📚 Year 7 Cambridge Statistics: Core Knowledge Summary | 剑桥七年级统计：核心知识点梳理
Welcome to your Year 7 Cambridge Statistics revision guide. Statistics is the branch of mathematics that deals with collecting, organising, displaying, analysing and interpreting data. In Year 7, you will learn how to handle data using frequency tables, graphs such as bar charts, line graphs and pie charts, and calculate averages and the range. You will also begin to explore probability – the chance that an event will happen. This article brings together all the essential knowledge you need, with clear explanations and examples, following the Cambridge Lower Secondary curriculum.
欢迎阅读你的剑桥七年级统计复习指南。统计是数学的一个分支，涉及收集、整理、展示、分析和解读数据。在七年级，你将学习如何使用频数表、条形图、折线图和饼图等图表来处理数据，以及如何计算平均数、中位数、众数和极差。你还将开始探索概率——即某事件发生的可能性。本文以剑桥初中课程为依据，汇集了所有你需要掌握的核心知识，并配有清晰的解释和示例。
1. What is Statistics? | 什么是统计？
Statistics helps us make sense of the world by turning raw data into meaningful information. Whether we are looking at test scores, weather records or favourite foods, statistics gives us tools to describe patterns, compare groups and make predictions.
统计帮助我们把原始数据转化为有意义的信息，从而理解世界。无论是考试成绩、天气记录还是最喜爱的食物，统计都为我们提供了描述规律、比较组别和进行预测的工具。
In Year 7, you focus on descriptive statistics — that is, methods for summarising and presenting data. You will also meet the first ideas of probability, which is the study of chance events.
在七年级，你重点学习的是描述性统计，即总结和呈现数据的方法。你还会接触概率的基本概念，即对随机事件的研究。
2. Types of Data | 数据的类型
Before you can work with data, you need to know what type you are dealing with. Data can be sorted into categorical data and numerical data.
在处理数据之前，你需要知道自己正在处理什么类型的数据。数据可以分为分类数据和数值数据。
Categorical data (also called qualitative data) describe qualities or groups that are not numbers. Examples include eye colour, favourite sport or the brand of a mobile phone.
分类数据（也称为定性数据）描述的是非数字的品质或类别。例如眼睛的颜色、最喜欢的运动或手机品牌。
Numerical data (also called quantitative data) involve numbers. This type is further split into discrete data, which can only take certain exact values (often whole numbers, like the number of students in a class), and continuous data, which can take any value within a range (such as height or temperature).
数值数据（也称为定量数据）涉及数字。这种类型又分为离散数据和连续数据：离散数据只能取某些确切的值（通常是整数，比如班级里的学生人数），而连续数据可以取某个范围内的任意值（比如身高或温度）。
3. Frequency Tables | 频数表
A frequency table is a simple way to organise raw data. It lists each category or value alongside its frequency — the number of times it appears. Tally marks are often used when collecting data to help keep an accurate count.
频数表是一种整理原始数据的简单方法。它列出了每个类别或数值以及相应的频数——即它出现的次数。在收集数据时，经常使用计数符号（画“正”字）来帮助准确计数。
For example, if you ask 20 students their favourite fruit and record the answers, you can build a frequency table showing each fruit and how many students chose it.
例如，如果你询问20名学生他们最喜欢的水果并记录答案，就可以制作一个频数表，显示每种水果及其被选择的学生人数。
4. Bar Charts | 条形图
A bar chart is used to display categorical data or discrete numerical data. The height of each bar represents the frequency. Bars are drawn with equal width and there are gaps between them to show that the categories are separate.
条形图用于展示分类数据或离散数值数据。每个条形的高度代表频数。条形的宽度相等，并且条形之间留有间隙，以表明各个类别是独立的。
Always label the axes: the horizontal axis shows the categories, and the vertical axis shows the frequency. Give the chart a clear title. When reading a bar chart, you can quickly compare which category has the highest or lowest frequency.
