📚 Year 7 Cambridge Statistics: Summer Prep & Bridging Course | 剑桥7年级统计：暑期预习与衔接课程
Transitioning into Year 7 Cambridge Mathematics means building a strong foundation in Statistics. This summer bridging guide covers essential concepts such as collecting data, drawing bar charts and pie charts, finding averages, and interpreting graphs. With clear examples and bilingual explanations, you will start the new term with confidence.
步入剑桥7年级数学，意味着要为统计打下扎实根基。这份暑期衔接指南将涵盖收集数据、绘制条形图与饼图、求取平均数以及解读图表等核心概念。通过清晰示例和中英双语讲解，你将以充足信心迎接新学期。
1. What is Statistics? | 什么是统计？
Statistics is the branch of mathematics that deals with collecting, organising, presenting, analysing, and interpreting data. In Year 7, you learn to turn raw information into meaningful charts and numbers that help us understand the world.
统计是数学的一个分支，涉及数据的收集、整理、展示、分析和解读。在7年级，你将学习如何把原始信息转化为有意义的图表和数字，从而帮助我们理解世界。
Every time you see a weather forecast, a sports score table, or a school survey result, you are looking at statistics in action. It helps us make decisions based on evidence rather than guesswork.
每当你看到天气预报、体育比分表或学校调查结果时，你看到的就是统计在发挥作用。它帮助我们基于证据而非猜测来做决定。
2. Types of Data | 数据类型
Data can be qualitative (descriptive) or quantitative (numerical). Quantitative data is further split into discrete data, which can only take certain values (e.g. number of students), and continuous data, which can take any value within a range (e.g. height).
数据可以分为定性数据（描述性）和定量数据（数值型）。定量数据又分为离散数据，只能取某些特定值（如学生人数），以及连续数据，可以在一定范围内取任意值（如身高）。
Knowing the data type helps you choose the right graph. For example, bar charts suit discrete categories, while line graphs are ideal for showing trends in continuous data over time.
了解数据类型有助于选择合适的图表。例如，条形图适合离散类别，而折线图则非常适合展示连续数据随时间变化的趋势。
3. Collecting Data | 收集数据
Data can be collected through surveys, experiments, or observations. A well‑designed survey uses clear questions and avoids bias. Tally charts are a simple way to record data as you collect it.
数据可以通过调查、实验或观察来收集。设计良好的调查使用清晰的问题并避免偏差。计数表是在收集数据时进行记录的简单方法。
Always think about whether your sample represents the whole group. If you ask only your friends about their favourite subject, the result may not reflect the entire year group.
始终要思考你的样本是否能代表整个群体。如果你只问朋友他们最喜欢的科目，结果可能无法反映整个年级的情况。
4. Frequency Tables and Tallies | 频率表与计数
A frequency table organises data by listing each category alongside the number of times it appears. Tallies are grouped in fives (||||) to make counting easier.
频率表通过列出每个类别及其出现次数来整理数据。计数符号五个一组（||||）以便于计数。
| Fruit | Tally | Frequency |
|---|---|---|
| Apple | |||| | 4 |
| Banana | |||| || | 7 |
| Orange | ||| | 3 |
From a frequency table, you can quickly spot the mode (the most frequent item) and check that your total equals the number of data points.
从频率表中，你可以快速辨认出众数（出现最频繁的项目），并检查总数是否等于数据点的总数。
5. Bar Charts | 条形图
A bar chart uses rectangular bars to represent the frequency of different categories. The bars have equal width and stand apart from each other. The height of each bar corresponds to its frequency.
条形图使用矩形条来表示不同类别的频率。条宽相等且彼此分离。每个条的高度与其频率相对应。
Always label the axes and give your chart a title. The horizontal axis shows the categories, and the vertical axis shows the frequency. Use a sensible scale so that all bars fit neatly.
始终要为坐标轴添加标签，并给图表加上标题。横轴显示类别，纵轴显示频率。使用合理的刻度，使所有条形都能整齐地容纳。
6. Pictograms | 象形图
A pictogram uses symbols or pictures to represent data. Each picture can stand for one unit or several units. A key is essential to show what one symbol represents.
象形图使用符号或图片来表示数据。每个图片可以代表一个或几个单位。图例至关重要，需要说明一个符号代表什么。
Pictograms make data visually appealing and are easy to compare at a glance. However, when numbers are large, a pictogram can become impractical.
