📚 IGCSE CAIE Statistics: Winter Holiday Intensive Revision Plan | IGCSE CAIE 统计：寒假强化复习计划
Winter break is the most important stretch for IGCSE Statistics students because it offers uninterrupted time to close knowledge gaps, practise past papers, and build the written interpretation skills that CAIE examiners reward. This plan divides revision into seven weekly topic blocks, followed by full-paper practice and exam-day strategy.
寒假是 IGCSE 统计学生最重要的复习阶段，因为它提供了整块时间以弥补知识漏洞、练习真题，并培养 CAIE 考官所看重的文字解释能力。本计划将复习分为七个主题周，之后进行全套真题训练和考试策略准备。
1. Know the Syllabus and Exam Structure | 了解考纲与试卷结构
Before starting, download the latest CAIE IGCSE Statistics syllabus and highlight the four assessment objectives: recalling and using statistical techniques, selecting and applying methods, interpreting data, and communicating findings clearly.
开始前先下载最新 CAIE IGCSE 统计大纲，并划出四个评估目标：回忆并运用统计方法、选择并应用方法、解释数据、清晰表达结论。
Make a topic checklist covering data collection, representation, averages and spread, probability, correlation and regression, time series, index numbers, and sampling. Rank each topic as confident, shaky, or weak so you can allocate time by priority.
制作主题清单，涵盖数据收集、图表表示、平均数与离散程度、概率、相关与回归、时间序列、指数和抽样。将每个主题标记为熟练、一般或薄弱，以便按优先级分配时间。
Use the official specimen paper to identify which topics carry the most marks. In IGCSE Statistics, written interpretation and comparison often score as much as calculation, so do not revise formulas in isolation.
使用官方样卷判断哪些主题占分最多。在 IGCSE 统计中，文字解释和比较往往和计算一样占分，因此不要孤立地背公式。
| Week | 周次 | Theme | 主题 | Key output | 关键产出 |
|---|---|---|
| 1 | Data collection and organisation | 数据收集与整理 | Frequency tables, charts, cumulative frequency | 频数表、图表、累计频数 |
| 2 | Averages and spread | 平均数与离散程度 | Mean, variance, IQR comparisons | 平均数、方差、四分位距比较 |
| 3 | Probability and Venn diagrams | 概率与韦恩图 | Tree diagrams, conditional probability | 树状图、条件概率 |
| 4 | Distributions and expectation | 分布与期望 | E(X), fair games | 期望值、公平游戏 |
| 5 | Correlation and regression | 相关与回归 | Scatter diagrams, line of best fit | 散点图、最佳拟合线 |
| 6 | Time series and index numbers | 时间序列与指数 | Moving averages, seasonal variation | 移动平均、季节性变化 |
| 7 | Sampling and estimation | 抽样与估计 | Stratified sampling, bias | 分层抽样、偏差 |
2. Week 1: Data Collection and Organisation | 第1周：数据收集与整理
Revise types of data: qualitative vs quantitative, discrete vs continuous, primary vs secondary. For each type, know a clear example and one advantage or limitation that could appear in a written question.
复习数据类型：定性数据与定量数据、离散数据与连续数据、一手数据与二手数据。对每种类型都要知道一个清晰的例子，以及可能在文字题中出现的优点或局限。
Practise grouping raw data into frequency tables, class intervals, and cumulative frequency tables. Check that class widths are consistent unless the question states otherwise, and that intervals do not overlap.
练习将原始数据整理为频数表、组距和累计频数表。检查组距是否一致，除非题目另有说明，并且区间不能重叠。
Draw and interpret bar charts, pie charts, histograms, frequency polygons, stem-and-leaf diagrams, and box-and-whisker plots. Label every axis, use equal scales for continuous data, and always give the key for stem-and-leaf diagrams.
绘制并解释条形图、饼图、直方图、频数多边形、茎叶图和箱线图。标注每个坐标轴，连续数据使用等距刻度，茎叶图必须给出图例。
For cumulative frequency, practise estimating the median, quartiles, and percentiles from the graph. Remember that the median is at 50% cumulative frequency, the lower quartile at 25%, and the upper quartile at 75%.
