📚 Core Knowledge Summary for Year 7 CIE Statistics | Year 7 CIE 统计：核心知识点梳理
Statistics is the branch of mathematics that deals with collecting, organising, presenting, analysing and interpreting data. In Year 7, you will build a solid foundation in handling data, learning how to represent it clearly and how to find simple summary numbers like the mean and the range. This article revisits all the core topics you need to know for the CIE checkpoint, with clear explanations and practical examples.
统计学是数学的一个分支，研究数据的收集、整理、展示、分析和解读。在七年级，你将打下扎实的数据处理基础，学会如何清晰地展示数据，如何求平均数、极差等简单的统计量。本文重新梳理 CIE 检查点考试需要掌握的所有核心知识点，并提供清晰的解释和实用的例子。
1. What is Statistics? | 统计是什么？
Statistics is the science of learning from data. It helps us turn raw numbers into useful information so we can understand patterns, answer questions and make decisions.
统计学是从数据中获取信息的科学。它帮助我们把原始数字变成有用的信息，从而理解模式、回答问题并做出决策。
We encounter statistics every day, from sports statistics and weather reports to school test results and social media polls.
我们每天都会遇到统计数据，从体育比赛统计、天气预报，到学校考试成绩和社交媒体投票。
In Year 7, statistics focuses on describing data rather than making predictions or testing hypotheses. You will learn how to organise a set of numbers, draw graphs and find basic measures that summarise the data.
在七年级，统计学重点在于描述数据，而不是做预测或检验假设。你将学习如何整理一组数字、绘制图表，以及求出概括数据的基本度量。
2. Types of Data | 数据类型
Data can be classified in two main ways: qualitative and quantitative. Qualitative data describes qualities or categories and is not numerical, for example, eye colour or favourite subject. Quantitative data consists of numbers and represents counts or measurements.
数据主要可以分成两类：定性数据和定量数据。定性数据描述性质或类别，不是数值，例如眼睛的颜色或最喜欢的科目。定量数据由数字组成，表示计数或测量值。
Quantitative data is further split into discrete and continuous data. Discrete data can only take certain values, usually whole numbers, like the number of students in a class. Continuous data can take any value within a range, such as height, weight or temperature.
定量数据又分为离散数据和连续数据。离散数据只能取特定的值，通常是整数，比如班级里的学生人数。连续数据可以在一个范围内取任何值，比如身高、体重或温度。
Knowing the type of data helps you decide which graph to draw and which summary measures are appropriate. For example, you cannot find the mean of a set of favourite colours, but you can count the mode.
了解数据类型有助于你决定该画哪种图表，以及用哪些概括度量比较合适。比如，你不能求一组最喜欢颜色的平均数，但可以找出它们的众数。
3. Collecting Data | 数据收集
Good statistics starts with good data. Data can be collected by conducting a survey, making observations, carrying out experiments or using existing records. The method must be chosen carefully so the data answers the question you are studying.
好的统计学始于好的数据。我们可以通过开展调查、进行观察、做实验或使用现有记录来收集数据。收集方法必须仔细选择，以便数据能够回答你正在研究的问题。
A survey often uses a questionnaire with closed or open questions. Closed questions give a limited set of answers, which are easier to tally. Open questions allow any answer and can be harder to analyse.
调查通常使用问卷，问题可以是封闭式或开放式的。封闭式问题给出的答案选择有限，更容易统计。开放式问题允许任意答案，分析起来更困难。
When you collect data, you also need to think about bias. A question that leads people towards a particular answer will produce biased data. For instance, asking “Do you agree that school lunches are delicious?” is less fair than “How would you rate school lunches?”
收集数据时，你还需要考虑偏差。如果问题引导人们给出某个特定答案，就会产生有偏的数据。例如，问“你是否同意学校午餐很美味？”就不如“你如何评价学校午餐？”公平。
4. Organising Data – Frequency Tables | 整理数据——频数表
A frequency table is one of the simplest ways to organise raw data. It shows how often each value or category occurs. Tally marks can help you count the frequencies accurately before you write the numbers.
频数表是整理原始数据最简单的方法之一。它显示每个值或类别出现的次数。在写下数字之前，使用计数符号可以帮助你准确地数出频数。
Below is an example of a frequency table for the colours of 20 cars in a car park.