始终要标注坐标轴：横轴显示类别，纵轴显示频数。为图表加上清晰的标题。阅读条形图时，你可以快速比较出哪个类别的频数最高或最低。
5. Line Graphs | 折线图
A line graph is particularly useful for showing how data changes over time. Points are plotted for each time period and then connected by straight lines. This makes trends and patterns easy to spot, such as a steady rise in temperature or a fall in sales.
折线图特别适用于显示数据如何随时间变化。为每个时间段描点，然后用直线将这些点连接起来。这样就能容易地发现趋势和规律，比如温度的稳定上升或销售额的下降。
When drawing a line graph, choose a sensible scale for both axes. The horizontal axis usually represents time (days, months, years), and the vertical axis shows the variable being measured. Make sure to plot each point accurately.
绘制折线图时，要为两个坐标轴选择合理的刻度。横轴通常代表时间（天、月、年），纵轴代表被测量的变量。确保准确描出每个点。
6. Pie Charts | 饼图
A pie chart displays data as sectors of a circle. The angle of each sector is proportional to the frequency of the category. The whole circle (360°) represents the total frequency.
饼图将数据展示为圆的各个扇形。每个扇形的角度与该类别的频数成正比。整个圆（360°）代表总频数。
To calculate the angle for a category, use the formula:
要计算某一类别的扇形的角度，使用以下公式：
Angle = (Category frequency ÷ Total frequency) × 360°
角度 = (类别频数 ÷ 总频数) × 360°
Pie charts are excellent for showing proportions at a glance, but they are not suitable for large numbers of categories or for precise comparisons.
饼图非常适合一目了然地显示比例，但不适合类别过多或需要精确比较的情况。
7. Averages: Mean, Median and Mode | 平均数、中位数与众数
An average is a single value that summarises a set of numbers. The three most common averages are the mean, the median and the mode. Each is calculated differently and can give a different picture of the data.
平均数是一个用来概括一组数字的单一数值。最常见的三种平均数是平均数（均值）、中位数和众数。它们的计算方法各不相同，并且可能从不同角度描绘数据。
The mean is found by adding up all the values and dividing by the number of values:
平均数（均值）是将所有数值相加，再除以数值的个数：
Mean = (Sum of all values) ÷ (Number of values)
平均数 = (所有数值之和) ÷ (数值的个数)
The mean is useful, but it can be affected by very high or very low values (outliers).
平均数很有用，但容易受到极高或极低值（异常值）的影响。
The median is the middle value when the data are arranged in order. If there is an even number of values, the median is the mean of the two middle numbers.
中位数是将数据按顺序排列后位于中间的值。如果有偶数个数值，中位数则是中间两个数的平均数。
The mode is the value that appears most often. A set of data can have one mode, more than one mode, or no mode at all if no value repeats.
众数是出现次数最多的值。一组数据可能有一个众数、多个众数，或者如果没有数值重复则没有众数。
8. Range | 极差
The range measures how spread out the data are. It is simply the difference between the largest and the smallest values.
极差衡量的是数据的分散程度。它只是最大值与最小值之间的差值。
Range = Largest value − Smallest value
极差 = 最大值 − 最小值
A small range tells you the data are fairly consistent, while a large range suggests greater variability. The range is easy to calculate but does not tell us about the distribution of the middle values.
极差小说明数据较为一致，极差大则意味着变异性较大。极差易于计算，但它不能反映中间数值的分布情况。
9. Introduction to Probability | 概率简介
Probability is a measure of how likely an event is to happen. It is expressed as a fraction, decimal or percentage between 0 and 1, where 0 means impossible and 1 means certain.
概率是衡量某事件发生可能性大小的量度。它用介于0和1之间的分数、小数或百分比表示，0表示不可能，1表示必然发生。
For example, when you toss a fair coin, the probability of getting heads is 1/2 or 0.5 or 50%. The formula for theoretical probability is:
例如，抛一枚公平的硬币时，得到正面的概率是 ½、0.5 或 50%。理论概率的公式为：
P(event) = Number of favourable outcomes ÷ Total number of equally likely outcomes
P(事件) = 有利结果的数量 ÷ 所有等可能结果的总数
Probabilities can also be written using words such as 'likely', 'unlikely', 'even chance' on a probability scale.