对于累计频数图，练习从图中估计中位数、四分位数和百分位数。记住中位数对应 50% 累计频数，下四分位数对应 25%，上四分位数对应 75%。
3. Week 2: Measures of Central Tendency and Spread | 第2周：集中趋势与离散程度
Master the mean, median, mode, range, quartiles and interquartile range. For grouped data, use the midpoint of each class to estimate the mean and state clearly that it is an estimate.
掌握平均数、中位数、众数、极差、四分位数和四分位距。对于分组数据，使用每组中点估计平均数，并明确说明这是一个估计值。
x̄ = Σx ÷ n, σ² = Σx² ÷ n − (Σx ÷ n)², σ = √σ²
Know how outliers are usually defined: values below Q₁ − 1.5 × IQR or above Q₃ + 1.5 × IQR. Be ready to identify an outlier and comment on how it affects the mean compared with the median.
了解异常值的常见定义：低于 Q₁ − 1.5 × IQR 或高于 Q₃ + 1.5 × IQR 的数值。要能识别异常值，并说明它如何影响平均数与中位数的比较。
When comparing two data sets, always refer to both a measure of central tendency and a measure of spread. For example: “Dataset A has a higher median of 7.2 minutes and a smaller interquartile range of 1.8 minutes, so it is faster on average and more consistent.”
比较两个数据集时，必须同时引用集中趋势和离散程度的度量。例如：“数据集 A 的中位数较高，为 7.2 分钟，四分位距较小，为 1.8 分钟，因此平均速度更快且更稳定。”
Practise choosing the most appropriate average. Use the median when data are skewed or contain outliers, and the mode for categorical data.
练习选择最合适的平均数。当数据偏斜或含有异常值时使用中位数，分类数据使用众数。
4. Week 3: Probability and Venn Diagrams | 第3周：概率与韦恩图
Revise basic probability using P(A) = n(A) ÷ n(S). Include mutually exclusive, independent, and complementary events, and be precise with the meanings of each term.
复习基本概率公式 P(A) = n(A) ÷ n(S)。包括互斥事件、独立事件和互补事件，并准确理解每个术语的含义。
P(A ∪ B) = P(A) + P(B) − P(A ∩ B), P(A|B) = P(A ∩ B) ÷ P(B)
Use tree diagrams for successive events and Venn diagrams for overlapping categories. Remember that probabilities on all branches from a single node must total 1, and multiply along branches for combined outcomes.
使用树状图处理连续事件，使用韦恩图处理重叠类别。记住从一个节点出发的所有分支概率之和必须为 1，并且沿分支相乘得到组合结果。
When a question asks for “given that”, use conditional probability. Read the wording carefully: “A and B” means intersection, “A or B” means union, and “at least one” usually means the complement of none.
当题目出现“在…条件下”时，使用条件概率。仔细读题：“A 和 B”表示交集，“A 或 B”表示并集，“至少一个”通常表示“一个都没有”的补事件。
Practise converting data tables into Venn diagrams, especially when two characteristics overlap. Always check that the sum of all regions equals the total sample size.
练习将数据表转换为韦恩图，尤其是两个特征重叠的情况。始终检查所有区域之和等于样本总数。
5. Week 4: Probability Distributions and Expectation | 第4周：概率分布与期望
Construct a probability distribution table where each outcome x has a probability P(X = x). Every probability must lie between 0 and 1, and the total must equal 1 before you calculate expectation.
构建概率分布表，每个结果 x 都有概率 P(X = x)。在计算期望值之前，每个概率必须在 0 到 1 之间，并且总和必须为 1。
E(X) = Σ x·P(X = x), Var(X) = Σ x²·P(X = x) − [E(X)]²
Interpret expected value as the long-run average per trial. It may not be a possible outcome itself; for example, the expected score on a die can be 3.5 even though no face shows 3.5.
将期望值解释为长期每次试验的平均值。它本身不一定是可能的试验结果；例如，骰子点数的期望值可以是 3.5，尽管没有一面是 3.5。
If a game charges an entry fee, compare the expected gain with the fee. If E(X) equals the fee, the game is fair; if E(X) is less than the fee, the game favours the organiser.
