IGCSE CAIE Statistics: Core Knowledge Points | IGCSE CAIE 统计：核心知识点梳理

📚 IGCSE CAIE Statistics: Core Knowledge Points | IGCSE CAIE 统计：核心知识点梳理

This article summarises the core topics tested in CAIE IGCSE Statistics. It covers data collection, sampling, diagrams, averages, measures of spread, probability, key distributions, and correlation and regression. Use it as a structured revision checklist for the IGCSE Statistics examination.

本文梳理 CAIE IGCSE 统计课程的核心考点，涵盖数据收集、抽样、图表、平均数、离散程度、概率、重要分布以及相关与回归。可作为 IGCSE 统计考试的结构化复习清单使用。

1. Types of Data and Data Collection | 数据类型与数据收集

In IGCSE Statistics, data are facts or numbers collected for analysis. Data can be qualitative, such as colour or gender, meaning non-numerical categories, or quantitative, such as height or test score, meaning numerical values. Quantitative data are further divided into discrete data, which can take only certain values, for example the number of students, and continuous data, which can take any value in a range, for example time or mass.

在 IGCSE 统计中，数据是用于分析的事实或数字。数据可以是定性数据，如颜色或性别等非数值分类；也可以是定量数据，如身高或测试分数等数值。定量数据又分为离散数据，即只能取某些特定值，例如学生人数；以及连续数据，即在一个区间内可取任意值，例如时间或质量。

Data can also be described by source. Primary data are collected directly by the researcher through questionnaires, interviews, experiments or observations. Secondary data come from existing sources such as government reports, websites or previous studies. Primary data are usually more specific and up to date but take more time and money to collect, while secondary data are quicker and cheaper but may be less reliable or not exactly match the purpose.

数据还可以按来源分类。初级数据由研究者通过问卷、访谈、实验或观察直接收集；次级数据来自政府报告、网站或已有研究等已有来源。初级数据通常更具体、更新，但收集成本和时间较高；次级数据获取快、成本低，但可能可靠性较差或不完全符合研究目的。

2. Sampling Methods | 抽样方法

A population is the entire set of individuals or items being studied, while a sample is a subset selected from the population. Sampling is used because testing the whole population is often too expensive, too slow or impossible. A good sample should be representative and large enough to reduce bias.

总体是被研究的全部个体或项目，样本是从总体中选出的子集。由于对全部总体进行测试通常成本太高、耗时太长或不可行，因此使用抽样。一个好的样本应具有代表性并足够大，以减少偏差。

Common sampling methods include simple random sampling, where every member has an equal chance of being chosen, stratified sampling, where the population is split into groups and sampled proportionally, systematic sampling, where every kth member is selected, quota sampling, where a fixed number is chosen from each category but non-randomly, and cluster sampling, where entire groups are selected. Simple random and stratified samples tend to be less biased, whereas quota and opportunity samples are easier to collect but are more likely to be biased.

常见抽样方法包括简单随机抽样，即每个成员被抽中的机会相等；分层抽样

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