概率也可以用“很可能”、“不太可能”、“均等机会”等词语在概率尺度上表示。
10. The Probability Scale | 概率尺度
The probability scale is a number line from 0 to 1 that helps us place the likelihood of events. Mark 0 as impossible, 1 as certain, and 0.5 as an even chance.
概率尺度是一条从0到1的数轴，帮助我们对事件的可能性进行定位。0 标为不可能，1 标为必然，0.5 表示机会均等。
Common descriptions and their approximate probabilities:
常用的描述词及其大致的概率值：
| Impossible (不可能) | 0 |
| Very unlikely (非常不可能) | Close to 0 |
| Unlikely (不太可能) | Less than 0.5 |
| Even chance (机会均等) | 0.5 |
| Likely (很可能) | Greater than 0.5 |
| Very likely (非常可能) | Close to 1 |
| Certain (必然) | 1 |
On the scale, events like 'the sun will rise tomorrow' sit near 1, while 'rolling a 7 on a fair six-sided die' sits at 0.
在尺度上，“明天太阳会升起”这样的事件接近 1，而“掷一枚公平的六面骰子得到 7”则位于 0。
11. Experimental vs Theoretical Probability | 实验概率与理论概率
Theoretical probability is what we expect to happen based on equally likely outcomes, like throwing a fair die. Experimental probability (also called relative frequency) comes from actually carrying out an experiment or observing events.
理论概率是基于等可能结果我们预期会发生的情况，例如掷一枚公平的骰子。实验概率（也叫相对频率）则来自于实际进行实验或观察事件。
The experimental probability is calculated as:
实验概率的计算公式为：
Experimental probability = Number of times the event occurs ÷ Total number of trials
实验概率 = 事件发生的次数 ÷ 试验总次数
ical probability remains 0.5. The more trials you carry out, the closer the experimental probability usually gets to the theoretical probability.
如果你抛硬币 100 次，得到 48 次正面，那么正面的实验概率为 48/100 = 0.48。而理论概率仍是 0.5。你进行的试验次数越多，实验概率通常就越接近理论概率。
12. Review and Tips for Success | 复习与成功技巧
When revising Year 7 statistics, make sure you can read and interpret different graphs, not just draw them. Practice calculating the mean, median, mode and range from both raw data and frequency tables. Always check the labels on axes and the scale before answering graph questions.
在复习七年级统计时，要确保你不仅会绘制图表，还能阅读和解释不同的图表。练习从原始数据和频数表中计算平均数、中位数、众数和极差。在回答图表问题时，务必先检查坐标轴标签和刻度。
For probability, remember to write answers as fractions in their simplest form, or as decimals or percentages if required. Show your working clearly by writing the probability formula. Revise the probability scale and be comfortable placing everyday events on it.
对于概率，要记住用最简分数、小数或百分比（视要求而定）来书写答案。通过写出概率公式来清楚地展示解题过程。复习概率尺度，并能熟练地将日常事件标注在尺度上。
Use real-life examples: collect your own small set of data, make a frequency table, draw a bar chart and find the averages. This hands-on practice will deepen your understanding far better than just reading.
运用现实生活中的例子：自己收集一小部分数据，制作频数表，绘制条形图，并求出平均数。这种动手实践比单纯的阅读能更好地加深你的理解。
Finally, check your work carefully to avoid simple mistakes, such as forgetting to order the data for the median or miscalculating the total frequency for pie chart angles.
最后，仔细检查你的作业，避免简单错误，比如在求中位数时忘记先对数据排序，或者在计算饼图扇形的角度时算错总频数。
Published by TutorHao | Statistics Revision Series | aleveler.com
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