WJEC GCSE Statistics Syllabus: Full Breakdown | WJEC GCSE 统计：课程大纲全面解析

📚 WJEC GCSE Statistics Syllabus: Full Breakdown | WJEC GCSE 统计：课程大纲全面解析

WJEC GCSE Statistics gives learners a practical understanding of how data is collected, presented, summarised and interpreted. The course is built around the statistical enquiry cycle, so you will not just learn separate techniques: you will use them to answer real questions involving variation, uncertainty and comparison.

WJEC GCSE 统计让学生掌握数据收集、呈现、汇总与解释的实用方法。课程围绕统计探究循环展开，因此你不仅要学习单个技巧，还要运用它们回答涉及变异、不确定性和比较的实际问题。

1. Course Overview | 课程概览

The WJEC GCSE Statistics course covers the full data-handling process: planning an investigation, collecting data, processing and representing data, calculating statistical measures, and drawing conclusions. It develops the statistical literacy needed for subjects such as economics, geography, psychology, biology and business.

WJEC GCSE 统计课程覆盖完整的数据处理过程：规划调查、收集数据、处理与表示数据、计算统计量并得出结论。课程培养经济、地理、心理学、生物学和商科等学科所需的统计素养。

The course also emphasises written communication: you must be able to interpret charts, compare data sets, comment on reliability and explain whether evidence supports a claim.

课程同时强调书面表达：你必须能够解读图表、比较数据集、评论数据的可靠性，并解释证据是否支持某个结论。

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2. Assessment Structure | 评估结构

Assessment is typically linear and examination-based, with a mix of short-response, data-response and extended questions. Candidates are expected to apply statistical techniques to both familiar and unfamiliar contexts, and to justify their choices of method and presentation.

评估通常为线性、以笔试为主，包含简答题、数据题和扩展题。考生需要将统计方法应用于熟悉和陌生的情境，并说明所选方法和呈现方式的理由。

The main assessment objectives are:

主要评估目标如下：

• AO1 Recall and use knowledge — 回忆并运用统计知识、定义和公式。
• AO2 Apply techniques — 在数据分析任务中应用统计方法。
• AO3 Analyse and evaluate — 解释结果、比较数据并批判性评估统计信息。

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3. Data Types and Sampling | 数据类型与抽样

You must be able to classify data as primary or secondary, qualitative or quantitative, and discrete or continuous. Primary data is collected by the researcher for a specific purpose, while secondary data already exists and may have been collected for a different aim.

你必须能够将数据分为一手数据与二手数据、定性数据与定量数据、离散数据与连续数据。一手数据由研究者为特定目的收集，而二手数据已经存在，可能出于不同目的收集。

Data type | 数据类型	Definition | 定义
Primary data | 一手数据	Collected directly by the researcher | 由研究者直接收集
Secondary data | 二手数据	Already available from another source | 来自其他来源的已有数据
Discrete data | 离散数据	Can only take distinct values, e.g. number of cars | 只能取特定值，例如汽车数量
Continuous data | 连续数据	Can take any value in a range, e.g. height | 可在一个区间内取任意值，例如身高

Sampling methods include simple random sampling, stratified sampling, systematic sampling, cluster sampling and quota sampling. Stratified sampling keeps the population structure by sampling proportionately from each group, which often makes it more representative.

抽样方法包括简单随机抽样、分层抽样、系统抽样、整群抽样和配额抽样。分层抽样按比例从各组中抽取样本以保持总体结构，因此通常更具代表性。

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4. Data Collection Methods | 数据收集方法

Common collection methods are questionnaires, interviews, experiments and observation. Each method has strengths and weaknesses: questionnaires can reach many people cheaply, but responses may be incomplete or misunderstood; interviews give richer detail but can be time-consuming and subject to interviewer bias.

常见的数据收集方法有问卷、访谈、实验和观察。每种方法都有优缺点：问卷能低成本覆盖较多人，但回答可能不完整或被误解；访谈能获得更详细信息，但耗时且可能受到访谈者偏见影响。

A good questionnaire should use clear language, avoid leading or sensitive questions, and be tested through a pilot study before full distribution. The pilot helps identify ambiguous wording and poor response options.

