📚 Year 8 WJEC Statistics: Core Knowledge Review | Year 8 WJEC 统计：核心知识点梳理
Welcome to your Year 8 WJEC Statistics revision guide. Statistics is the science of collecting, organising, analysing, and interpreting data to make informed decisions. In Year 8, you will build on earlier work with data and probability, developing skills in handling different types of data, constructing and interpreting charts, calculating averages and measures of spread, and understanding basic probability. This article presents a comprehensive review of the core topics you need to master for your assessments.
欢迎来到 Year 8 WJEC 统计学复习指南。统计学是一门收集、整理、分析和解释数据以做出明智决策的科学。在 Year 8，你将在先前数据和概率知识的基础上，进一步发展处理不同类型数据、绘制和解读图表、计算平均数和离散程度、理解基本概率等技能。本文全面梳理了你在评估中需要掌握的核心主题。
1. Types of Data | 数据类型
In statistics, we work with data. Data is information that has been collected. It can be in the form of numbers, words, measurements, or observations.
在统计学中，我们处理数据。数据是已收集的信息，可以是数字、文字、测量值或观察结果的形式。
Data can be classified into two main types: qualitative data and quantitative data.
数据主要分为两类：定性数据和定量数据。
Qualitative data describes qualities, characteristics, or categories that cannot be measured with numbers. For example, favourite colour, type of pet, or hair colour.
定性数据描述无法用数字测量的品质、特征或类别。例如，最喜欢的颜色、宠物类型或头发颜色。
Quantitative data is numerical data that can be counted or measured. Examples include height, number of siblings, test scores, and temperature.
定量数据是可以计数或测量的数值数据。例如身高、兄弟姐妹的数量、考试分数和温度。
Quantitative data can be further split into discrete and continuous data.
定量数据可以进一步分为离散数据和连续数据。
Discrete data can only take specific, separate values, usually whole numbers. For example, the number of students in a class (you cannot have half a student).
离散数据只能取特定的、分离的值，通常是整数。例如，一个班级的学生人数（不可能有半个学生）。
Continuous data can take any value within a range. Measurements like height, weight, and time are continuous because they can be measured to any degree of accuracy.
连续数据可以在一个范围内取任何值。身高、体重和时间等测量值是连续的，因为它们可以测量到任何精度。
2. Methods of Data Collection | 数据收集方法
Before we can analyse data, we must collect it. Data can be gathered in many ways, depending on what we want to find out.
在分析数据之前，我们必须收集数据。数据的收集方式有很多，取决于我们想要了解什么。
A survey or questionnaire is a common method for collecting information from people. Questions should be clear and unbiased to ensure the data is reliable.
调查或问卷是从人们那里收集信息的常用方法。问题应清晰且无偏见，以确保数据可靠。
An experiment involves deliberately changing one factor to observe the effect on another, while keeping other conditions constant. For example, measuring how different light levels affect plant growth.
实验涉及故意改变一个因素来观察其对另一个因素的影响，同时保持其他条件不变。例如，测量不同光照水平如何影响植物生长。
Observation involves watching and recording features of a situation without interfering. This can be useful for collecting data on animal behaviour or traffic flow.
观察涉及在不干预的情况下观察和记录情况的特征。这对于收集动物行为或交通流量的数据很有用。
Data can also be primary or secondary. Primary data is collected by you for a specific purpose. Secondary data is data that someone else has already collected, such as information from a government website or textbook.
数据还可以分为原始数据（一手数据）和二手数据。原始数据是你为特定目的自行收集的数据。二手数据是别人已经收集好的数据，例如来自政府网站或教科书的信息。
3. Frequency Tables and Bar Charts | 频数表与条形图
Once data is collected, it is often organised into a frequency table. A frequency table shows how often each value or category occurs. Tally marks are used to count easily.
收集数据后，通常会将其整理成频数表。频数表显示每个值或类别出现的频率。使用计分符号（正字）可以轻松计数。
For categorical data, a bar chart is a very useful way to display the frequencies. Each category has a bar, and the height of the bar represents the frequency. The bars should have equal width and be separated by gaps.
