📚 Winter Intensive Revision Plan for OCR Year 12 Statistics | OCR 12年级统计：寒假强化复习计划
This plan is designed to help you use the winter break effectively to consolidate all the AS-level Statistics topics required for OCR Year 12. By following a structured approach, you can address knowledge gaps, build confidence, and be fully prepared for your upcoming assessments.
这份复习计划旨在帮助你利用寒假有效巩固 OCR 12 年级统计所需的所有 AS 级别主题。通过结构化复习，你可以弥补知识漏洞，建立信心，并为即将到来的考试做好充分准备。
1. Diagnostic Self-Assessment | 摸底自测
Begin by completing a full AS Statistics past paper under timed conditions. This will highlight your strengths and pinpoint topics that need more attention.
首先在计时条件下完成一套完整的 AS 统计历年真题。这将突出你的优势，并查明需要更多关注的主题。
Record your scores for each section: data collection, representation, probability, distributions, and hypothesis testing. Create a list of errors and the associated concepts.
记录每个部分的得分：数据收集、表示、概率、分布和假设检验。列出错误及相关概念。
2. Mastering Data Collection | 掌握数据收集
Review all sampling techniques: simple random, stratified, systematic, quota, and convenience sampling. Understand their advantages, disadvantages, and when each is appropriate.
复习所有抽样技术：简单随机抽样、分层抽样、系统抽样、配额抽样和便利抽样。理解它们的优点、缺点以及适用场合。
Distinguish between a population and a sample, and between a sampling frame and a census. Know the types of data: qualitative/categorical vs quantitative, discrete vs continuous.
区分总体与样本，以及抽样框与普查。了解数据类型：定性/分类数据与定量数据，离散数据与连续数据。
Be able to criticise data collection methods, identifying bias, lack of representativeness, and practical constraints.
能够批判数据收集方法，识别偏差、缺乏代表性及实际限制。
3. Data Presentation & Interpretation | 数据表示与解读
Revisit how to construct and interpret histograms, cumulative frequency diagrams, box plots, and stem-and-leaf diagrams. For grouped data, ensure you can calculate frequency density (frequency ÷ class width) to draw histograms.
重温如何绘制并解读直方图、累积频率图、箱线图以及茎叶图。对于分组数据，确保能计算频率密度（频率 ÷ 组距）来绘制直方图。
Learn to identify outliers using the rule: outlier < Q₁ − 1.5 × IQR or > Q₃ + 1.5 × IQR, where IQR = Q₃ − Q₁. Interpret the shape of a distribution (symmetric, positively or negatively skewed) from these diagrams.
学会使用规则识别离群值：离群值 < Q₁ − 1.5 × IQR 或 > Q₃ + 1.5 × IQR，其中 IQR = Q₃ − Q₁。根据这些图表解读分布形态（对称、正偏态或负偏态）。
4. Measures of Central Tendency & Dispersion | 集中趋势与离散度量
Calculate the mean, median, and mode for raw and grouped data. The sample mean is given by x̄ = Σx / n. For grouped data, use midpoints.
计算原始数据和分组数据的均值、中位数和众数。样本均值公式为 x̄ = Σx / n。对于分组数据，使用组中值。
Measures of spread include range, interquartile range (IQR), variance, and standard deviation. The sample variance formula is s² = Σ(x − x̄)² / (n − 1), and the population variance is σ² = Σ(x − μ)² / N. The standard deviation is the square root of the variance.
离差的度量包括极差、四分位距 (IQR)、方差和标准差。样本方差公式为 s² = Σ(x − x̄)² / (n − 1)，总体方差为 σ² = Σ(x − μ)² / N。标准差是方差的平方根。
Understand that adding a constant shifts the mean but does not change the variance; multiplying by a constant scales both the mean and the standard deviation.
理解加上常数只会平移均值但不改变方差；乘以常数会缩放均值和标准差。
Be able to select the most appropriate measure of central tendency and spread for a given data set, especially when outliers are present.
能够为给定数据集选择最合适的集中趋势和离散度量，尤其是存在离群值时。
5. Probability Fundamentals | 概率基础
Review the basic probability rules: for any event A, 0 ≤ P(A) ≤ 1; the total probability of all mutually exclusive outcomes is 1. Use Venn diagrams and two-way tables to organize probabilities.
复习基本概率规则：对于任何事件 A，0 ≤ P(A) ≤ 1；所有互斥结果的总概率为 1。使用维恩图和双向表格来组织概率。
The addition formula for two events: P(A ∪ B) = P(A) + P(B) − P(A ∩ B). For mutually exclusive events, P(A ∩ B) = 0, so P(A ∪ B) = P(A) + P(B).
两个事件的加法公式：P(A ∪ B) = P(A) + P(B) − P(A ∩ B)。对于互斥事件，P(A ∩ B) = 0，因此 P(A ∪ B) = P(A) + P(B)。
Independent events satisfy P(A ∩ B) = P(A) × P(B). Be careful not to confuse independence with mutual exclusivity.
独立事件满足P(A ∩ B) = P(A) × P(B)。注意不要混淆独立与互斥。
6. Conditional Probability & Tree Diagrams | 条件概率与树状图
Conditional probability P(A|B) = P(A ∩ B) / P(B). This measures the probability of A given that B has occurred. Use tree diagrams to handle successive events and calculate combined probabilities.
条件概率 P(A|B) = P(A ∩ B) / P(B)。这衡量在 B 已经发生的条件下 A 发生的概率。使用树状图处理连续事件并计算组合概率。
When drawing a tree diagram, label branches with probabilities. For a sequence of two events, multiply along branches to find the probability of the intersection. Add probabilities of branches that satisfy a condition.
绘制树状图时，用概率标记分支。对于两个事件的序列，沿分支相乘求交集的概率。将满足条件的分支概率相加。
Practice reverse conditional probability problems where you are given a later probability and asked to find an earlier branch probability, often using the formula or a tree diagram with unknown probabilities.
练习逆向条件概率问题，即给定后期概率求前期分支概率，通常使用公式或带有未知概率的树状图。
7. Discrete Random Variables & Binomial Distribution | 离散随机变量与二项分布
A discrete random variable X takes distinct values with probabilities P(X = x). You can display its probability distribution in a table. The expected value (mean) is E(X) = Σ [x · P(X = x)], and the variance is Var(X) = Σ [x² · P(X = x)] − [E(X)]².
离散随机变量 X 取不同值，对应概率 P(X = x)。其概率分布可以用表格显示。期望值（均值）为 E(X) = Σ [x · P(X = x)]，方差为 Var(X) = Σ [x² · P(X = x)] − [E(X)]²。
The binomial distribution models the number of successes in n independent trials, each with
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