一份好的问卷应使用清晰语言，避免引导性或敏感问题，并在正式发放前通过试点研究进行测试。试点有助于发现模糊措辞和不良选项。

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5. Representing Data | 数据表示

Data can be represented using bar charts, pie charts, histograms, frequency polygons, cumulative frequency curves, box plots, stem-and-leaf diagrams and scatter diagrams. The best choice depends on the data type and the message you want to highlight.

数据可以用条形图、饼图、直方图、频数多边形、累积频率曲线、箱线图、茎叶图和散点图表示。最佳选择取决于数据类型以及你想强调的信息。

• Histogram — 用于连续数据，柱面积与频数成正比。
• Cumulative frequency curve — 用于估计中位数和四分位数。
• Box plot — 展示最小、下四分位、中位、上四分位和最大值的图形。
• Pie chart — 显示各部分在整体中所占比例。

Always label axes, use consistent scales and give a title. A diagram should be clear enough for another person to read without seeing the original data.

务必标注坐标轴、使用一致的比例并给出标题。图表应足够清晰，让读者无需查看原始数据就能理解。

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6. Measures of Central Tendency | 集中趋势度量

The mean, median and mode describe the centre of a data set. The mean uses all values and is affected by outliers, the median is the middle value and is robust to outliers, and the mode is the most frequent value.

平均数、中位数和众数用于描述数据集的中心位置。平均数使用所有数值并受异常值影响，中位数是中间值且对异常值稳健，众数是最常出现的值。

Mean: x̄ = ∑x ÷ n

For grouped data, the mean is estimated using midpoints and frequencies:

对于分组数据，使用组中值和频数估计平均数：

Grouped mean: x̄ = ∑fx ÷ ∑f

The position of the median is found using (n + 1) ÷ 2 for ungrouped data. For large grouped data sets, interpolation within the cumulative frequency curve can estimate the median.

对于未分组数据，中位数的位置通过 (n + 1) ÷ 2 确定。对于大型分组数据集，可在累积频率曲线上进行插值估计中位数。

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7. Measures of Dispersion | 离差度量

Dispersion tells us how spread out the data is. The range is the simplest measure, but it only uses the two extreme values. The interquartile range IQR = Q3 − Q1 covers the middle 50% and is less affected by outliers.

离散程度告诉我们数据的分散程度。极差是最简单的度量，但只使用两个极端值。四分位距 IQR = Q3 − Q1 覆盖中间 50%，不易受异常值影响。

Standard deviation measures the average distance of values from the mean. A larger standard deviation indicates greater spread. You may be given the formula or expected to use it from memory:

标准差衡量各数值与平均数的平均距离。标准差越大，数据越分散。你可能会看到公式，或需要记住它：

Standard deviation: σ = √(∑(x − x̄)² ÷ n)

For grouped data, replace x with the midpoint and multiply by frequency: σ = √(∑f(x − x̄)² ÷ ∑f).

对于分组数据，用组中值代替 x 并乘以频数：σ = √(∑f(x − x̄)² ÷ ∑f)。

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8. Probability | 概率

Probability measures the chance of an event occurring and always lies between 0 and 1. A probability of 0 means impossible, and a probability of 1 means certain. For equally likely outcomes, probability is calculated as the number of favourable outcomes divided by the total number of outcomes.

概率衡量事件发生的可能性，范围始终在 0 到 1 之间。概率为 0 表示不可能，1 表示必然。对于等可能结果，概率等于有利结果数除以总结果数。

P(A) = n(A) ÷ n(S)

For mutually exclusive events A and B, the addition rule is:

对于互斥事件 A 和 B，加法规则为：

P(A ∪ B) = P(A) + P(B)

The complement rule states that P(not A) = 1 − P(A). Relative frequency from an experiment can be used as an estimate of probability when outcomes are not equally likely.

互补规则指出 P(非 A) = 1 − P(A)。当结果不等可能时，可用实验中的相对频率估计概率。

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9. Combined Events and Tree Diagrams | 组合事件与树形图

Tree diagrams are a powerful way to model two or more successive events. To find the probability of a sequence of outcomes, multiply along the branches. To find the probability of one or another sequence, add the branch probabilities.

