α2​

得出誤差降低50%，樣本量需要擴大到原來的4倍

5.某公司希望估計其生產的某種面向企業用戶的產品在市場上的占有率，請問下面哪些抽樣方法是不合理的？

A.從公司客戶數據庫中隨機抽取1000家企業用戶進行調研

B.調研市場上的所有上市公司對於這類產品的使用情況

C.從市場中的企業中隨機抽取調研企業

D.針對熟悉的企業，排除調研員上門調研

答案：ABD

解析：只有C是隨機抽樣

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<html><head>  <title>Evernote Export</title>  <basefont face="微軟雅黑" 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: 微軟雅黑;      font-size: 10pt;    }  </style></head><body><a name="1875"/>
<div><span><div style="font-size: 14px; margin: 0; padding: 0; width: 100%;"><h3 style="line-height: 160%; box-sizing: content-box; font-weight: 700; font-size: 27px; color: #333;">【數據分析師 Level 1 】3-1.數據采集方法</h3><h4 style="line-height: 160%; box-sizing: content-box; font-size: 20px; color: #333;">數據的來源</h4><h5 style="line-height: 160%; box-sizing: content-box; font-weight: 700; font-size: 16px; color: #333;">一手數據 VS 二手數據</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;">一手數據（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;">也稱為原始數據，顧名思義，是指直接獲取，沒有經過加工或者第三方傳遞獲得的數據。比如傳統調研中的問卷測評、小組訪談、面對面溝通等形式獲得的數據，或者是互聯網時代用戶直接填寫的個人信息數據以及平台抓取得行為數據等等</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;">二手數據（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;">主要是相對於一手數據而言，指的是通過第三方或者是現有的數據資料獲取的數據。比如國家統計局數據、知名文獻中羅列的數據等等。一手數據的來源渠道，一般比較固定，往往是和自身直接相關。比如搭建的網站、組織的活動，開展的調研等。而二手數據則相對比較多樣化，凡是會產出數據相關信息的第三方機構都可以作為來源渠道。</li></ul></li></ul><h5 style="line-height: 160%; box-sizing: content-box; font-weight: 700; font-size: 16px; color: #333;">優劣勢分析</h5><p style="line-height: 160%; box-sizing: content-box; margin: 10px 0; color: #333;">一手數據和二手數據，在實際應用中都是非常重要的。他們不同的優缺點，可以很好地互補，從而幫助企業在效果和效率間找到比較好的平衡</p><table style="margin: 2px 0 14px; color: #333; width: 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;">優點</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;">缺點</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;">一手數據</td><td style="line-height: 160%; box-sizing: content-box; padding: 5px 14px 5px 12px; border: 1px solid #eaeaea;">相關性強 准確度高 理解准確</td><td style="line-height: 160%; box-sizing: content-box; padding: 5px 14px 5px 12px; border: 1px solid #eaeaea;">成本貴 耗時長 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;">二手數據</td><td style="line-height: 160%; box-sizing: content-box; padding: 5px 14px 5px 12px; border: 1px solid #eaeaea;">成本低 時間短 清洗工作少</td><td style="line-height: 160%; box-sizing: content-box; padding: 5px 14px 5px 12px; border: 1px solid #eaeaea;">比較普適，相關性弱  准確度不可控制  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;">在實際項目中，一般會把兩類數據進行結合，總結來看，一手和二手數據的選擇，可以參考下圖的形式判斷</p><p style="line-height: 160%; box-sizing: content-box; margin: 10px 0; color: #333;"><img src="【數據分析師 Level 1 】3-1_files/一手數據和二手數據.png" type="image/png" data-filename="一手數據和二手數據.png"/></p><p style="line-height: 160%; box-sizing: content-box; margin: 10px 0; color: #333;">同時，在一手數據的使用過程中，需要特別注意的是，要對采集回來的數據進行<strong style="line-height: 160%; box-sizing: content-box; font-weight: 700;">邏輯合理性驗證</strong></p><p style="line-height: 160%; box-sizing: content-box; margin: 10px 0; color: #333;">而二手數據，因為收集的過程由第三方完成。因此數據的可信性和准確度，就依賴於第三方機構的可信性。</p><h4 style="line-height: 160%; box-sizing: content-box; font-size: 20px; color: #333;">抽樣方法</h4><h5 style="line-height: 160%; box-sizing: content-box; font-weight: 700; font-size: 16px; color: #333;">如何獲取一手數據？</h5><p style="line-height: 160%; box-sizing: content-box; margin: 10px 0; color: #333;">當我們需要獲取一手數據的時候，一種常見的方式就是<strong style="line-height: 160%; box-sizing: content-box; font-weight: 700;">抽樣調查</strong></p><p style="line-height: 160%; box-sizing: content-box; margin: 10px 0; color: #333;">抽樣調查不止在傳統行業中比較常用，在現在的互聯網企業中也時常會用到。