📚 KS3 CCEA Statistics: Core Knowledge Review | KS3 CCEA 统计：核心知识点梳理
Statistics helps us collect, organise, display and interpret data to make informed decisions. In this KS3 CCEA revision guide, we walk through the fundamental concepts you need to master, from types of data to the basics of probability. Each topic is presented in paired English and Chinese explanations to support both language tracks.
统计学帮助我们收集、整理、展示和解读数据，从而做出明智的决策。在这份 KS3 CCEA 复习指南中，我们将梳理你需要掌握的核心概念，从数据类型到概率基础。每个主题都以中英双语段落配对呈现，方便双语学习。
1. Types of Data | 数据类型
Data can be split into two main families: categorical (qualitative) and numerical (quantitative). Categorical data describe characteristics like favourite colour, type of pet or eye colour. Numerical data are numbers that represent counts or measurements.
数据可以分为两大类：类别数据（定性）和数值数据（定量）。类别数据描述特征，例如最喜欢的颜色、宠物类型或眼睛颜色。数值数据是代表计数或测量的数字。
Numerical data can be further divided into discrete and continuous. Discrete data can only take certain values, often whole numbers — for example, the number of students in a class or the score on a dice. Continuous data can take any value within a range, like height, mass or time taken to run a race.
数值数据可以进一步分为离散和连续数据。离散数据只能取某些特定值，通常是整数——例如班级里的学生人数或骰子的点数。连续数据可以在一个范围内取任意值，例如身高、质量或跑步所花的时间。
2. Collecting Data | 数据收集
Data is gathered through surveys, questionnaires, experiments or observations. The population is the whole set of individuals or items we are interested in. Because it is often impractical to survey an entire population, we usually work with a sample — a smaller, representative subset.
数据通过调查、问卷、实验或观察收集。总体是我们感兴趣的全体个体或项目的集合。由于调查整个总体通常不现实，我们通常使用样本——一个较小的、有代表性的子集。
To avoid bias, samples should be selected randomly so that every member of the population has an equal chance of being chosen. Bias occurs when the sample does not fairly represent the population, leading to misleading conclusions.
为避免偏差，样本应随机选取，使总体中的每个成员都有相同的机会被选中。当样本不能公平地代表总体时就会出现偏差，从而导致误导性的结论。
3. Frequency Tables | 频率表
A frequency table organises raw data to show how many times each value or category occurs. We use tally marks to count easily: each group of five is recorded as four vertical strokes and a diagonal crossing line.
频率表整理原始数据，显示每个值或类别出现的次数。我们用划记符号轻松计数：每五个为一组，由四个竖线和一个斜线交叉表示。
The frequency column lists the count for each item. Sometimes we also add a cumulative frequency column, which adds up frequencies step by step to show a running total. For example, if ‘red’ appears 4 times and ‘blue’ 7 times, the cumulative frequency for ‘blue’ is 4 + 7 = 11.
频率列列出每个项目的计数值。有时我们还会添加累计频率列，它逐步累加频率以显示滚动总数。例如，如果“红色”出现 4 次，“蓝色”出现 7 次，那么“蓝色”的累计频率就是 4 + 7 = 11。
4. Bar Charts and Pictograms | 条形图和象形图
A bar chart displays categorical data using rectangular bars of equal width. The height of each bar corresponds to the frequency of the category. Bars should be separated by gaps to show the categories are distinct.
条形图用等宽的矩形条展示类别数据。每个条形的高度对应类别的频率。条形之间应当留有间隙，以表明类别是独立的。
Pictograms use simple pictures or symbols to represent data. A key tells the reader what each symbol stands for, for example, one smiley face could represent 2 students. Pictograms make data visually appealing but require careful attention to the key when interpreting values.
象形图使用简单的图画或符号来表示数据。图例告诉读者每个符号代表什么，例如，一个笑脸可以代表 2 名学生。象形图使数据看起来更生动，但在解读数值时需要仔细留意图例。
5. Pie Charts | 饼图
Pie charts show how a whole is divided into different categories. Each slice (sector) represents a proportion of the total. The size of the angle at the centre is calculated using the formula:
饼图展示一个整体如何被划分为不同的类别。每块扇形代表总数的一部分。中心角的大小使用以下公式计算：
Sector angle = (Frequency of category ÷ Total frequency) × 360°
Once we have worked out all the angles, we can draw the pie chart using a protractor. It is useful to label each sector or provide a legend. Pie charts are particularly effective when comparing proportions of a whole, but they can be harder to read when there are many small categories.
