📚 Year 10 WJEC Statistics: Winter Break Intensive Revision Plan | 寒假强化复习计划
Winter break is the perfect opportunity to consolidate your Year 10 Statistics knowledge and build the confidence needed for upcoming assessments. This structured revision plan breaks down the WJEC specification into manageable daily topics, ensuring you revisit every core concept while practising key skills. Follow each section, complete the suggested activities, and you will return to school fully prepared to tackle more advanced statistical problems.
寒假是巩固 Year 10 统计学知识、建立考试信心的最佳时机。这份结构化的复习计划将 WJEC 课程内容拆解成可管理的每日主题，帮助你重温每一个核心概念，同时训练关键技能。跟随每一小节完成建议的练习活动，你就能在返校时做好充分准备，迎战更高级的统计问题。
1. Understanding Data Types and Collection | 理解数据类型与数据收集
Before diving into calculations, revisit the fundamental distinction between qualitative and quantitative data. Qualitative (categorical) data describes attributes like colour or eye shade, while quantitative data consists of numerical measurements. Within quantitative data, remember that discrete data can only take specific values (e.g. number of siblings), whereas continuous data can take any value within an interval (e.g. height). A solid understanding helps you choose the right representation later.
在深入计算之前，先回顾定性数据与定量数据的根本区别。定性数据（分类数据）描述颜色或眼睛颜色等属性，而定量数据由数值测量组成。在定量数据中，要记住离散数据只能取特定值（如兄弟姐妹数量），连续数据则可以在一个区间内取任何值（如身高）。扎实的理解有助于你后期选择合适的图形表示。
You must also know the difference between a census and a sample survey. A census collects data from every member of a population, giving accurate but often impractical results. A sample surveys only a portion, saving time and cost, but may introduce bias. Keep these trade-offs in mind for exam questions on data collection.
你还必须知道普查与抽样调查的区别。普查从总体中的每一个成员收集数据，结果准确但通常不切实际。抽样只调查一部分，节省时间和成本，但可能引入偏差。在回答数据收集类的考题时，要牢记这些权衡因素。
2. Mastering Sampling Methods | 掌握抽样方法
WJEC expects you to describe and compare different sampling techniques. Random sampling gives every member an equal chance of selection, reducing bias. Stratified sampling divides the population into groups (strata) and selects a random sample from each in proportion to the group size, ensuring representation of key subgroups. Systematic sampling selects members at regular intervals from an ordered list, which is easy to implement but can miss patterns. Be ready to identify the most suitable method for a given scenario.
WJEC 要求你描述并比较不同的抽样技术。随机抽样让每个成员被抽中的机会均等，减少了偏差。分层抽样把总体分成不同的层，然后按比例从每一层随机抽取样本，保证了关键子群体的代表性。系统抽样从有序名单中每隔固定间隔抽取成员，实施简便但可能会错过规律性模式。准备好针对给定的场景选出最合适的方法。
Avoid confusing quota sampling (which is non-random) with stratified sampling. Quota sampling involves interviewing a set number of people from each category but without random selection, making it less reliable. Practise identifying the strengths and limitations of each method using past paper scenarios.
避免混淆配额抽样（非随机）与分层抽样。配额抽样是在每个类别中采访固定数量的人，但不进行随机选择，因此可靠性较低。使用过往真题情景练习识别每种方法的优势和局限性。
3. Organising Data: Frequency Tables | 整理数据：频率表
A well-constructed frequency table is the starting point for most statistical analysis. For discrete data, list each distinct value with its frequency. For continuous data, group the data into class intervals that are of equal width wherever possible. Always check that your intervals do not overlap and that every data point can be assigned to exactly one interval. Clear tables prevent mistakes in later calculations.
一份精心构建的频率表是大多数统计分析的起点。对于离散数据，列出每个不同的值及其频数。对于连续数据，尽量用宽度相等的组距将数据分组。务必检查你的组距没有重叠，并且每个数据点都能被精确地归入一个区间。清晰的表格能避免后期计算出错。
When constructing grouped frequency tables, use inequality notation correctly (e.g. 0 < x ≤ 10). Add columns for cumulative frequency and relative frequency early – they will be essential for cumulative frequency graphs and for comparing datasets of different sizes.
