📚 Year 10 WJEC Statistics: Summer Preview and Bridging Course | WJEC Year 10 统计：暑期预习与衔接课程
Welcome to your Year 10 WJEC Statistics journey! This summer bridging guide will help you refresh key ideas from Key Stage 3 and build a solid foundation for the GCSE course. You will explore how data is collected, summarised, and interpreted — skills that are essential not only for exams but for making sense of the world around you. By working through this preview, you will enter Year 10 feeling confident and prepared.
欢迎来到 Year 10 WJEC 统计课程！本暑期衔接指南将帮助你复习 Key Stage 3 的核心概念，并为 GCSE 课程奠定扎实基础。你将学习如何收集、总结和解读数据——这些技能不仅对考试至关重要，也有助于你理解周围的世界。通过这篇预习，你将带着信心与准备步入 Year 10。
1. Why Study Statistics? The Big Picture | 为什么学习统计？全局视角
Statistics is the science of collecting, analysing and drawing conclusions from data. In Year 10, you will move beyond simple charts and averages to learn about sampling methods, probability models and statistical investigations. These skills are used in medicine, sports, business and government to make evidence-based decisions. The WJEC specification emphasises real-world applications, so you will often see questions based on surveys, experiments and everyday scenarios.
统计学是收集、分析数据并得出结论的科学。在 Year 10，你将超越简单的图表和平均数，学习抽样方法、概率模型以及统计调查。这些技能被应用于医学、体育、商业和政府决策中，用以基于证据做出判断。WJEC 考纲强调实际应用，因此你会经常遇到基于调查、实验和日常场景的题目。
2. Types of Data: Categorical vs Numerical | 数据类型：分类数据与数值数据
Before you can analyse data, you must identify its type. Categorical (or qualitative) data describes qualities or groups, such as eye colour or favourite subject. Numerical (or quantitative) data involves numbers and can be discrete — counted values like number of pets — or continuous — measured values like height. Recognising the data type helps you choose the right chart and the right summary statistics.
在分析数据之前，你必须确定它的类型。分类（定性）数据描述的是属性或类别，例如眼睛颜色或最喜欢的科目。数值（定量）数据涉及数字，可以是离散型——如宠物数量这类可计数的值，也可以是连续型——如身高这类测量值。识别数据类型有助于你选择合适的图表和汇总统计量。
| Data Type | Description | Examples |
|---|---|---|
| Categorical | Groups or labels | Gender, car colour |
| Numerical discrete | Counted whole numbers | Shoe size, number of siblings |
| Numerical continuous | Measured, any value in a range | Weight, time, temperature |
3. Collecting Data: Surveys and Sampling | 数据收集：调查与抽样
A statistical investigation starts with a clear question and a plan for gathering information. In Year 10, you will learn about primary data (collected by you) and secondary data (from existing sources). You will also explore different sampling techniques, including random sampling, systematic sampling and stratified sampling. Understanding bias is critical — a poor sample can lead to misleading conclusions.
统计调查始于一个清晰的问题和数据收集计划。在 Year 10，你将学习原始数据（自己收集的）和二手数据（来自现有来源）的区别，还会探索不同的抽样方法，包括随机抽样、系统抽样和分层抽样。理解偏差至关重要——糟糕的样本会导致误导性的结论。
- Random sampling: every member of the population has an equal chance of being selected.
- Systematic sampling: choosing every nth item from a list.
- Stratified sampling: dividing the population into groups (strata) and sampling proportionally from each.
- 随机抽样：总体中每个成员被选中的机会均等。
- 系统抽样：从列表中每隔一定数量选取一个样本。
- 分层抽样：将总体分成若干层，按比例从每一层中抽样。
4. Organising Data: Frequency Tables | 数据整理：频数分布表
Once data is collected, it is often messy. A frequency table helps you organise raw data into a clear summary. For discrete data, you list each value alongside how often it appears. For continuous data, you group values into class intervals. You will also learn to calculate cumulative frequency, which is a running total of frequencies and forms the basis for cumulative frequency graphs used in later topics.
收集到数据后，通常杂乱无章。频数分布表能帮助你将原始数据整理成清晰的汇总。对于离散数据，你列出每个数值及其出现的次数；对于连续数据，你需要将数值分入组区间。你还将学习计算累积频数，它是对频数进行累加，并为后续学习中使用的累积频数图奠定基础。
Cumulative frequency at a class = sum of frequencies up to and including that class
累积频数（某组）= 该组及之前各组频数的总和
5. Presenting Data: Bar Charts and Pie Charts | 数据展示：条形图与饼图
Charts turn numbers into pictures. Bar charts are ideal for categorical or discrete data; the height of each bar represents the frequency. Always label axes, use equal bar widths and leave gaps between bars. Pie charts show proportions of a whole, with each slice’s angle calculated as (frequency ÷ total frequency) × 360°. In WJEC exams, you may be asked to interpret or construct these diagrams from given data.
图表能将数字转化为图像。条形图适用于分类或离散数据，每个条形的高度代表频数。务必标注坐标轴，保持条形宽度相等，并在条形之间留有空隙。饼图展示整体中各部分的比例，每个扇形的角度通过 (频数 ÷ 总频数) × 360° 计算。在 WJEC 考试中，你可能需要根据给定数据解读或绘制这些图表。
Angle for a category = (Category frequency ÷ Total frequency) × 360°
类别角度 = (类别频数 ÷ 总频数) × 360°
6. Presenting Data: Line Graphs and Scatter Plots | 数据展示：折线图与散点图
Line graphs are used to display trends over time, with time on the horizontal axis and the variable of interest on the vertical axis. Scatter plots show the relationship between two numerical variables. By looking at the pattern of points, you can describe correlation — positive, negative or none. In Year 10, you will also learn to draw a line of best fit and use it to make predictions, always being careful about interpolation and extrapolation.
