📚 Year 10 Edexcel Statistics: Summer Bridging Course | Year 10 Edexcel 统计：暑期预习与衔接课程
Welcome to your summer bridging course for Year 10 Edexcel Statistics! This resource helps you move from Year 9 into GCSE Statistics with confidence. You will explore how data is collected, summarised and interpreted, building skills that are essential for the exam and for understanding the world around you. Short, focused study over the summer will give you a real head start.
欢迎参加 Year 10 Edexcel 统计学的暑期衔接课程！本资料旨在帮助你从 Year 9 平稳过渡到 GCSE 统计学，并建立信心。你将探索如何收集、概括和解读数据，这些技能不仅对考试至关重要，也能让你更好地理解周遭的世界。利用暑假进行简短、集中的学习，会让你赢在起跑线上。
1. Introduction to Statistics: Why Data Matters | 统计学简介：数据的重要性
Statistics is the science of collecting, organising, analysing and drawing conclusions from data. In today’s world, data drives decisions in medicine, business, sport and government. Learning statistics helps you tell the difference between a sound claim and a misleading one. You will learn to present data clearly, calculate summary measures and use probability to measure uncertainty.
统计学是收集、整理、分析数据并得出结论的科学。当今世界，数据驱动着医学、商业、体育和政府等领域的决策。学习统计能帮助你分辨可靠的说法与误导性的说法。你将学会清晰地展示数据、计算概括性指标，并用概率来衡量不确定性。
2. Types of Data: Categorical vs. Numerical | 数据类型：分类数据与数值数据
Data can be categorical (qualitative) or numerical (quantitative). Categorical data describe groups or qualities, such as ‘favourite colour’ or ‘type of pet’. Nominal data have no natural order (e.g. hair colour), while ordinal data have an order (e.g. satisfaction ratings: poor, fair, good). Numerical data involve numbers and can be discrete, obtained by counting (e.g. number of cars in a car park), or continuous, obtained by measuring (e.g. height, mass, time). Choosing the right diagram and average depends on recognising these types correctly.
数据可以分为分类数据（定性数据）和数值数据（定量数据）。分类数据描述组别或属性，例如“最喜欢的颜色”或“宠物类型”。名义数据没有自然顺序（如头发颜色），而有序数据存在顺序（如满意度评分：差、一般、好）。数值数据涉及数字，可以是离散的，通过计数得到（如停车场中的汽车数量），也可以是连续的，通过测量得到（如身高、质量、时间）。选择正确的图表和平均数取决于能否正确识别这些类型。
3. Collecting Data: Surveys and Sampling | 数据收集：调查与抽样
We collect data through surveys, experiments or observations. A survey often uses a questionnaire with clear, unbiased questions. When we cannot survey an entire population, we select a sample. A good sample is representative and avoids bias. Common sampling methods include: simple random sampling (every member has an equal chance), stratified sampling (the population is split into groups and members are selected in proportion to group size) and systematic sampling (every nth member is chosen). Interviewing only your friends about school meals introduces bias – the sample must reflect the whole population.
我们通过调查、实验或观察来收集数据。调查通常会使用一份包含清晰、无偏问题的问卷。当我们无法对整个人口进行调查时，就需要选取一个样本。一个好的样本要有代表性且避免偏差。常见的抽样方法包括：简单随机抽样（每个成员被选中的机会均等）、分层抽样（将总体分为若干层，并按照层的大小比例选取）和系统抽样（每隔固定个数抽取一个成员）。如果只向自己的朋友调查学校午餐，就会引入偏差——样本必须能够反映整个人口的特征。
4. Organising Data: Frequency Tables | 数据整理：频数表
A frequency table is the first step in making sense of raw data. You list each data value or group and record how many times it occurs – its frequency. A tally column helps you count accurately. For grouped data, class intervals such as 10–19, 20–29 are used. From a frequency table you can quickly find totals, calculate averages and begin to spot patterns.
频数表是理解原始数据的第一步。你列出每个数据值或数据组，并记录它出现的次数——即频数。计号列有助于准确计数。对于分组数据，会使用诸如 10–19、20–29 这样的组距。通过频数表，你可以迅速求出总和、计算平均数，并开始发现数据的分布模式。
Here is a simple frequency table for the number of pets owned by students:
下面是一个关于学生拥有宠物数量的简单频数表：
| Number of pets | Tally | Frequency |
|---|---|---|
| 0 | ||| | 3 |
| 1 | |||| | 4 |
| 2 | || | 2 |
5. Charts and Graphs: Bar Charts and Pie Charts | 图表：条形图与饼图
Bar charts are ideal for categorical and discrete data. Each bar’s height shows the frequency, and there are gaps between bars to emphasise that the categories are separate. You should always label axes and give the chart a clear title. Pie charts display how a total is split into parts. The angle for each sector is found using the formula:
条形图非常适合表示分类数据和离散数据。每个条形的高度代表频数，条形之间留有间隙，以强调类别是相互独立的。你应当始终为坐标轴添加标签，并给图表加上清晰的标题。饼图则用于展示一个总体如何被划分为若干部分。每个扇形的角度可以用以下公式计算：
Angle = (frequency / total frequency) × 360°
For example, if 10 out of 40 students prefer oranges, the angle for oranges is (10 ÷ 40) × 360° = 90°. Both chart types help you see proportions quickly.