象形图让数据视觉上更具吸引力，一目了然。然而，当数字较大时，象形图可能变得不太实用。
7. Line Graphs | 折线图
Line graphs are used to display data that changes over time. Points are plotted and then joined with straight lines. This helps you see trends, such as increasing or decreasing values.
折线图用来展示随时间变化的数据。先标出数据点，然后用直线连接起来。这有助于你看到趋势，例如数值在上升还是下降。
Choose a line graph when you have continuous data and want to show movement. Always check that the time intervals on the horizontal axis are evenly spaced.
当你有连续数据并希望展示变化趋势时，请选择折线图。务必检查横轴上的时间间隔是否均匀分布。
8. Pie Charts | 饼图
A pie chart displays data as sectors of a circle. The size of each sector is proportional to the frequency it represents. The entire circle stands for the total data set.
饼图以圆形扇区的形式展示数据。每个扇区的大小与其代表的频率成比例。整个圆代表数据总和。
To draw a pie chart, you first find the total frequency, then calculate the angle for each category using the formula: angle = (category frequency ÷ total frequency) × 360°.
要绘制饼图，首先求出总频率，然后用公式计算每个类别的圆心角：角度 = （类别频率 ÷ 总频率）× 360°。
9. Averages: The Mean | 平均数：均值
The mean is the most common average. It is calculated by adding up all the values and dividing by the number of values.
均值是最常用的平均数。计算方法是将所有数值相加，再除以数值的个数。
Mean = (Sum of all data values) ÷ (Number of values)
均值 = （所有数据值之和） ÷ （数值的个数）
For example, the mean of 3, 5, 7, and 9 is (3+5+7+9) ÷ 4 = 6. The mean can be a decimal even when the original data are whole numbers.
例如，3、5、7、9 的均值是 （3+5+7+9）÷ 4 = 6。即使原始数据是整数，均值也可能是小数。
10. Averages: Median and Mode | 平均数：中位数与众数
The median is the middle value when the data are arranged in order. If there are two middle values, the median is the mean of those two numbers.
中位数是将数据按大小顺序排列后位于中间的值。如果有两个中间值，则中位数是这两个数的均值。
The mode is the value that appears most often. A data set can have one mode, more than one mode (bimodal or multimodal), or no mode at all.
众数是出现次数最多的值。一组数据可以有一个众数、多个众数（双众数或多众数），或完全没有众数。
11. Range | 极差
The range measures how spread out the data are. It is the difference between the largest and the smallest value.
极差衡量数据的分散程度。它是最大值与最小值之差。
Range = Largest value − Smallest value
极差 = 最大值 − 最小值
A small range tells you the data are very close together, while a large range indicates more variation. Range is affected by outliers.
极差小说明数据彼此接近，极差大则表明变化较大。极差会受到异常值的影响。
12. Interpreting Charts and Data | 解读图表与数据
Being able to read a chart is as important as drawing one. Look at the title, axis labels, scales, and key. Ask yourself what the data tells you and whether any conclusions are reliable.
能够读懂图表与绘制图表同样重要。查看标题、轴标签、刻度和图例。问问自己数据传达了哪些信息，所得结论是否可靠。
Always check for misleading graphs. Sometimes a scale does not start at zero, making differences look bigger than they really are. A critical eye is a key statistical skill.
务必留意误导性图表。有时刻度并非从零开始，使差异看起来比实际更大。拥有批判性眼光是一项关键的统计技能。
13. Summer Practice Tips | 暑期练习建议
To prepare for Year 7, start by collecting real‑life data: record the weather temperature for a week, survey your family’s favourite fruits, or count the colours of cars passing by. Draw frequency tables and different charts from your data.
为7年级做准备，可以从收集现实数据开始：记录一周的气温，调查家人最喜欢的水果，或数一数路过汽车的颜色。根据你的数据绘制频率表和不同类型的图表。
Practise calculating mean, median, mode, and range with small sets of data. Use online interactive tools or simply pencil and paper. The goal is to become fluent in both the vocabulary and the calculations before the new term begins.
用小数据集练习计算均值、中位数、众数和极差。可以使用在线互动工具，或简单地用铅笔和纸。目标是在新学期开始前熟练词汇和计算。
Published by TutorHao | Statistics Revision Series | aleveler.com
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