下面是一个频数表示例，统计停车场 20 辆汽车的颜色。
| Colour | Tally | Frequency |
|---|---|---|
| Red | |||| | 5 |
| Blue | ||| | 3 |
| Black | |||| || | 7 |
| White | |||| | 5 |
| Total | 20 |
The total frequency should equal the total number of data items. Frequency tables also make it easy to identify the mode – the colour with the highest frequency.
总频数应当等于数据项的总数。频数表也让我们很容易看出众数——即频数最高的颜色。
5. Bar Charts and Pictograms | 条形图和象形图
A bar chart represents categorical or discrete data using rectangular bars. The height of each bar shows the frequency. Bars must be of equal width and should not touch, unless you are dealing with a histogram, which is beyond Year 7.
条形图用矩形条表示分类数据或离散数据。每个条形的高度表示频数。条形的宽度必须相等，条形之间不应接触，除非你在画直方图，这超出了七年级的范围。
Always label the axes, give the chart a title and use a consistent scale. If you are drawing a bar chart by hand, work out the scale first so that the tallest bar fits comfortably on the graph paper.
一定要标注坐标轴，给图表加标题，并使用一致的刻度。如果你用手绘制条形图，要先确定刻度，让最高的条形能舒适地画在方格纸上。
A pictogram uses simple pictures or symbols to represent data. Each picture stands for a certain number of items. You must include a key that explains what each symbol represents.
象形图用简单的图画或符号来表示数据。每个图画代表一定数量的物品。你必须包含一个图例来解释每个符号代表什么。
For example, if one smiley face represents 2 students, then half a face represents 1 student. Pictograms are often eye-catching but can be less accurate when fractions of a symbol are needed.
例如，如果一张笑脸代表 2 名学生，那么半张笑脸就代表 1 名学生。象形图通常很吸引眼球，但在需要用到部分符号时，准确性就会降低。
6. Pie Charts | 饼图
A pie chart is a circle divided into sectors. Each sector represents a category, and its angle is proportional to the frequency of that category. Pie charts are useful for showing how a whole is split into parts.
饼图是一个被分成扇形的圆。每个扇形代表一个类别，其角度与该类别的频数成正比。饼图很适合展示一个整体如何被分成各个部分。
To draw a pie chart, first calculate the total frequency. Then, for each category, compute the angle: (Category frequency ÷ Total frequency) × 360°. Use a protractor to measure and draw each angle.
要绘制饼图，首先计算总频数。然后，对每个类别计算角度：（类别频数 ÷ 总频数）× 360°。用量角器测量并画出每一个角度。
For example, if 15 out of 60 students prefer apples, the angle for the apple sector is (15 ÷ 60) × 360° = 90°. Always label each sector or provide a legend, and give the chart a title.
例如，如果有 60 名学生，其中 15 名偏爱苹果，那么苹果扇形的角度就是 (15 ÷ 60) × 360° = 90°。记得给每个扇形加标签或提供图例，并给图表加上标题。
When interpreting a pie chart, you can work backwards: if a sector has an angle of 120° and you know the total frequency, you can find the frequency for that category by multiplying the total by (120° ÷ 360°).
解读饼图时，可以反向计算：如果一个扇形的角度是 120°，而且你知道总频数，就可以用总频数乘上 (120° ÷ 360°) 来求出该类别的频数。
7. Line Graphs and Scatter Graphs | 折线图和散点图
A line graph is used to show how a quantity changes over time. The horizontal axis often represents time, and the vertical axis represents the measured quantity. Points are plotted and joined with straight lines to show the trend.
折线图用来表示一个量随时间变化的情况。横轴通常代表时间，纵轴代表测得的量。先描点，再用直线连接，以显示变化的趋势。
Be careful when reading values between plotted points – assume the change is steady only if the context allows it. Also, look for peaks, troughs and periods where the value stays the same.
在读图上两个点之间的数值时要小心——只有在条件允许时才能假设变化是均匀的。同时，留意峰值、谷值以及数值保持不变的时期。
A scatter graph (scatter plot) is used to display the relationship between two sets of quantitative data. Each point represents a pair of values. If the points tend to go upwards to the right, there is a positive correlation; if they go downwards, a negative correlation. If no pattern appears, there is no correlation.
