📚 Year 8 Edexcel Statistics: Summer Preview and Bridging Course | Edexcel Year 8 统计：暑期预习与衔接课程
Welcome to the Year 8 Edexcel Statistics summer preview and bridging course! This guide is designed to help you review the key statistical concepts from Year 7 and give you a head start on the new topics you will encounter in Year 8. Whether you are looking to build confidence or get ahead, this structured revision will ensure you enter the new school year ready to collect, analyse, and interpret data like a true statistician.
欢迎来到 Year 8 Edexcel 统计暑期预习与衔接课程！本指南旨在帮助你复习 Year 7 的关键统计概念，并提前了解 Year 8 你将遇到的新主题。无论你是想建立信心还是提前学习，这份有条理的复习材料将确保你在新学年开始时，能够像一名真正的统计学家那样收集、分析和解读数据。
1. Why Statistics Matters | 为什么统计很重要
Statistics helps us make sense of data, identify patterns, and make informed decisions. From weather forecasts to sports analytics, statistics is everywhere.
统计学帮助我们理解数据、识别模式并做出明智的决策。从天气预报到体育分析，统计学无处不在。
In Year 8, you will learn how to design surveys, display data clearly, calculate averages, and begin exploring probability. These skills form the backbone of data handling and are essential for GCSE and beyond.
在 Year 8，你将学习如何设计调查、清晰地展示数据、计算平均数，并开始探索概率。这些技能构成了数据处理的基础，对 GCSE 及以后的学习至关重要。
Building a strong foundation now will make future topics like scatter graphs, correlation, and hypothesis testing much easier. Statistics is not just about numbers—it is about telling the story behind the numbers.
现在打下坚实的基础，将使未来的主题如散点图、相关性和假设检验变得更容易。统计学不仅仅是关于数字——它还关乎讲述数字背后的故事。
2. Types of Data | 数据类型
Data can be split into two main types: qualitative (categorical) and quantitative (numerical). Qualitative data describes qualities or categories, such as colours, names, or favourite subjects.
数据可以分为两大类：定性（类别）数据和定量（数值）数据。定性数据描述性质或类别，例如颜色、姓名或最喜欢的科目。
Quantitative data can be discrete (countable, like the number of students in a class) or continuous (measurable, like height in cm or temperature). Discrete data takes only specific values, while continuous data can take any value within a range.
定量数据可以是离散的（可数的，如班级学生人数）或连续的（可测量的，如身高厘米数或温度）。离散数据只取特定值，而连续数据可以取某一范围内的任何值。
Recognising data types helps you choose the right chart and summary statistics. For example, bar charts are ideal for qualitative data, whereas histograms (which you will meet later) are for continuous data.
识别数据类型有助于你选择合适的图表和概括性统计量。例如，柱状图适用于定性数据，而直方图（你稍后会学到）适用于连续数据。
3. Designing a Survey and Collecting Data | 设计调查与收集数据
A good statistical investigation starts with a clear question and a well-designed data collection sheet or questionnaire. The question should be specific, unbiased, and possible to answer.
一个好的统计调查始于一个清晰的问题和精心设计的数据收集表或问卷。问题应当具体、无偏见且能够回答。
Avoid leading questions like ‘Don’t you agree that homework is too much?’ and overlapping categories such as ‘0–5, 5–10’. Always include an option that covers all possibilities, like ‘Other’ or ‘None’.
避免诱导性问题，如 “你不觉得作业太多了吗？”，以及重叠的类别，如 “0–5, 5–10″。务必包含一个涵盖所有可能性的选项，如 “其他” 或 “无”。
In Year 8, you will learn to criticise existing surveys and suggest improvements, as well as design your own. A pilot survey can help identify flaws before the main data collection.
在 Year 8，你将学习批评现有调查并提出改进建议，以及设计自己的调查。试点调查有助于在主要数据收集前发现缺陷。
4. Organising Data: Frequency Tables | 整理数据：频率表
Once collected, data is often organised into a frequency table, which lists each value or category alongside how many times it occurs. Tally marks are a handy way to record data as you go.
收集数据后，通常将其整理成频率表，列出每个数值或类别及其出现的次数。画记符是记录数据时一种方便的方法。
For grouped continuous data, we use class intervals, making sure there are no gaps and all intervals are equal width where possible. The intervals must be written clearly, e.g., 0 ≤ h < 10, 10 ≤ h < 20.