折线图用于显示数据随时间变化的趋势，横轴通常为时间，纵轴为关注的变量。散点图则展示两个数值变量之间的关系。通过观察点的分布，你可以描述相关性——正相关、负相关或无相关。在 Year 10，你还将学习绘制最佳拟合线，并利用它进行预测，同时注意内插和外推的区别与风险。
- Positive correlation: as one variable increases, the other tends to increase.
- Negative correlation: as one variable increases, the other tends to decrease.
- 正相关：一个变量增大时，另一个变量也倾向于增大。
- 负相关：一个变量增大时，另一个变量倾向于减小。
7. Measures of Central Tendency | 集中趋势的度量
An average summarises a dataset with a single typical value. The three main averages are the mode, median and mean. The mode is the most frequent value, the median is the middle value when data are ordered, and the mean is calculated by adding all values and dividing by the number of values. Each average has strengths and weaknesses — for example, the mean is affected by extreme values, while the median is resistant to outliers.
平均数用一个典型值来概括整个数据集。三种主要的平均数是众数、中位数和均值。众数是出现次数最多的值，中位数是将数据排序后位于中间的值，均值则是所有数值之和除以数据个数。每种平均数都有优缺点——例如，均值受极端值影响较大，而中位数对异常值不敏感。
Mean = (Sum of all values) ÷ (Number of values)
均值 = (所有数值之和) ÷ (数值个数)
Median position = (n + 1) ÷ 2 (for an ordered list of n numbers)
中位数位置 = (n + 1) ÷ 2（对于包含 n 个数的有序列表）
8. Measures of Spread: Range and Quartiles | 离散程度的度量：极差与四分位数
Knowing the average is not enough; we also need to understand how spread out the data are. The range is the simplest measure, found by subtracting the smallest value from the largest. Quartiles divide an ordered dataset into four equal parts. The lower quartile (Q1) is the median of the lower half, the upper quartile (Q3) is the median of the upper half, and the interquartile range (IQR = Q3 − Q1) captures the middle 50% of the data. These concepts are essential for constructing box plots later in the course.
仅知道平均数还不够，我们还需了解数据的分散程度。极差是最简单的度量，由最大值减去最小值得到。四分位数将有序数据集分成四等份。下四分位数 (Q1) 是下半部分的中位数，上四分位数 (Q3) 是上半部分的中位数，四分位距 (IQR = Q3 − Q1) 则涵盖了中间 50% 的数据。这些概念对后续课程中箱线图的绘制至关重要。
- Range = Maximum − Minimum
- IQR = Q3 − Q1
- 极差 = 最大值 − 最小值
- 四分位距 = 上四分位数 − 下四分位数
9. Introduction to Probability | 概率入门
Probability is the branch of mathematics that deals with chance and uncertainty. In Year 10, you will learn to assign probabilities on a scale from 0 (impossible) to 1 (certain), using fractions, decimals or percentages. You will explore theoretical probability based on equally likely outcomes, as well as experimental probability from repeated trials. Expect to work with sample spaces, Venn diagrams and tree diagrams as you build a toolkit for solving WJEC probability problems.
概率是研究机会和不确定性的数学分支。在 Year 10，你将学习用 0（不可能）到 1（必然）之间的分数、小数或百分比来表示概率。你将探索基于等可能结果的理论概率，以及通过重复实验得到的实验概率。随着学习的深入，你将使用样本空间、韦恩图和树状图来解决 WJEC 概率问题。
P(Event) = Number of favourable outcomes ÷ Total number of possible outcomes
P(事件) = 有利结果的数量 ÷ 所有可能结果的总数
10. Summer Bridging Tasks and Tips | 暑期衔接任务与建议
To make a flying start in Year 10, try these summer activities. First, review your Year 9 notes on averages and charts — make sure you can calculate the mean, median, mode and range without hesitation. Second, practise collecting small data sets: ask friends about their screen time or record daily temperatures for a week, then present the data using a bar chart or line graph. Third, begin to use the correct statistical vocabulary, such as ‘primary data’ and ‘continuous variable’, to describe what you see. Finally, explore simple probability experiments, like tossing coins or rolling dice, and compare your experimental results with theoretical expectations. A little curiosity and regular practice will give you a huge advantage when school starts.
为了在 Year 10 抢占先机，不妨尝试以下暑期活动。首先，复习 Year 9 关于平均数和图表的笔记——确保你能毫不迟疑地计算均值、中位数、众数和极差。其次，练习收集小数据集：询问朋友们的屏幕使用时间，或记录一周的每日温度，然后用条形图或折线图展示数据。第三，开始使用正确的统计术语，例如“原始数据”和“连续变量”，来描述你所观察到的现象。最后，探索简单的概率实验，比如抛硬币或掷骰子，并将实验结果与理论预期作对比。保持好奇心和定期练习，会让你在开学时获得巨大优势。
- Refresh core skills: mean, median, mode, range, bar charts, pie charts, scatter graphs.
- Start a mini project: design a question, collect data, create a display and write a short conclusion.
- Use online sources: watch WJEC statistics revision videos and try interactive quizzes to test your knowledge.
- 巩固核心技能：均值、中位数、众数、极差、条形图、饼图、散点图。
- 开展一个小项目：设计一个问题，收集数据，制作展示图表并写下简短结论。
- 利用在线资源：观看 WJEC 统计复习视频，尝试互动测验来检验所学。
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