如果游戏收取入场费，将期望收益与费用进行比较。若 E(X) 等于费用，则游戏公平；若 E(X) 小于费用，则游戏对组织者有利。
Practise finding unknown probabilities from a distribution by using the fact that probabilities sum to 1, then answer questions about expected profit or loss.
利用概率之和为 1 的性质，练习求出分布中的未知概率，然后回答关于期望利润或损失的问题。
6. Week 5: Correlation, Regression and Scatter Diagrams | 第5周：相关、回归与散点图
Draw scatter diagrams with labelled axes. Describe correlation as strong, moderate, or weak and as positive, negative, or zero, always referring to the scatter of points.
绘制散点图并标注坐标轴。将相关描述为强、中或弱，以及正、负或零相关，始终结合点的分布模式进行说明。
Know the difference between correlation and causation. A high correlation does not prove that one variable causes the other; there may be a third factor or coincidence.
知道相关与因果关系的区别。高相关并不能证明一个变量导致另一个变量；可能存在第三个因素或纯属巧合。
Fit a line of best fit by eye or use the regression equation y = a + bx. Use the line to estimate values, but interpolation is safer than extrapolation because the relationship may not continue outside the data range.
通过目测拟合最佳拟合线，或使用回归方程 y = a + bx。利用该线估计数值，但内插比外推更可靠，因为数据范围之外的关系可能不延续。
Calculate Spearman’s rank correlation coefficient rₛ for ranked data. Values close to +1 show strong positive agreement, close to −1 show strong negative agreement, and near 0 show little or no monotonic relationship.
对于排序数据，计算斯皮尔曼等级相关系数 rₛ。接近 +1 表示强正相关，接近 −1 表示强负相关，接近 0 表示几乎没有单调关系。
7. Week 6: Time Series and Index Numbers | 第6周：时间序列与指数
Plot a time series and identify trend, seasonal variation, cyclic variation, and irregular fluctuations. Use moving averages to smooth the series so the underlying trend becomes clearer.
绘制时间序列并识别趋势、季节性变化、周期性变化和不规则波动。使用移动平均平滑序列，使潜在趋势更清晰。
Seasonal variation = actual value − trend, Index number = (current value ÷ base value) × 100
Find seasonal variation as actual value minus trend value, and use it to make short-term predictions. State when a prediction becomes less reliable because it goes beyond the available data.
用实际值减去趋势值计算季节性变化，并利用它进行短期预测。当预测超出可用数据范围时，要说明预测的可靠性下降。
For index numbers, use the price relative formula and interpret values. An index of 112 means a 12% increase from the base period, while an index of 85 means a 15% decrease.
对于指数，使用价格相对数公式并解释数值。指数为 112 表示比基期上涨 12%，指数为 85 表示比基期下降 15%。
Weighted index numbers reflect importance, so practise using weights to combine separate price relatives. Check that the weights sum correctly before calculating the final index.
加权指数反映重要性，因此练习使用权数合并不同的价格相对数。在计算最终指数之前，检查权数总和是否正确。
8. Week 7: Sampling and Estimation | 第7周：抽样与估计
Know random, systematic, stratified, quota, and cluster sampling. For each method, be able to explain one advantage and one disadvantage using precise statistical language.
了解随机抽样、系统抽样、分层抽样、配额抽样和整群抽样。对每种方法，能用准确的统计语言说明一个优点和一个缺点。
Stratified sampling uses the rule: population proportion = sample proportion. For example, if 30% of a population are girls, then 30% of the sample should be girls.
分层抽样使用规则：总体比例 = 样本比例。例如，如果总体中 30% 是女生，则样本中 30% 也应为女生。
Use a sample mean to estimate a population mean. Increasing sample size generally reduces sampling error, but it does not remove bias if the sampling method is flawed.
用样本平均数估计总体平均数。增大样本量通常可以减少抽样误差，但如果抽样方法有缺陷，它并不能消除偏差。
Practise identifying sources of bias, such as self-selected samples, undercoverage, or measurement errors. Link each source of bias to its likely effect on the estimate.
练习识别偏差来源，如自
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