📚 Year 8 Edexcel Statistics: Core Knowledge Review | Year 8 Edexcel 统计：核心知识点梳理
Statistics is the science of collecting, analysing, and interpreting data. In Year 8 Edexcel Mathematics, you will build a solid foundation in statistical thinking that helps you understand the world through numbers. This article summarises the key concepts you need to master, from types of data to probability and the statistical enquiry cycle.
统计学是收集、分析和解释数据的科学。在 Year 8 Edexcel 数学课程中，你将建立统计思维的坚实基础，通过数字理解世界。本文总结你需要掌握的核心概念，从数据类型到概率和统计调查循环。
1. Types of Data | 数据类型
Data is information that has been collected. It can be categorised as qualitative or quantitative. Qualitative data (also called categorical data) describes qualities or categories, such as eye colour, favourite food, or car brands.
数据是已收集的信息。它可以分为定性数据和定量数据。定性数据（也称分类数据）描述品质或类别，如眼睛颜色、最喜欢的食物或汽车品牌。
Quantitative data measures quantities and can be discrete or continuous. Discrete data arises from counting and can only take certain values, like the number of students in a class (you can’t have 28.5 students). Continuous data comes from measuring and can take any value in a range, such as height, weight, or temperature.
定量数据测量数量，可分为离散和连续。离散数据通过计数得到，只能取特定值，如班级学生人数（不可能有28.5个学生）。连续数据通过测量得到，可以在一个范围内取任意值，如身高、体重或温度。
2. Collecting Data | 数据收集
Data can be collected first-hand or second-hand. Primary data is data you collect yourself through experiments, surveys, or observations. It is reliable but can be time-consuming to gather.
数据可以一手或二手收集。原始数据是你自己通过实验、调查或观察收集的数据。它可靠但收集耗时。
Secondary data is data that someone else has already collected, such as data from the internet, books, or government reports. It is quicker to obtain, but you must check its reliability and relevance.
二手数据是他人已经收集好的数据，例如来自互联网、书籍或政府报告的数据。获取更快，但必须检查其可靠性和相关性。
A well-designed questionnaire should avoid leading questions and use clear, unbiased wording. The sample size should be large enough to be representative of the population.
设计良好的问卷应避免诱导性问题，使用清晰、无偏见的措辞。样本量应足够大，以代表总体。
3. Frequency Tables and Tallies | 频数表与划记
A frequency table organises raw data into a table showing how often each value or category occurs. Tally marks help count the frequencies efficiently, usually in groups of five.
频数表将原始数据整理成一个表格，显示每个值或类别出现的频率。划记符号有助于高效计数，通常以五个为一组。
For example, if you survey 20 students about their favourite fruit, you can record tallies and then write the total frequency for each fruit.
例如，如果你调查20名学生最喜欢的水果，你可以记录划记，然后写出每种水果的总频数。
4. Bar Charts and Pictograms | 条形图和象形图
Bar charts represent categorical data using rectangular bars. The height or length of each bar corresponds to the frequency. Bars should have equal widths and gaps between them, as the data is categorical, not continuous.
条形图使用矩形条表示分类数据。每个条的高度或长度对应频数。条应有相同的宽度，条与条之间应有间隙，因为数据是分类的，而非连续。
Pictograms use symbols or pictures to represent data. A key shows what each symbol stands for. For instance, one picture of a book might represent 5 books read. Pictograms make data easy to compare visually.
象形图使用符号或图片表示数据。图例说明每个符号代表什么。例如，一本书的图片可能代表读了5本书。象形图使数据在视觉上易于比较。
5. Pie Charts and Angles | 饼图与角度
A pie chart shows proportions of a whole. The whole circle (360°) represents the total frequency. Each category’s angle is calculated by: (Frequency of category ÷ Total frequency) × 360°.
饼图显示整体的各部分比例。整个圆（360°）代表总频数。每个类别的角度计算为：（类别频数 ÷ 总频数）× 360°。
When constructing a pie chart, use a protractor to measure angles accurately. Label each sector clearly or provide a legend. Pie charts are excellent for showing percentage shares.