例如，如果 40 名学生中有 10 人更喜欢橙子，那么橙子对应的扇形角度为 (10 ÷ 40) × 360° = 90°。这两种图表都能帮助你快速查看比例关系。
6. Stem-and-Leaf Diagrams | 茎叶图
A stem-and-leaf diagram organises numerical data while keeping each original value visible. The ‘stem’ is the leading digit(s), and the ‘leaf’ is the final digit. For instance, the number 42 has stem 4 and leaf 2. You must always include a key, such as 4|2 means 42. Arrange the stems in order and list the leaves in order, too. Stem-and-leaf plots make it easy to spot the mode, the median and the range.
茎叶图可以整理数值数据，同时保留每一个原始数值。“茎”是前一位或多位数字，“叶”是最后一位数字。例如，数字 42 的茎为 4，叶为 2。你必须始终附上图例，例如 4|2 表示 42。茎要按顺序排列，叶也要按顺序列出。茎叶图便于快速找到众数、中位数和极差。
Consider the data: 23, 25, 31, 33, 33, 40. The ordered stem‑and‑leaf diagram is:
考虑数据：23, 25, 31, 33, 33, 40。排序后的茎叶图如下：
2 | 3 5
3 | 1 3 3
4 | 0
Key: 2|3 = 23
From this, you can see the mode is 33, the median is (31+33)/2 = 32, and the range is 40 – 23 = 17.
由此可以看出，众数是 33，中位数是 (31+33)/2 = 32，极差为 40 – 23 = 17。
7. Averages: Mean, Median, Mode | 平均数：均值、中位数、众数
Three commonly used averages summarise a dataset. The mode is the value that appears most often. It is the only average that can be used for categorical data. The median is the middle value when data are sorted. For n values, the median is at position (n+1)/2. If two numbers sit in the middle, take their mean. The mean uses all values:
三种常用的平均数可以概括一个数据集。众数是出现次数最多的值。它是唯一能用于分类数据的平均数。中位数是将数据排序后位于中间的值。对于 n 个数据，中位数的位置是 (n+1)/2。如果中间有两个数，则取它们的均值。均值则使用了所有数值：
x̄ = Σx / n
For the data set 5, 8, 12, 5: mode = 5, ordered values are 5, 5, 8, 12 so median = (5+8)/2 = 6.5, and mean = (5+8+12+5)/4 = 7.5. The mean is sensitive to extreme values, while the median is resistant to outliers. You should choose the most appropriate average for your data.
对于数据集 5, 8, 12, 5：众数 = 5，排序后为 5, 5, 8, 12，因此中位数 = (5+8)/2 = 6.5，均值 = (5+8+12+5)/4 = 7.5。均值易受极端值影响，而中位数不受异常值干扰。你应当根据数据特点选择最合适的平均数。
8. Measures of Spread: Range and Interquartile Range | 离散度量：极差与四分位距
Spread tells you how varied your data are. The simplest measure is the range:
离散程度说明数据的变异大小。最简单的度量是极差：
Range = highest value – lowest value
The range is easy to calculate but can be distorted by a single outlier. The interquartile range (IQR) measures the spread of the middle 50% of data and is more robust:
极差计算简便，但易受单一异常值的影响。四分位距（IQR）衡量的是中间 50% 数据的散布情况，较为稳健：
IQR = Q₃ – Q₁
Q₁ (lower quartile) is the median of the lower half of the data, and Q₃ (upper quartile) is the median of the upper half. For example, with the ordered data 5, 5, 8, 12, 15, 18, 20: Q₁ = 5, Q₃ = 18, so IQR = 18 – 5 = 13. The IQR tells you that the central half of the values lie within an interval of length 13.
Q₁（下四分位数）是数据下半部分的中位数，Q₃（上四分位数）是上半部分的中位数。例如，对于排序数据 5, 5, 8, 12, 15, 18, 20：Q₁ = 5，Q₃ = 18，因此 IQR = 18 – 5 = 13。这个 IQR 告诉你，中间一半的数据落在宽度为 13 的区间内。
9. Introduction to Probability | 概率入门
Probability measures how likely an event is to happen. It is expressed as a number between 0 (impossible) and 1 (certain), often as a fraction, decimal or percentage. The basic rule for equally likely outcomes is:
概率衡量事件发生的可能性。它用一个介于 0（不可能）与 1（必定发生）之间的数字表示，常用分数、小数或百分比表达。等
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