比如一些優惠活動或者特定客群營銷等方案的測試，就需要用到抽樣的方式選擇測試群體。在做抽樣調查時，我們都希望盡可能地減少誤差，讓抽樣的樣本能夠充分代表整體的特征。那么誤差和哪些因素相關呢，抽樣誤差（Sampling Error）的大小，主要由樣本容量的大小和抽樣方式來決定。</p><p style="line-height: 160%; box-sizing: content-box; margin: 10px 0; color: #333;">一般，我們認為抽樣可以分為兩類：一類我們叫做概率抽樣（Probability Samling），也叫做客觀抽樣。第二類，我們叫做非概率抽樣（Non-probability Sampling），也叫做主觀抽樣。下面我們介紹兩種抽樣方法</p><h5 style="line-height: 160%; box-sizing: content-box; font-weight: 700; font-size: 16px; color: #333;">概率抽樣</h5><p style="line-height: 160%; box-sizing: content-box; margin: 10px 0; color: #333;">顧名思義，是一種基於概率的抽樣方式，因此也被稱為客觀抽樣。從理論的角度來說，概率抽樣是符合科學和統計原則的，抽樣誤差可以估計。也是在可能的情況下，最優先被推薦使用的抽樣方法。但是，精確度高的方法，往往操作的復雜度和耗費的成本也會相對偏高。概率抽樣，雖然可以避免主觀判斷帶來的謬誤，但是它常常受限於項目經費、時間和保密性等原則，從而難以實際使用</p><h5 style="line-height: 160%; box-sizing: content-box; font-weight: 700; font-size: 16px; color: #333;">非概率抽樣</h5><p style="line-height: 160%; box-sizing: content-box; margin: 10px 0; color: #333;">和概率抽樣相反，非概率抽樣是一種簡單、易使用的抽樣方式。它主要通過抽樣者的判斷，包括對樣本特征的判斷和對項目成本的考量，綜合特殊的要求或者設定，最終選擇合適的樣本。因此，這種方法會收到主觀因素的影響，不符合統計科學的原則，抽樣誤差是無法估計和計算的。但是在實際應用中，大量的案例還是證明了非概率誤差依然有一定的有效性。在樣本量充足的前提下，通過設定簡單的配比，以及選擇有經驗的抽樣者，基本上可以保證抽樣結果的有效性。而且由於非概率抽樣比較容易重復操作，因此用此飛概率抽樣反復進行同一試驗，結果往往也有趨同性。另外，這一抽樣方式，雖然無法衡量抽樣誤差，但是由於抽樣過程可以進行設計和控制，因此可以更簡單有效地控制非抽樣誤差（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;">總結來說，概率抽樣和非概率抽樣，我們可以通過以下的表格進行區別</strong></p><table style="margin: 2px 0 14px; color: #333; width: 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;">特點</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;">優點</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;">缺點</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;">概率抽樣</td><td style="line-height: 160%; box-sizing: content-box; padding: 5px 14px 5px 12px; border: 1px solid #eaeaea;">根據科學原則抽取樣本</td><td style="line-height: 160%; box-sizing: content-box; padding: 5px 14px 5px 12px; border: 1px solid #eaeaea;">抽樣誤差可以估計客觀</td><td style="line-height: 160%; box-sizing: content-box; padding: 5px 14px 5px 12px; border: 1px solid #eaeaea;">成本貴 耗時長 操作復雜 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;">非概率抽樣</td><td style="line-height: 160%; box-sizing: content-box; padding: 5px 14px 5px 12px; border: 1px solid #eaeaea;">根據抽樣者的主觀判斷抽取樣本</td><td style="line-height: 160%; box-sizing: content-box; padding: 5px 14px 5px 12px; border: 1px solid #eaeaea;">成本低 時間短 操作簡單 可行性強</td><td style="line-height: 160%; box-sizing: content-box; padding: 5px 14px 5px 12px; border: 1px solid #eaeaea;">無法衡量抽樣誤差  存在主管謬誤 對抽樣者經驗要求高</td></tr></tbody></table><h5 style="line-height: 160%; box-sizing: content-box; font-weight: 700; font-size: 16px; color: #333;">概率抽樣方法</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;">介紹了概率抽樣和非概率抽樣之后，我們重點看一下概率抽樣方法，常用的概率抽樣方法主要有以下4種</strong></p><h6 style="line-height: 160%; box-sizing: content-box; font-size: 13px; color: #333;">簡單隨機抽樣（Simaple Random Sampling）</h6><p style="line-height: 160%; box-sizing: content-box; margin: 10px 0; color: #333;">使用簡單隨機抽樣方式進行抽樣，總體中的每個樣本都有同等的被抽取到的機會。因此，可以用以下的公式，來確定樣本量和抽樣誤差之間的關系</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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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; width: 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; width: .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; width: 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; width: 0; height: 3em; -ms-high-contrast-adjust: none;"></span><span style="line-height: 160%; box-sizing: content-box; width: 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="width: 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; width: 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; width: .