计算出所有角度后，我们就可以用量角器画出饼图。为每个扇区加上标签或提供图例会很有帮助。饼图在比较整体的各部分比例时特别有效，但如果有很多细小类别，图表的可读性就会降低。
6. Line Graphs and Time Series | 线图和时间序列
Line graphs plot data points and join them with straight lines. They are often used to show how something changes over time; this is called a time series. The horizontal axis usually represents time, and the vertical axis shows the measured variable.
线图描出数据点并用直线连接。它们常用于显示事物如何随时间变化，这称为时间序列。横轴通常表示时间，纵轴表示测量的变量。
Line graphs make it easy to spot trends — whether values are rising, falling or staying level. When interpreting a time series, look out for patterns such as seasonal peaks or sudden jumps that may indicate special events.
线图便于观察趋势——数值是上升、下降还是持平。在解读时间序列时，要留意季节性高峰或突然跃升等模式，它们可能暗示特殊事件的发生。
7. Scatter Graphs and Correlation | 散点图和相关性
A scatter graph displays two sets of numerical data as points on a coordinate grid. Each point represents a pair of values. Scatter graphs help us see if there is a relationship, or correlation, between the two variables.
散点图将两组数值数据以点的形式显示在坐标格中。每个点代表一对数值。散点图可以帮助我们观察两个变量之间是否存在关系或相关性。
If points slope upwards from left to right, we have positive correlation — as one variable increases, the other tends to increase. If the points slope downwards, it is negative correlation — one variable increases while the other decreases. No clear pattern means no correlation. We can draw a line of best fit to model the relationship and make predictions.
如果点从左到右向上倾斜，就是正相关——一个变量增加，另一个也倾向增加。如果点向下倾斜，就是负相关——一个变量增加而另一个减少。没有明显模式就是无相关。我们可以绘制一条最佳拟合线来模拟关系并进行预测。
8. Averages: Mean, Median, Mode | 平均数：均值、中位数、众数
An average is a measure of central tendency that summarises a data set with a single typical value. The three main averages are mode, median and mean.
平均数是集中趋势的度量，用一个有代表性的值来概括一组数据。三个主要的平均数是众数、中位数和均值。
The mode is the value that appears most often. The median is the middle value when the data are placed in order. If there is an even number of values, the median is the midpoint of the two middle numbers. The mean is calculated by adding up all the values and dividing by the number of values:
众数是出现次数最多的值。中位数是将数据从小到大排序后位于中间的值。如果有偶数个数据，中位数是中间两个数的中点。均值是通过将所有数值相加再除以数值的个数计算得出：
Mean = Σx ÷ n
For example, for the data set 4, 6, 6, 8, 11: mode = 6, median = 6, and mean = (4+6+6+8+11) ÷ 5 = 7.
例如，对于数据集 4, 6, 6, 8, 11：众数 = 6，中位数 = 6，均值 = (4+6+6+8+11) ÷ 5 = 7。
9. Range and Spread | 极差与数据分布
While averages tell us about a typical value, the range tells us how spread out the data are. The range is simply the difference between the largest and smallest values.
平均数告诉我们典型值是什么，而极差告诉我们数据的分散程度。极差就是最大值与最小值之间的差。
Range = Largest value – Smallest value
A small range indicates that the data are clustered closely together; a large range suggests they are more spread out. Comparing the ranges of two sets of data can reveal which set has greater consistency or variability.
极差小表示数据密集地聚集在一起；极差大表示数据较为分散。比较两组数据的极差可以揭示哪一组数据更加一致或更具变异性。
10. Introduction to Probability | 概率入门
Probability measures the chance of an event occurring. It is always a number between 0 and 1, where 0 means impossible and 1 means certain. We can express probability as a fraction, decimal or percentage.
概率衡量事件发生的可能性，是一个介于 0 到 1 之间的数，0 表示不可能，1 表示必然发生。我们可以用分数、小数或百分比来表示概率。
When all outcomes are equally likely, the probability of an event is:
当所有结果等可能发生时，一个事件的概率为：
Probability = Number of favourable outcomes ÷ Total number of outcomes
The sum of probabilities of all possible outcomes is always 1. In simple experiments, such as rolling a fair six-sided dice, the probability of rolling a 4 is 1/6. Understanding probability helps us make predictions about what might happen in the future based on the data we have.
所有可能结果出现的概率之和总是 1。在简单实验中，例如掷一个公平的六面骰子，掷出 4 的概率是 1/6。理解概率有助于我们根据现有数据预测未来可能发生的事情。
Published by TutorHao | Statistics Revision Series | aleveler.com
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