构建分组频率表时，要正确使用不等式符号（如 0 < x ≤ 10）。提早增加累积频率和相对频率列——它们对于绘制累积频率图以及比较不同大小的数据集至关重要。
4. Visualising Data: Bar Charts, Pie Charts and Histograms | 数据可视化：条形图、饼图和直方图
Bar charts are used for discrete or categorical data, with gaps between bars to highlight that the categories are separate. Pie charts show proportions of a whole, where each sector angle equals (frequency / total frequency) × 360°. A common mistake is to plot a pie chart when categories overlap or fail to sum to a meaningful total; always check the context.
条形图用于离散或分类数据，条与条之间留有间隙以强调类别是独立的。饼图展示整体中各部分的比例，每个扇形的角度等于（频数 / 总频数） × 360°。一个常见错误是在类别有重叠或总计无意义的情况下绘制饼图；始终检查题目背景。
Angle = (frequency / total frequency) × 360°
Histograms are the correct choice for continuous data and appear extensively in WJEC. Unlike bar charts, histogram bars touch and the area of each bar is proportional to the frequency. When class widths are unequal, you must plot frequency density on the vertical axis. Use the relationship:
直方图是连续数据的正确选择，在 WJEC 考试中频繁出现。与条形图不同，直方图的条形彼此紧贴，且每个条形的面积与频数成比例。当组距宽度不相等时，纵轴必须使用频率密度。请利用以下关系：
Frequency density = frequency / class width
5. Stem-and-Leaf and Box Plots | 茎叶图和箱线图
Stem-and-leaf diagrams preserve the original data values while displaying the shape of the distribution. Always provide a key (e.g. 3 | 7 means 37) and order the leaves from smallest to largest. From an ordered stem-and-leaf, you can quickly find the median, quartiles, and even spot any outliers. Practise drawing back-to-back stem-and-leaf diagrams to compare two datasets.
茎叶图在展示分布形状的同时保留了原始数据值。务必提供图例（如 3 | 7 表示 37）并将叶从小到大排列。从有序的茎叶图中，你可以快速找到中位数、四分位数，甚至发现异常值。练习绘制背靠背茎叶图来比较两个数据集。
Box plots (or box-and-whisker diagrams) use the five-number summary: minimum, lower quartile Q₁, median, upper quartile Q₃, and maximum. Draw them to scale on a number line and use the 1.5 × IQR rule to identify outliers. Outliers are marked as individual points beyond the whiskers. Constructing parallel box plots is a powerful way to compare distributions in context.
箱线图使用五数概括：最小值、下四分位数 Q₁、中位数、上四分位数 Q₃ 和最大值。在数轴上按比例绘制，并使用 1.5 × IQR 规则识别异常值。异常值被标记为须线之外的独立点。绘制平行的箱线图是在实际情境中比较分布的有力方法。
Lower fence = Q₁ – 1.5 × IQR, Upper fence = Q₃ + 1.5 × IQR
6. Measures of Central Tendency: Mean, Median, Mode | 集中趋势度量：均值、中位数、众数
The mean is the arithmetic average, calculated as the sum of all data values divided by the number of values. For grouped data, you estimate the mean using the midpoint of each interval. Remember that the mean is sensitive to extreme values, so it may not always represent the typical value well. Use the formula for the mean of ungrouped data:
均值是算术平均数，用所有数据值的总和除以数值个数来计算。对于分组数据，你使用每个区间的中点来估计均值。记住，均值对极端值敏感，因此它未必总能很好地代表典型值。使用这一公式计算未分组数据的均值：
Mean = Σx / n
For grouped data, apply Mean ≈ Σfx / Σf, where f is the frequency and x is the interval midpoint. The median is the middle value when data are ordered; its position is (n + 1) / 2. The mode is the most frequent value or class. In a histogram, the modal class is the interval with the highest bar. Comparing these three measures helps you describe skewness and choose the most appropriate average for a given situation.
