📚 Year 8 WJEC Statistics: Core Knowledge Review | Year 8 WJEC 统计：核心知识点梳理
Statistics in Year 8 builds on earlier data handling skills, introducing new ways to collect, represent, and analyse data. This guide reviews the core topics covered in the WJEC curriculum, including types of data, charts, averages, range, and basic probability. Understanding these concepts will help you interpret information and make informed decisions.
八年级的统计学习建立在早期数据处理技能的基础上，引入了收集、表示和分析数据的新方法。本指南回顾了 WJEC 课程涵盖的核心主题，包括数据类型、图表、平均数、极差和基础概率。理解这些概念将帮助你解读信息并做出明智的决定。
1. Types of Data | 数据类型
Data is information that has been collected. It can be classified as qualitative or quantitative. Qualitative data describes categories or qualities – for example, hair colour (brown, black, blonde) or types of pet (cat, dog, rabbit). Quantitative data is numerical, meaning it involves numbers, such as test scores, temperature, or age.
数据是收集到的信息。它可以分为定性数据和定量数据。定性数据描述类别或品质——例如，头发颜色（棕色、黑色、金色）或宠物类型（猫、狗、兔）。定量数据是数字的，意味着它涉及数字，比如考试成绩、温度或年龄。
Quantitative data is further split into discrete and continuous. Discrete data can only take specific, separate values – usually whole numbers. The number of goals scored in a match or the number of students in a class are discrete. Continuous data can take any value within a given range; for example, height, mass, and time are continuous because they can be measured to any level of accuracy.
定量数据又分为离散型和连续型。离散数据只能取特定的、分离的值——通常是整数。一场比赛的进球数或班级学生人数是离散的。连续数据可以在给定范围内取任何值；例如，身高、质量和时间是连续的，因为它们可以测量到任意精度。
Recognising the data type is important because it determines which charts and statistics are appropriate to use.
识别数据类型很重要，因为它决定了哪些图表和统计量适合使用。
2. Data Collection | 数据收集
Data can be gathered through surveys, questionnaires, observations, or experiments. A well-designed question should be clear, unbiased, and easy to answer. For instance, asking ‘How many hours do you spend on homework each night?’ is better than a vague question like ‘Do you do a lot of homework?’
数据可以通过调查、问卷、观察或实验来收集。精心设计的问题应该清晰、无偏见且易于回答。例如，询问“你每晚花多少时间做作业？”优于“你做很多作业吗？”这样模糊的问题。
We distinguish between primary and secondary data. Primary data is collected by the person who will use it, such as conducting your own survey. Secondary data is data that has already been collected by someone else, for example, information from websites, books, or government reports. Both can be useful, but primary data allows more control over how it is gathered.
我们区分一手数据和二手数据。一手数据由使用者自己收集，比如进行自己的调查。二手数据是别人已经收集好的数据，例如来自网站、书籍或政府报告的信息。两者都很有用，但一手数据可以更好地控制收集方式。
Always plan how you will record your data before you start collecting, using tally marks or a data recording sheet.
在开始收集数据之前，一定要计划好如何记录数据，使用计数符号或数据记录表。
3. Frequency Tables | 频数表
A frequency table is a simple way to organise raw data. It shows how many times each value or category occurs. First, list the categories or values in the first column, then use a tally column to count, and finally record the total frequency in the third column.
频数表是整理原始数据的简单方法。它显示每个值或类别出现的次数。首先，在第一列列出类别或数值，然后用计数符号列进行计数，最后在第三列记录总频数。
Tally marks are grouped in fives (||||). For example, a survey of favourite colours might show: Red – |||| (5), Blue – ||| (3), Green – || (2). The total of the frequencies should equal the number of data items collected.
计数符号以五个一组（||||）。例如，一项对最喜欢颜色的调查可能显示：红色 – |||| (5)，蓝色 – ||| (3)，绿色 – || (2)。频数总和应等于收集到的数据项数量。
Frequency tables can be used for both discrete and grouped continuous data. For continuous data, we often group values into class intervals, such as 0-9, 10-19, etc.
频数表可用于离散数据和分组连续数据。对于连续数据，我们通常将值分组到分组区间，例如 0-9、10-19 等。
4. Bar Charts and Pictograms | 条形图和象形图
Bar charts represent data using rectangular bars. The length or height of each bar is proportional to the frequency. Bars should be of equal width and there should be gaps between the bars to show that the categories are separate. The chart must have a clear title, and both axes must be labelled.
条形图使用矩形条表示数据。每个条的长度或高度与频数成正比。条的宽度应相等，条与条之间应有间隙，以表明类别是分开的。图表必须有清晰的标题，并且两个坐标轴都要标记。
Pictograms use simple pictures or symbols to represent a certain number of items. A key is essential to tell the reader how many units each symbol stands for. For instance, one smiley face might represent 2 students. Be careful to draw the symbols the same size and evenly spaced to avoid misleading the viewer.
象形图使用简单的图画或符号来表示一定数量的项目。图例至关重要，它告诉读者每个符号代表多少个单位。例如，一个笑脸可能代表 2 名学生。要注意将符号画成同样大小且均匀间隔，以免误导读者。
5. Pie Charts | 饼图
Pie charts display data as slices of a circle. Each slice represents a category, and the angle of the slice is proportional to the frequency. To calculate the angle for a category, use the formula: Angle = (Frequency ÷ Total frequency) × 360°. The total of all angles must equal 360°.
饼图将数据显示为圆的扇形区。每个扇形代表一个类别，扇形的角度与频数成正比。要计算某个类别的角度，使用公式：角度 = (频数 ÷ 总频数) × 360°。所有角度的总和必须等于 360°。
Use a protractor to measure and draw the angles accurately. It is helpful to draw a small circle next to the sector and label it with the category name or percentage. Pie charts are most useful when we want to compare parts of a whole, but they are not suitable for large numbers of categories.
使用量角器精确测量并绘制角度。在扇形旁边画一个小圆圈并标注类别名称或百分比是很有帮助的。当我们想要比较整体的各个部分时，饼图最有用，但不适合类别过多的情况。
6. Line Graphs and Scatter Graphs | 线图和散点图
A line graph is used to show changes over time, such as temperature recorded each hour or a student’s test scores across a term. Plot the data points and join them with straight lines. Time is usually placed on the horizontal axis. The line makes it easy to see trends, such as increasing or decreasing values.
线图用于显示随时间的变化，例如每小时记录的温度或学生一个学期的考试成绩。描出数据点并用直线连接起来。时间通常放在横轴上。这条线使得趋势易于观察，例如上升或下降的值。
A scatter graph (or scatter plot) is used to look for a relationship between two sets of numerical data. Each point on the graph represents a pair of values. If the points tend to slope upward to the right, there is a positive correlation; if they slope downward, a negative correlation. If no pattern is seen, there is no correlation. Do not join the points in a scatter graph – instead, draw a line of best fit if there is a clear trend.
散点图（或散布图）用于寻找两组数值数据之间的关系。图上的每个点代表一对数值。如果点倾向于向右上方倾斜，则存在正相关；如果点向下倾斜，则为负相关。如果没有看到任何模式，则没有相关性。不要在散点图中连接各点——如果有明显趋势，可以画一条最佳拟合线。
7. Mean, Median, Mode | 平均数、中位数、众数
Three common averages help us summarise
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