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; width: 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; width: 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; width: .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表示樣本量<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; width: 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; width: .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; width: 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; width: 0; height: 3em; -ms-high-contrast-adjust: none;"></span><span style="line-height: 160%; box-sizing: content-box; width: 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="width: 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; width: 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; width: .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;">為置信區間，如果沒有指定，一般常用取值為1.96（即95%置信區間）<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;">為總體標准差<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/>為抽樣誤差范圍<br/>因此根據這個公式，可以實現n和E之間的互相推導</p><p style="line-height: 160%; box-sizing: content-box; margin: 10px 0; color: #333;">簡單隨機抽樣中，默認了一個假設，也就是被抽中的機會是均等的，聽上去似乎很正常，但是實際上要做到這一點，並不容易。由於改的外觀特征和抽樣者的心理因素等影響，每個個體被抽到的機會並不是均勻地。因此在實際應用中，通常用抽簽或者隨機數等形式來進行操作，減少偏差。這樣的形式，也決定了在大型調研中簡單隨機抽樣的方式比較難以采用，一般多應用於小型的調研，或者測試客戶群體選擇等。</p><h6 style="line-height: 160%; box-sizing: content-box; font-size: 13px; color: #333;">分層抽樣（Stratifide Sampling）</h6><p style="line-height: 160%; box-sizing: content-box; margin: 10px 0; color: #333;">正如之前提到的，簡單隨機抽樣的假設並不總是成立，如果總體可以按照一些特征分成若干層。層與層之間差異明顯，每個層內部的個體特征相近，那么我們可以對每個層做簡單隨機抽樣。抽樣結果合並的集合，就是我們最終確認的抽樣樣本。</p><p style="line-height: 160%; box-sizing: content-box; margin: 10px 0; color: #333;">在實際操作中，我們可以按照每一層的個體數量來決定抽取數量，是的每個層抽取的比例都相等，這樣的抽樣我們叫做按比例分層抽樣。一般，如果每層重要性差不多，數量差異也不是很大的情況下，我們都是這樣操作的。</p><p style="line-height: 160%; box-sizing: content-box; margin: 10px 0; color: #333;">而如果有一些層非常重要，或者有些層的個體數非常少，那我們就要采用非按比例分層抽樣的方法。</p><p style="line-height: 160%; box-sizing: content-box; margin: 10px 0; color: #333;">如果總體中個體間呈現明顯的幾類，那么使用分層抽樣可以更好地反映總體，避免隨機抽樣可能帶來的樣本集中或特征缺失的情況。因此，在概率抽樣中，分層抽樣也是使用最多的一種。我們在對城市，或者是大型的業務線進行研究的時候，都可以采用分層抽樣。</p><h6 style="line-height: 160%; box-sizing: content-box; font-size: 13px; color: #333;">系統抽樣（Systematic Sampling）</h6><p style="line-height: 160%; box-sizing: content-box; margin: 10px 0; color: #333;">除了分層抽樣之外，系統抽樣也對簡單隨機抽樣，進行了改進。使用系統抽樣的時候，仍然需要將個體進行編號，然后根據抽樣樣本容量決定抽樣的間距。因此又叫等距抽樣或者機械抽樣。這種方法，減少了抽樣過程中的人力和時間消耗。不過，系統抽樣一般很少作為單獨的抽樣方法是用，通常是配合其他方法一起進行。</p><h6 style="line-height: 160%; box-sizing: content-box; font-size: 13px; color: #333;">分段抽樣（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樣本的方法，這些方法可以統稱為單階段抽樣。然而在有些情況下，我們並不能一次性完成樣本的抽取，比如在全國范圍內選擇一定數量的用戶作為試點調查。這個時候我們需要分階段地去完成抽樣過程，這種方法，我們叫做分段抽樣。</p><p style="line-height: 160%; box-sizing: content-box; margin: 10px 0; color: #333;">分段抽樣，我們首先把總體划分成一些大小差不多的群體。在這些群體中隨機抽取幾個。被抽中的群體，就作為下一步進行隨機抽樣的“總體”</p><p style="line-height: 160%; box-sizing: content-box; margin: 10px 0; color: #333;">因此，在學習過程中，一定要注意區分分段抽樣和分層抽樣。雖然兩者都是對總體進行了一定的划分。但是分層抽樣是按照一定特征進行划分，划分的目的是為了避免特征的過分集中和缺失。抽取的過程也是一步完成的，只有在分層之后才會進行隨機抽樣。而分段抽樣則不同，它是由於總體太大，無法直接進行抽取，所以才需要進行多步抽樣。每一次對總體的划分都是為了進行隨機抽取，而抽取后，下一步的“總體”就會得到一定程度的減小。</p><p style="line-height: 160%; box-sizing: content-box; margin: 10px 0; color: #333;"><img src="【數據分析師 Level 1 】3-1_files/選擇抽樣方法.png" type="image/png" data-filename="選擇抽樣方法.png"/></p><h4 style="line-height: 160%; box-sizing: content-box; font-size: 20px; color: #333;">例題精講</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;">1.二手數據的特點是（）</strong></p><p style="line-height: 160%; box-sizing: content-box; margin: 10px 0; color: #333;">A.數據缺乏可靠性</p><p style="line-height: 160%; box-sizing: content-box; margin: 10px 0; color: #333;">B.