对于分组数据，使用 均值 ≈ Σfx / Σf，其中 f 是频数，x 是组距中点。中位数是数据按顺序排列后的中间值；其位置为 (n + 1) / 2。众数是出现次数最多的数值或组。在直方图中，众数类就是条形最高的区间。比较这三种度量有助于你描述偏态，并针对给定情况选择最合适的平均数。
7. Measures of Spread: Range and Interquartile Range | 离散度量：极差和四分位距
Range is the simplest measure of spread: maximum minus minimum. However, it is heavily affected by outliers. The interquartile range (IQR = Q₃ – Q₁) is far more robust because it focuses on the middle 50% of data, making it the preferred measure for skewed distributions. Always quote the IQR alongside the median when summarising a box plot.
极差是最简单的离散度量：最大值减最小值。然而，它受异常值影响极大。四分位距（IQR = Q₃ – Q₁）要稳健得多，因为它聚焦于中间 50% 的数据，因此是对偏态分布首选的度量。在总结箱线图时，始终将 IQR 与中位数放在一起报告。
For grouped data, find the quartiles from a cumulative frequency graph. Draw a smooth curve through the cumulative frequency points, then read off the values corresponding to ¼, ½, and ¾ of the total frequency. Use these to calculate the IQR and construct a box plot. Practise interpreting what a large IQR tells you about consistency and variability in a real-world context.
对于分组数据，通过累积频率图找到四分位数。绘制一条通过累积频率点的光滑曲线，然后根据总频数的 ¼、½ 和 ¾ 读取对应的数值。用这些值计算 IQR 并构建箱线图。练习解释较大的 IQR 在现实情境中关于一致性和变异性的含义。
8. Introduction to Probability | 概率导论
Probability measures how likely an event is to happen, on a scale from 0 (impossible) to 1 (certain). For equally likely outcomes, the theoretical probability of an event A is:
概率衡量事件发生的可能性，范围是从 0（不可能）到 1（必然）。对于等可能结果，事件 A 的理论概率为：
P(A) = number of favourable outcomes / total number of outcomes
Relative frequency is an experimental estimate of probability, obtained by repeating a trial many times. The more trials you carry out, the closer the relative frequency gets to the theoretical probability – the law of large numbers. WJEC questions often ask you to compare expected and observed frequencies to assess whether a game or process is fair.
相对频率是概率的实验估计，通过多次重复试验获得。你进行的试验次数越多，相对频率就越接近理论概率——这是大数定律。WJEC 考题经常要求你比较期望频数与观察频数，以判断某个游戏或过程是否公平。
Expected frequency is calculated as P(event) × number of trials. Always test for bias by comparing expected frequencies with the results actually observed. If the difference is large, the model may not be appropriate.
期望频数的计算方式是 P(事件) × 试验次数。始终通过比较期望频数与实际观察结果来检验偏差。如果差异很大，使用的概率模型就可能不合适。
9. Probability Trees and Combined Events | 概率树与组合事件
Tree diagrams help you list all possible outcomes for two or more sequential events. To construct a tree, branch out with the different outcomes at each stage, writing the probability of each branch. The probability of a particular combination is found by multiplying probabilities along the branches. Always check that the probabilities on branches from the same point sum to 1.
树形图帮助你列出两个或多个连续事件的所有可能结果。构建树形图时，在每一阶段分出不同结果的枝，并写出每一枝的概率。找到特定结果组合的概率，需要将路径上各枝的概率相乘。务必检查从同一点发出的各枝上概率之和为 1。
For independent events, the outcome of one event does not affect the other. P(A and B) = P(A) × P(B). For conditional probability, the probability of B may change after A has occurred. Use the multiplication rule for conditional probability: P(A and B) = P(A) × P(B | A). You do not need to learn the formal notation in Year 10, but you should be able to handle ‘given that’ statements using a completed tree diagram.
