Sampling Methods in A-Level Statistics | A-Level 统计学中的抽样方法

📚 Sampling Methods in A-Level Statistics | A-Level 统计学中的抽样方法

Sampling is a core topic in the Edexcel A-Level Mathematics statistics strand. It underpins how data are collected, how conclusions are drawn, and how bias can enter a study. This article explains the main sampling methods, their advantages and disadvantages, and the language expected in exam answers.

抽样是 Edexcel A-Level 数学统计部分的核心主题。它是数据收集、结论推断以及偏差如何进入研究的基础。本文解释主要的抽样方法、它们的优缺点，以及考试答案中需要使用的语言。

1. Population, Sample and Census | 总体、样本与普查

In a statistical investigation, the population is the entire collection of individuals, items, or measurements that we wish to study. A sample is a subset of the population selected for the actual data collection. A census gathers information from every member of the population without exception. For example, if the aim is to estimate the mean height of 17-year-old students in the UK, the population is all such students; measuring only 500 of them produces a sample.

在统计调查中，总体是我们希望研究的全部个体、项目或测量值的集合。样本是从总体中抽取出来用于实际数据收集的一部分。普查则是在没有遗漏的情况下从总体中的每一个成员收集信息。例如，如果目标是估计英国 17 岁学生的平均身高，那么所有这样的学生构成总体；只测量其中 500 人就得到一个样本。

The population is defined precisely by the research question, and the sample should be selected from a well-defined sampling frame. In A-Level exam questions, you must be able to distinguish between the population and the sample, and to explain when a census may be preferred. A census can give complete accuracy for the population at the time of collection, but it is often very expensive, time-consuming, and impractical when the population is large or when testing destroys the items.

总体由研究问题精确定义，样本则应从一个定义明确的抽样框中抽取。在 A-Level 考试题中，你需要能区分总体与样本，并能解释何时普查可能更可取。普查可以对收集数据时的总体给出完整准确的结果，但它通常非常昂贵、耗时，并且当总体很大或测试会破坏物品时不切实际。

2. Why Sampling? | 为什么要抽样

Sampling is usually preferred because it is cheaper, faster, and easier to manage than a census. Collecting data from a sample produces less data to process, so analysis can be completed more

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