不適合自己的研究需要</p><p style="line-height: 160%; box-sizing: content-box; margin: 10px 0; color: #333;">C.采集數據的成本低，但搜集比較困難</p><p style="line-height: 160%; box-sizing: content-box; margin: 10px 0; color: #333;">D.采集數據的成本低，搜集比較容易</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：熟悉一手數據和二手數據的特點</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.與概率抽樣相比，非概率抽樣的缺點是（）</strong></p><p style="line-height: 160%; box-sizing: content-box; margin: 10px 0; color: #333;">A.調查成本比較高</p><p style="line-height: 160%; box-sizing: content-box; margin: 10px 0; color: #333;">B.不適合探索性研究</p><p style="line-height: 160%; box-sizing: content-box; margin: 10px 0; color: #333;">C.樣本統計量的分布是確定的</p><p style="line-height: 160%; box-sizing: content-box; margin: 10px 0; color: #333;">D.無法使用樣本的結果對總體相應的參數進行推斷</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：熟悉概率抽樣和非概率抽樣的異同</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.為了估計A市願意坐地鐵上下班的人數的比例，在收集數據時，最有可能采用的數據搜集方法是？</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.實驗</p><p style="line-height: 160%; box-sizing: content-box; margin: 10px 0; color: #333;">C.隨機抽樣</p><p style="line-height: 160%; box-sizing: content-box; margin: 10px 0; color: #333;">D.公開發表的資料</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：在不考慮人力和時間的前提下，上述選項中操作最簡單，需要考慮的問題最少的是隨機抽樣，也能盡可能保證每個個體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.用簡單隨機重復抽樣方法抽取樣本單位，如果要使抽樣平均誤差降低50%，則樣本容量需要擴大到原來的（）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.不變</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：根據簡單隨機抽樣的樣本量確定公式</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; width: .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; width: 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; width: 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; width: 0; height: 3em; -ms-high-contrast-adjust: none;"></span><span style="line-height: 160%; box-sizing: content-box; width: 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="width: 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; width: 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; width: 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; width: .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; width: 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; width: 0; height: 3em; -ms-high-contrast-adjust: none;"></span><span style="line-height: 160%; box-sizing: content-box; width: 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="width: 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; width: 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; width: .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; width: 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; width: 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; width: .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;">得出誤差降低50%，樣本量需要擴大到原來的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.某公司希望估計其生產的某種面向企業用戶的產品在市場上的占有率，請問下面哪些抽樣方法是不合理的？</strong></p><p style="line-height: 160%; box-sizing: content-box; margin: 10px 0; color: #333;">A.從公司客戶數據庫中隨機抽取1000家企業用戶進行調研</p><p style="line-height: 160%; box-sizing: content-box; margin: 10px 0; color: #333;">B.調研市場上的所有上市公司對於這類產品的使用情況</p><p style="line-height: 160%; box-sizing: content-box; margin: 10px 0; color: #333;">C.從市場中的企業中隨機抽取調研企業</p><p style="line-height: 160%; box-sizing: content-box; margin: 10px 0; color: #333;">D.針對熟悉的企業，排除調研員上門調研</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是隨機抽樣</p></div><center style="display:none !important;visibility:collapse !important;height:0 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