对于分组的连续数据，我们使用组距，确保没有间隙，并尽可能使所有组距宽度相等。组距必须清晰地书写，例如 0 ≤ h < 10, 10 ≤ h < 20。
From a frequency table we can find the mode (most frequent) and later calculate the mean. Here is an example of a frequency table for the number of pets owned by 30 families:
从频率表中我们可以找到众数（最频繁出现的值），稍后还可以计算平均数。以下是一个关于 30 个家庭养宠物数量的频率表示例：
| Number of pets (x) | Frequency (f) |
|---|---|
| 0 | 8 |
| 1 | 12 |
| 2 | 6 |
| 3 | 4 |
| Total | 30 |
5. Bar Charts and Frequency Polygons | 柱状图与频数多边形
A bar chart uses bars of equal width to represent categorical or discrete data, with the height showing the frequency. Gaps between bars indicate that the categories are separate. Always label both axes, give the chart a title, and use a sensible scale.
柱状图使用等宽的条形来表示分类或离散数据，条形的高度表示频率。条形之间的间隙表示类别是独立的。务必标注两个坐标轴、给图表一个标题，并使用合适的刻度。
A frequency polygon is created by joining the midpoints of the tops of bars with straight lines, often used to show the shape of a distribution for grouped continuous data. To complete the polygon, join the first and last midpoints to the horizontal axis at the midpoints of the extra class intervals below and above the data range.
频数多边形是通过用直线连接条形顶部的中点而创建的，通常用于显示分组连续数据的分布形状。要完成多边形，需将第一个和最后一个中点与水平轴在数据范围下方和上方额外组距的中点处连接。
Both bar charts and frequency polygons should be drawn on graph paper or carefully scaled axes. In Year 8, you will practise constructing these accurately and interpreting trends.
柱状图和频数多边形都应绘制在方格纸或精确标度的坐标轴上。在 Year 8，你将练习准确地构建这些图形并解读趋势。
6. Pie Charts and Stem-and-Leaf Diagrams | 饼图与茎叶图
A pie chart displays proportions of a whole. To draw one, calculate the angle for each category using the formula:
饼图显示整体的比例。要绘制饼图，需要使用以下公式计算每个类别的角度：
Angle = (Frequency ÷ Total frequency) × 360°
角度 = (频率 ÷ 总频率) × 360°
Measure angles from the centre with a protractor, label each sector clearly, and use colour or shading to distinguish them. Pie charts are excellent for showing relative sizes.
用量角器从圆心量出角度，清晰地标注每个扇区，并用颜色或阴影加以区分。饼图非常适合显示相对大小。
A stem-and-leaf diagram keeps the original data values while showing the distribution. The stem is all but the last digit; the leaf is the final digit. An ordered stem-and-leaf diagram sorts the leaves from smallest to largest.
茎叶图在显示分布的同时保留了原始数据值。茎是除最后一位数字外的所有数位；叶是最后一位数字。有序茎叶图会将叶子从小到大排序。
Back-to-back stem-and-leaf diagrams allow comparison of two datasets sharing the same stem. Leaves for one dataset extend to the left, the other to the right. Remember to include a key explaining what stem and leaf represent.
背靠背茎叶图可以比较共享同一茎的两个数据集。一个数据集的叶子向左延伸，另一个向右延伸。记得要包含一个图例，说明茎和叶代表什么。
7. Averages: Mean, Median and Mode | 平均数：均值、中位数、众数
The mean is the arithmetic average: add all values and divide by the number of values. For a frequency table, use:
均值是算术平均数：将所有数值相加后除以数值的个数。对于频率表，使用：
Mean = Σ(f × x) ÷ Σf
均值 = Σ(f × x) ÷ Σf
where x is the data value and f is the frequency. Always multiply each value by its frequency before summing.
其中 x 是数据值，f 是频率。求和前务必先将每个值乘以其频率。
The median is the middle value when data is ordered. If there are n values, the median is at the (n+1)/2 th position. For grouped data, you will estimate the median using interpolation, which is an extension skill in Year 8.
中位数是将数据排序后位于中间的数值。如果有 n 个值，中位数位于第 (n+1)/2 个位置。对于分组数据，你将使用插值法估算中位数，这是 Year 8 的一项拓展技能。
The mode is the most frequent value. A dataset can have one mode, more than one (bimodal), or no mode. The mode is the only average suitable for qualitative data.
众数是最常出现的值。一个数据集可能有一个众数、多个众数（双峰），或者没有众数。众数是唯一适用于定性数据的平均数。
Choosing the right average depends on the data type and the presence of outliers. The mean uses all data but is sensitive to extreme values; the median is robust to outliers.
选择正确的平均数取决于数据类型和是否存在异常值。均值使用了所有数据，但对极端值敏感；中位数对异常值具有稳健性。
8. Measures of Spread: Range and Interquartile Range | 离散程度：极差与四分位距
The range is the difference between the largest and smallest values: Range = Max − Min. It gives a simple measure of spread but is affected by outliers.
极差是最大值与最小值的差：极差 = 最大值 − 最小值。它提供了一种简单的离散程度度量，但受异常值影响。
The interquartile range (IQR) measures the spread of the middle 50% of the data: IQR = Upper quartile (Q3) − Lower quartile (Q1). To find quartiles, order the data and identify the medians of
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