对于分类数据，条形图是一种非常实用的显示频率的方式。每个类别有一个条形，条形的高度代表频率。条形应具有相同的宽度，并且条形之间应有间隙。
Bar charts can be drawn vertically or horizontally. The vertical axis (y-axis) is labelled with frequency, and the horizontal axis (x-axis) shows the categories.
条形图可以垂直或水平绘制。纵轴（y轴）标注频率，横轴（x轴）显示类别。
When drawing a bar chart, it is important to choose a suitable scale so that the tallest bar fits within the graph. Always label both axes and give the chart a title.
绘制条形图时，选择适当的刻度非常重要，以便最高的条形能容纳在图中。务必为两个轴添加标签并为图表加上标题。
Dual bar charts can be used to compare two sets of data side by side for each category, using different colours or patterns for each set.
双条形图可用于并排比较每个类别的两组数据，每组数据使用不同的颜色或图案。
4. Pie Charts and Pictograms | 饼图与象形图
A pie chart displays data as slices of a circle. The size of each slice is proportional to the frequency of the category it represents. The whole circle represents the total frequency.
饼图将数据显示为圆形的扇区。每个扇区的大小与其所代表类别的频率成比例。整个圆代表总频率。
To construct a pie chart, you must calculate the angle for each category using the formula:
要构建饼图，必须使用以下公式计算每个类别的角度：
Angle = (Frequency ÷ Total Frequency) × 360°
Always check that the angles add up to 360°. Draw the circle, measure the angles from a starting point, and label each sector clearly.
务必检查所有角度之和是否为 360°。画圆，从起点开始测量角度，并清楚地标记每个扇区。
A pictogram uses small pictures or symbols to represent data. A key must state what each picture stands for. For example, one picture of a book might represent 5 books read.
象形图使用小图片或符号表示数据。必须用图例说明每个图片代表什么。例如，一本书的图片可能代表读了 5 本书。
Pictograms are visually appealing but can be less precise if a symbol has to be split to show a part of the amount, such as half a picture.
象形图在视觉上很吸引人，但如果必须分割符号来表示部分数量（例如半个图片），则精度较差。
5. Stem-and-Leaf Diagrams | 茎叶图
A stem-and-leaf diagram is a way of displaying numerical data in order while keeping the original values. Each data value is split into a stem (usually the tens or leading digits) and a leaf (the ones or trailing units).
茎叶图是一种在保持原始数值的同时有序显示数值数据的方法。每个数据值被分成茎（通常是十位或前导数字）和叶（个位或后续单位）。
To construct a stem-and-leaf, first identify the stems, then write each leaf next to its stem. The leaves must be ordered from smallest to largest. A key is essential to show how to read the diagram.
要构建茎叶图，首先确定茎，然后将每个叶写在其茎旁边。叶子必须从小到大排序。必须有一个图例来说明如何解读该图。
For example, the data set 12, 15, 21, 23, 23, 27 would be shown as:
例如，数据集 12, 15, 21, 23, 23, 27 可表示为：
1 | 2 5
2 | 1 3 3 7
Key: 1 | 2 means 12
Stem-and-leaf diagrams make it easy to find the median, mode, and range. They also preserve the original data, unlike a bar chart.
茎叶图便于找到中位数、众数和极差。与条形图不同，它们还保留了原始数据。
Sometimes you may see a back-to-back stem-and-leaf diagram, which compares two related sets of data by sharing a central stem.
有时你会看到背靠背茎叶图，它通过共享一个中央茎来比较两组相关的数据。
6. Measures of Central Tendency | 集中趋势的度量
An average is a single value that represents the typical or central value in a set of data. The three main averages are the mean, the median, and the mode.
平均数是一个代表数据集中典型或中心值的单个数值。三个主要的平均数是均值（平均数）、中位数和众数。
The mode is the value that occurs most often. A data set can have one mode (unimodal), more than one mode (bimodal or multimodal), or no mode. The mode is the only average that can be used for qualitative data.
