📚 Core Topics in Year 10 OCR Statistics | Year 10 OCR 统计核心知识点梳理
Statistics is the study of collecting, organising, summarising, and drawing conclusions from data. Year 10 OCR Statistics covers a wide range of fundamental techniques that allow students to describe data, explore relationships, and assess uncertainty. This article provides a structured review of the core topics, ensuring learners have clear definitions, methods, and examples aligned with the OCR specification.
统计学是研究如何收集、整理、汇总数据并从中得出结论的学科。Year 10 OCR统计学涵盖了广泛的基本技术，使学生能够描述数据、探索关系并评估不确定性。本文对核心知识点进行了系统梳理，确保学习者掌握符合OCR大纲要求的清晰定义、方法和示例。
1. Data Collection and Sampling Methods | 数据收集与抽样方法
Data can be obtained via a census, which surveys the entire population, or a sample, which surveys only a part.
数据可以通过普查（调查整个总体）或样本（仅调查一部分）获得。
A simple random sample gives every member an equal chance of selection without bias.
简单随机抽样让每个成员有均等被选中的机会，且无偏差。
for the number sampled from a stratum is: (stratum size ÷ population size) × sample size.
分层抽样将总体分为不同的组（层），然后从每层按比例抽样。每层抽样数量的公式为：（层容量 ÷ 总体容量）× 样本容量。
g selects every k-th member after a random start, where k = population size / sample size.
系统抽样在随机起点后每隔k个成员选取一个，其中k = 总体容量 / 样本容量。
Convenience sampling uses readily available individuals, but it often introduces bias and is not representative.
便利抽样利用最容易接触到的个体，但往往引入偏差，不具备代表性。
2. Types of Data | 数据类型
Data can be classified as qualitative (categorical) or quantitative (numerical). Qualitative data describe qualities, while quantitative data measure quantities.
数据可以分为定性（分类）数据或定量（数值）数据。定性数据描述的是品质，定量数据测量的是数值大小。
Quantitative data may be discrete (countable, e.g. number of students) or continuous (measurable, e.g. height).
定量数据可以是离散型（可数的，如学生人数）或连续型（可测量的，如身高）。
Qualitative data can be nominal (no natural order, like hair colour) or ordinal (ordered categories, like exam grades A*-C).
定性数据可以是名义型（无自然顺序，如头发颜色）或顺序型（有顺序的类别，如考试等级A*-C）。
| Data Type | Examples |
|---|---|
| Discrete Quantitative | Number of pets, shoe size |
| Continuous Quantitative | Weight, time, temperature |
| Nominal Qualitative | Favourite colour, country |
| Ordinal Qualitative | Satisfaction rating (poor–excellent) |
The type of data determines which statistical measures and graphs are appropriate.
数据类型决定了适合使用哪些统计量和图形。
3. Frequency Tables and Charts | 频率分布表与图表
A frequency table records how often each value or category occurs. Tally marks help organise raw data.
频率表记录了每个数值或类别出现的次数。画记符号
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