树形图是对两个或多个连续事件建模的有效工具。求一系列结果的概率时，沿分支相乘；求若干序列中任一序列发生的概率时，将各分支概率相加。

If events A and B are independent, then P(A and B) = P(A) × P(B). If they are not independent, use conditional probability:

若事件 A 和 B 独立，则 P(A 且 B) = P(A) × P(B)。若它们不独立，则使用条件概率：

P(A | B) = P(A ∩ B) ÷ P(B)

Always check that branch probabilities from the same point sum to 1, and that final outcome probabilities sum to 1.

务必检查同一点出发的各分支概率之和为 1，且最终结果概率之和为 1。

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10. Correlation and Regression | 相关与回归

A scatter diagram shows the relationship between two variables. Positive correlation means both variables tend to increase together, negative correlation means one increases while the other decreases, and no correlation means there is no clear trend.

散点图显示两个变量之间的关系。正相关意味着两个变量倾向于同时增加，负相关意味着一个增加而另一个减少，无相关则表示没有明显趋势。

Spearman’s rank correlation coefficient, rₛ, measures the strength and direction of a monotonic relationship. It can be calculated from ranked data:

Spearman 等级相关系数 rₛ 度量单调关系的强度和方向。它可由排序数据计算：

rₛ = 1 − (6∑d²) ÷ (n(n² − 1))

In the formula, d is the difference between each pair of ranks and n is the number of pairs. A regression line such as y = a + bx can be used to make predictions, provided the data shows a sufficiently strong linear trend and you do not extrapolate far beyond the range.

公式中，d 是每对数据的秩差，n 是数据对数。只要数据呈现足够强的线性趋势，就可以使用回归线 y = a + bx 进行预测，但不要过度外推到数据范围之外。

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11. Time Series and Index Numbers | 时间序列与指数

Time series data records values over equal time intervals, such as monthly sales. A moving average smooths out short-term fluctuations and reveals the underlying trend. A 3-point moving average replaces each value with the mean of itself and its immediate neighbours.

时间序列数据记录等时间间隔内的数值，例如月度销售额。移动平均可以平滑短期波动并揭示潜在趋势。三点移动平均用每个值与其前后相邻值的平均数替换该值。

Index numbers compare values over time relative to a base period. The base value is usually set to 100:

指数用于比较一段时间内相对于基期的数值变化。基期值通常设为 100：

Index number = (Current value ÷ Base value) × 100

If the index rises from 100 to 112, this indicates a 12% increase from the base period. Index numbers are especially useful for comparing changes in prices, wages or quantities when the raw units differ.

如果指数从 100 上升到 112，表示比基期增长了 12%。当原始单位不同时，指数特别适合比较价格、工资或数量的变化。

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12. Statistical Enquiry Cycle and Exam Tips | 统计探究循环与考试技巧

The PPDAC cycle is a useful structure for any statistical investigation: Problem, Plan, Data, Analysis, Conclusion. In the problem phase, define the question and population. In the plan phase, decide on data collection and sampling methods.

PPDAC 循环是任何统计调查的有用框架：问题、计划、数据、分析、结论。在问题阶段，明确研究问题和总体；在计划阶段，确定数据收集和抽样方法。

In the data phase, collect or source the data. In analysis, summarise the data with diagrams and statistical measures. In conclusion, interpret the findings, discuss limitations and suggest improvements.

在数据阶段，收集或获取数据；在分析阶段，用图表和统计量汇总数据；在结论阶段，解释结果、讨论局限性并提出改进建议。

In the exam, show all working, give units, label charts completely and answer questions in context. If asked to compare data, quote specific figures such as the median, IQR or standard deviation rather than making vague comments.

考试中要写出所有计算步骤、标明单位、完整标注图表并联系题目情境作答。如果要求比较数据，应引用具体数值，如中位数、四分位距或标准差，而不是笼统评论。

Published by TutorHao | Statistics Revision Series | aleveler.com

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