散点图用来呈现两组定量数据之间的关系。每个点代表一对数值。如果点的趋势是整体向右上方走，就存在正相关；如果向右下方走，则是负相关；如果没有明显的模式，那就没有相关关系。
In Year 7, you will mainly describe the correlation as positive, negative or none, and you will not need to draw a line of best fit.
在七年级，你只需要描述相关关系为正、负或无，不需要画出最佳拟合线。
8. Mean, Median and Mode | 平均数、中位数与众数
The mean, median and mode are measures of central tendency – they describe the centre of a set of data.
平均数、中位数和众数都是集中趋势的度量，它们描述一组数据的中心位置。
The mode is the value that appears most often. A set of data can have one mode, more than one mode (bimodal or multimodal) or no mode at all if all values occur equally often.
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），或者根本没有众数（当所有的值出现次数相同时）。
The median is the middle value when the data is arranged in order. If there is an odd number of values, the median is the one in the middle. If there is an even number, the median is the mean of the two middle values.
中位数是将数据按大小顺序排列后位于正中间的值。如果数据的个数是奇数，中位数就是正中间的那个数；如果是偶数，中位数就是中间两个数的平均数。
The mean is the sum of all the values divided by the number of values. It is what most people call the average.
平均数（均值）是所有数值的总和除以数值的个数。它就是大多数人口中的“平均”。
Mean = (Sum of all data values) ÷ (Number of data values)
For example, the mean of 4, 8, 6 is (4+8+6) ÷ 3 = 18 ÷ 3 = 6. The mean can be affected by very high or very low values, while the median is not.
例如，4、8、6 的均值是 (4+8+6) ÷ 3 = 18 ÷ 3 = 6。平均数会受到特别高或特别低的数值的影响，而中位数则不受影响。
9. Range – A Measure of Spread | 极差——离散程度的度量
The range tells us how spread out the data is. It is the difference between the largest value and the smallest value.
极差告诉我们数据的分散程度。它是最大值与最小值的差。
Range = Largest value – Smallest value
A small range means the data values are close together; a large range means they are more spread out. For example, in the data set {3, 7, 7, 9, 14}, the range is 14 – 3 = 11.
极差小意味着数据值比较集中；极差大意味着分布较广。例如，在数据集 {3, 7, 7, 9, 14} 中，极差为 14 – 3 = 11。
Together with the mean or median, the range gives a good summary of the data. Two classes may have the same mean test score, but the one with a smaller range has more consistent performance.
极差与平均数或中位数一起，能很好地概括数据。两个班级可能有相同的平均考试分数，但极差较小的那一班，成绩会更稳定。
10. Introduction to Probability | 概率入门
Probability measures how likely an event is to happen. It is a number between 0 and 1. A probability of 0 means the event is impossible; a probability of 1 means it is certain. Probabilities can also be written as fractions, decimals or percentages.
概率衡量一个事件发生的可能性大小。它是一个介于 0 到 1 之间的数。概率为 0 表示事件不可能发生；概率为 1 表示事件一定发生。概率还可以写成分数、小数或百分数。
When all outcomes are equally likely, the probability of an event is given by:
当所有结果出现的可能性相同时，一个事件的概率由下式给出：
Probability = (Number of favourable outcomes) ÷ (Total number of possible outcomes)
For example, when you roll a fair six-sided dice, the probability of rolling a 2 is 1 ÷ 6, because there is one favourable outcome and six possible outcomes in total.
例如，你掷一个均匀的六面骰子时，掷出 2 的概率是 1 ÷ 6，因为有一个有利结果，总共六个可能结果。
The probability of an event not happening is 1 minus the probability that it does happen. If the chance of rain tomorrow is 0.3, then the chance it will not rain is 1 – 0.3 = 0.7.
一个事件不发生的概率等于 1 减去它发生的概率。如果明天下雨的概率是 0.3，那么不下雨的概率就是 1 – 0.3 = 0.7。
In Year 7, you will work with simple experiments like tossing coins, rolling dice and using spinners. You will also learn to list all the possible outcomes using a sample space.
在七年级，你会学习抛硬币、掷骰子和转盘等简单实验。你还会学习用样本空间列出所有可能的结果。
Published by TutorHao | Statistics Revision Series | aleveler.com
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