对于独立事件，一个事件的结果不影响另一个。P(A 与 B) = P(A) × P(B)。对于条件概率，A 发生之后 B 的概率可能会改变。使用条件概率的乘法法则：P(A 与 B) = P(A) × P(B | A)。在 Year 10 你不需要学习正式记号，但你要能够利用完整的树形图处理“已知…的条件下”这样的描述。
10. Scatter Graphs and Correlation | 散点图与相关性
Scatter graphs display the relationship between two quantitative variables. Plot each data point carefully using the horizontal axis for the independent (explanatory) variable and the vertical axis for the dependent (response) variable. Describe the correlation as positive, negative, or no correlation, and comment on its strength (strong, moderate, or weak). A strong correlation does not necessarily imply causation.
散点图展示两个定量变量之间的关系。小心地标出每个数据点，水平轴为自变量（解释变量），垂直轴为因变量（响应变量）。将相关性描述为正相关、负相关或不相关，并评述其强度（强、中等或弱）。强相关并不一定意味着因果。
Draw a line of best fit by eye, passing through the middle of the points. You can use this line to make predictions – interpolation (within the data range) is reliable, but extrapolation (outside the range) must be treated with caution. In WJEC, you will often be asked to estimate a missing value or predict a future outcome using the line of best fit.
通过目测画一条最佳拟合线，使其穿过数据点的中心区域。你可以用这条线进行预测——内插（数据范围内）是可靠的，但外推（数据范围外）必须谨慎对待。在 WJEC 考试中，常会要求你利用最佳拟合线估计缺失值或预测未来结果。
11. Interpreting Statistical Diagrams and Writing Comparisons | 解读统计图表并写出比较
Many marks in WJEC Statistics are awarded for interpretation and comparison. When asked to compare two distributions from box plots or histograms, always make at least two points: one about a measure of central tendency (e.g. the median) and one about a measure of spread (e.g. the IQR). Back these up with numerical values from the diagram and link them to the context. For example, ‘The median waiting time at clinic A (12 min) is higher than at clinic B (8 min), suggesting clinic B is generally quicker.’
WJEC 统计考试中有许多分数来自解读与比较。当被要求根据箱线图或直方图比较两个分布时，至少要陈述两点：一点关于集中趋势度量（如中位数），另一点关于离散度量（如 IQR）。用图表中的数值加以支撑，并与情境联系起来。例如，“诊所 A 的等候时间中位数（12 分钟）高于诊所 B（8 分钟），说明诊所 B 整体更快。”
Practise using comparative phrases such as ‘on average’, ‘more consistent’, ‘wider spread’, and ‘the distributions overlap’. Always answer in full sentences and refer to specific features like whiskers, medians, or modal classes. This skill will boost your grade significantly.
练习使用诸如“平均而言”、“更一致”、“分布更广”以及“分布有重叠”等比较性措辞。始终用完整的句子作答，并指涉具体的特征，如须线、中位数或众数类。这项技能会显著提高你的成绩。
12. Building Your Winter Revision Timetable | 制定你的寒假复习时间表
Now that you have the content broken down, allocate two to three days per topic over the holiday. Begin each session by reviewing the key formulas and concepts briefly, then complete a set of mixed practice questions from a WJEC-style statistics textbook or past paper. Mark your work carefully, and keep a mistake log where you write down what went wrong and the correct approach. Spend the last few days of the break attempting a full past paper under timed conditions to build exam stamina.
现在你已经把内容拆分开来，假期里可为每个主题安排两到三天。每段学习开始时，先简要复习关键公式和概念，然后完成一组来自 WJEC 风格统计教材或历年真题的混合练习题。仔细批改你的作业，并建立一个错题本，记下错因和正确的解法。寒假最后几天，在限时条件下完成一套完整的过往真题，以锻炼考试耐力。
Stay consistent – even 40 minutes of focused statistics revision each day will make a substantial difference. If a particular topic feels tricky, use online videos or revisit the examples in your class notebook before moving on. Remember, the goal is understanding, not speed. Good luck with your revision, and enjoy a productive winter break!
保持连贯性——每天哪怕只有 40 分钟专注的统计复习，也会带来显著的不同。如果某个主题感到棘手，先使用在线视频或重温课堂笔记本上的示例，再继续推进。记住，目标是理解，而非速度。祝复习顺利，度过一个高效的寒假！
Published by TutorHao | Statistics Revision Series | aleveler.com
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