📚 IGCSE WJEC Statistics: Winter Intensive Revision Plan | IGCSE WJEC 统计：寒假强化复习计划
A winter break can be the turning point for WJEC IGCSE Statistics students. Instead of treating the holiday as lost time, a focused three-week plan can consolidate data handling, probability, and inference skills while leaving room for rest.
寒假可以成为 WJEC IGCSE 统计学科的关键转折点。与其把假期当作空白时间，不如用一份聚焦的三周计划巩固数据处理、概率与推断技能，同时留出休息空间。
1. Understanding the WJEC IGCSE Statistics Exam | 了解 WJEC IGCSE 统计考试结构
WJEC IGCSE Statistics assesses both written methods and interpretation. Papers typically cover collecting data, charts, averages, spread, probability, bivariate data, time series, index numbers, standardised rates, and the chi-squared test. Many questions require calculator work but also demand clear explanations.
WJEC IGCSE 统计既考查书写计算方法，也考查对结果的解读。试卷通常覆盖数据收集、图表、平均数、离散程度、概率、双变量数据、时间序列、指数、标准化率以及卡方检验等内容。多数题目需要使用计算器，但也要求清晰的文字解释。
Before planning revision, download the latest specification and mark scheme. Make a checklist of topics and traffic-light them: green for confident, amber for inconsistent, red for weak.
在制定复习计划前，先下载最新大纲和评分方案。制作主题清单并用交通灯标注：绿色代表有信心，琥珀色代表不稳定，红色代表薄弱。
2. How to Structure the Winter Break | 如何规划寒假
A ten-day to fifteen-day programme works well. Split each day into two 45-minute sessions: one for knowledge review and one for exam-style questions. Include one rest day per week to prevent burnout.
十到十五天的复习计划较为合适。每天分为两个 45 分钟时段：一个用于知识复习，另一个用于真题练习。每周安排一个休息日以防止过度疲劳。
| Time | English activity | 中文活动 |
|---|---|---|
| 09:00-09:45 | Revisit a topic and make concise notes | 复习一个主题并做简洁笔记 |
| 10:00-10:45 | Attempt past-paper questions | 完成历年真题 |
| 16:00-16:30 | Mark work and log mistakes | 批改并记录错题 |
| 21:00-21:15 | Rapid recall of key terms | 快速回忆关键术语 |
Keep your workspace free from distractions and leave your phone in another room during revision. Short but consistent sessions are more effective than one long exhausting day.
复习时保持学习环境不受干扰，把手机放在另一个房间。短而持续的练习比一整天疲劳复习更有效。
3. Week 1: Data Types, Sampling and Diagrams | 第一周：数据类型、抽样与图表
Start with data types: qualitative, quantitative discrete, and quantitative continuous. Be able to identify primary and secondary data. Sampling methods include random, systematic, stratified, quota, and cluster sampling; you must explain advantages and disadvantages, not just name them.
先复习数据类型：定性数据、定量离散数据和定量连续数据。要能识别一手数据和二手数据。抽样方法包括随机、系统、分层、配额和整群抽样；不仅要写出名称，还要能解释各自的优缺点。
For charts, practise frequency tables, bar charts, histograms with unequal class widths, cumulative frequency curves, box plots, and stem-and-leaf diagrams. Always check units, labels, and scale.
关于图表，练习频数表、条形图、不等组距直方图、累积频数曲线、箱线图和茎叶图。始终检查单位、标签和刻度。
Frequency density = frequency ÷ class width
4. Week 1: Averages and Measures of Spread | 第一周：平均数与离散程度
Averages include mode, median, and mean. For grouped data, use the midpoint of each class to estimate the mean. The modal class is the group with the highest frequency.
平均数包括众数、中位数和平均值。对于分组数据，用每组的组中值来估计平均数。众数组是频数最高的组。
Mean x̄ = Σfx / Σf
Median position = (n+1)/2 | Range = max − min | IQR = Q₃ − Q₁
Standard deviation σ = √(Σ(x − x̄)² / n) | Sample s = √(Σ(x − x̄)² / (n − 1))
Remember that standard deviation measures how spread out the data are around the mean. A smaller standard deviation means more consistency. Use the full data set formula unless the question asks for an estimate.
标准差衡量数据在平均值周围的离散程度。标准差越小，说明数据越稳定。除非题目要求估计，通常使用全数据集公式。
5. Week 2: Probability and the Normal Distribution | 第二周：概率与正态分布
Probability rules are core. For mutually exclusive events, P(A or B) = P(A) + P(B). If events are not mutually exclusive, subtract P(A and B). For independent events, P(A and B) = P(A) × P(B).
概率规则是核心。对于互斥事件，P(A 或 B)=P(A)+P(B)。如果不是互斥事件，要减去 P(A 与 B)。对于独立事件，P(A 与 B)=P(A)×P(B)。
P(A or B) = P(A) + P(B) − P(A and B)
P(A and B) = P(A) × P(B) for independent events
Use tree diagrams for combined events, and remember that probabilities on each branch total 1. Conditional probability questions often require you to use a two-way table or tree diagram.
用树状图处理复合事件，并记住每条分支上的概率和为 1。条件概率题通常需要你使用双向表或树状图。
Also revise the normal distribution shape: symmetric bell curve; about 68% of values lie within 1 standard deviation of the mean, 95% within 2, and 99.7% within 3.
还要复习正态分布的形状：对称钟形曲线；约 68% 的数值落在平均值的 1 个标准差范围内，95% 在 2 个标准差内，99.7% 在 3 个标准差内。
6. Bivariate Data and Correlation | 双变量数据与相关
Scatter graphs show the relationship between two variables. Correlation can be positive, negative, or zero. Use a line of best fit to make predictions, but avoid extrapolation beyond the data range.
散点图展示两个变量之间的关系。相关可以是正相关、负相关或无相关。使用最佳拟合线进行预测，但避免超出数据范围的外推。
Pearson’s correlation coefficient r ranges from −1 to +1. Spearman’s rank correlation coefficient is used when data are ranked or non-linear. Know the formula and how to interpret strength and direction.
皮尔逊相关系数 r 的范围是 −1 到 +1。斯皮尔曼等级相关系数用于等级数据或非线性关系。要掌握公式及其强弱和方向的解读。
Spearman’s rank: rₛ = 1 − (6Σd²) / (n(n² − 1))
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