绘制饼图时，使用量角器准确测量角度。清晰地标记每个扇区或提供图例。饼图非常适合显示百分比份额。
6. Averages: Mean, Median, Mode | 平均数：均值、中位数、众数
An average is a single value used to describe the centre of a data set. The mode is the value that appears most often. A data set can have one mode, more than one mode (bimodal), or no mode at all.
平均数是用于描述数据集中心的一个单值。众数是出现最频繁的值。一个数据集可以有一个众数、多个众数（双峰）或没有众数。
The median is the middle value when the data is ordered from smallest to largest. If there is an even number of values, the median is the mean of the two middle numbers.
中位数是将数据从小到大排序后位于中间的值。如果有偶数个值，中位数是中间两个数的均值。
The mean (often called the average) is calculated by adding all the values together and dividing by the number of values.
Mean = Sum of all data values ÷ Number of data values
均值（通常称为平均数）的计算方法是将所有数据值相加，再除以数据值的个数。
For a frequency table, use: Mean = Σ(value × frequency) ÷ Σfrequency. The mean is sensitive to extreme values (outliers).
对于频数表，使用：均值 = Σ（值 × 频数）÷ Σ 频数。均值对极端值（异常值）敏感。
7. Range and Measures of Spread | 极差与离散度
The range measures how spread out the data is. It is the difference between the largest and smallest values.
Range = Largest value − Smallest value
极差衡量数据的离散程度。它是最大值与最小值之差。
A larger range indicates greater variability. The range is easy to calculate but is affected by outliers. Other measures of spread, such as interquartile range, are introduced in later years.
较大的极差表明更大的变异性。极差易于计算，但受异常值影响。其他离散度量，如四分位距，将在更高年级介绍。
8. Scatter Graphs and Correlation | 散点图与相关
A scatter graph (or scatter plot) displays the relationship between two sets of numerical data. Each point has an x-coordinate and a y-coordinate. By plotting points, you can see if there is a correlation.
散点图（或散点图）显示两组数值数据之间的关系。每个点都有一个x坐标和一个y坐标。通过绘制点，你可以看出是否存在相关性。
Positive correlation means as one variable increases, the other also increases. Negative correlation means as one variable increases, the other decreases. No correlation means there is no clear relationship.
正相关意味着当一个变量增加时，另一个也增加。负相关意味着当一个变量增加时，另一个减少。无相关意味着没有明确的关系。
Correlation does not imply causation – just because two variables are related does not mean one causes the other.
相关并不意味着因果关系——仅仅因为两个变量相关，并不意味着一个导致另一个。
9. Introduction to Probability | 概率入门
Probability is a measure of how likely an event is to happen. It can be expressed as a fraction, decimal, or percentage between 0 (impossible) and 1 (certain).
概率是衡量事件发生可能性的度量。它可以表示为介于0（不可能）和1（肯定）之间的分数、小数或百分比。
The probability scale: 0 = impossible, 0.5 = even chance, 1 = certain. Words such as ‘likely’, ‘unlikely’, and ‘certain’ are used informally.
概率尺度：0 = 不可能，0.5 = 一半机会，1 = 肯定。像“很可能”、“不太可能”和“肯定”等词语非正式使用。
For equally likely outcomes, theoretical probability is:
P(event) = Number of favourable outcomes ÷ Total number of possible outcomes
对于等可能结果，理论概率为：
P（事件）= 有利结果的数量 ÷ 可能结果的总数
Probability can be shown on a probability line or in a two-way table.
概率可以用概率线或双向表呈现。
10. 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. Experimental probability (relative frequency) is based on actual trials or experiments.
理论概率是我们基于等可能结果预期发生的事情。实验概率（相对频率）基于实际试验或实验。
Experimental probability = Number of times event occurs ÷ Total number of trials
实验概率 = 事件发生次数 ÷ 试验总次数
The more trials you carry out, the closer the experimental probability tends to get to the theoretical probability – this is the law of large numbers.
你进行的试验越多，实验概率越趋近于理论概率——这是大数定律。
For example, if you flip a fair coin 50 times and get 22 heads, the experimental probability of heads is 22/50 = 0.44. The theoretical probability is 0.5.
例如，如果你抛一枚公平硬币50次，得到22次正面，则正面的实验概率为22/50 = 0.44。理论概率是0.5。
11. The Statistical Enquiry Cycle
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