众数是出现频率最高的值。一个数据集可以有一个众数（单峰）、多个众数（双峰或多峰）或没有众数。众数是唯一可用于定性数据的平均数。
The median is the middle value when the data is arranged in order. If there are two middle values, the median is the number halfway between them.
中位数是将数据按顺序排列后的中间值。如果有两个中间值，中位数就是这两个数的中间值。
The mean is found by adding together all the data values and then dividing by the number of values. It is the average most people refer to in everyday language.
平均数（均值）是通过将所有数据值相加，然后除以数值的个数来计算的。它是大多数人在日常语言中所指的平均数。
Mean = (Sum of all data values) ÷ (Number of data values)
The mean takes every value into account, so it can be affected by very large or very small outliers. The median is more resistant to extreme values.
均值考虑了每一个数值，因此可能受极大或极小的异常值影响。中位数对极端值有更强的抵抗力。
7. Range and Spread | 极差与离散程度
While averages tell us about the centre of a data set, we also need to describe how spread out the data is. The simplest measure of spread is the range.
虽然平均数告诉我们数据集的中心，但我们还需要描述数据的离散程度。最简单的离散程度度量是极差。
The range is the difference between the highest and lowest values in the data set.
极差是数据集中最大值和最小值之间的差值。
Range = Highest value – Lowest value
A small range indicates that the data points are close together and more consistent. A large range suggests greater variability or an outlier.
极差小表明数据点彼此接近，更趋于一致。极差大则表明变异性较大或存在异常值。
When comparing two sets of data, it is useful to calculate both an average (often the mean or median) and the range. This gives a picture of both the typical value and the consistency of the data.
比较两组数据时，计算平均数（通常是均值或中位数）和极差都很有用。这样既能了解典型值，也能了解数据的一致性。
For example, if two classes have similar mean test scores, but one class has a much smaller range, that class performed more consistently.
例如，如果两个班级的平均考试成绩相似，但其中一个班的极差小得多，则该班的成绩更为稳定。
8. Introduction to Probability | 概率基础
Probability is a measure of how likely an event is to happen. It is expressed as a number between 0 and 1. A probability of 0 means the event is impossible; a probability of 1 means it is certain.
概率是衡量事件发生可能性的一种度量，用一个在 0 到 1 之间的数表示。概率为 0 表示事件不可能发生；概率为 1 表示事件必定发生。
Probability can be written as a fraction, a decimal, or a percentage. An even chance has a probability of 0.5, 1/2, or 50%.
概率可以写成分数、小数或百分数。均等机会的概率为 0.5、1/2 或 50%。
The probability of an event occurring can be calculated using the formula:
事件发生的概率可以使用以下公式计算：
P(Event) = Number of favourable outcomes ÷ Total number of possible outcomes
This formula applies when all outcomes are equally likely. Examples include rolling a fair dice or flipping a fair coin.
当所有结果的可能性相等时，此公式适用。例子包括掷一个公平的骰子或抛一枚公平的硬币。
The sample space is the set of all possible outcomes. A probability scale line can help visualise where events lie between impossible and certain.
样本空间是所有可能结果的集合。概率尺度线可以帮助直观地显示事件在不可能和确定之间的位置。
If the probability of an event occurring is p, then the probability of the event not occurring (its complement) is 1 – p. The sum of probabilities of all possible outcomes in a sample space is always 1.
如果一个事件发生的概率为 p，那么该事件不发生的概率（其互补事件）为 1 – p。样本空间中所有可能结果的概率之和总是 1。
9. Scatter Graphs and Correlation | 散点图与相关性
A scatter graph is used to display the relationship between two sets of numerical data, often called bivariate data. Each point on the graph represents a pair of values.
散点图用于显示两组数值数据（通常称为双变量数据）之间的关系。图上的每个点代表一对值。
The pattern of points on a scatter graph can show correlation. Correlation describes the strength and direction of the relationship between the two variables.
散点图上点的模式可以展示相关性。相关性描述了两个变量之间关系的强度和方向。
If the points tend to slope upwards from left to right, there
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