📚 How to Draw and Interpret Pie Charts | 如何绘制与解读饼图
Data surrounds us every day, and visual representations help us understand information quickly. Pie charts are one of the most common ways to display parts of a whole, using slices of a circle to represent categories. In KS3 Cambridge Mathematics, you will learn how to read, interpret, and construct pie charts accurately, using angles and proportions. This revision guide explains each step clearly, from recognising sectors to calculating angles with a protractor, so you can tackle any question involving pie charts with confidence.
数据每天都围绕在我们身边，而可视化表示能帮助我们快速理解信息。饼图是最常见的展示整体各部分的方式之一，用圆形的切片来表示不同类别。在 KS3 剑桥数学课程中，你将学习如何准确地读取、解读和绘制饼图，运用角度和比例。本复习指南将清晰地解释每一个步骤，从识别扇形到用量角器计算角度，让你自信应对任何与饼图相关的问题。
1. What is a Pie Chart? | 什么是饼图？
A pie chart is a circular statistical graphic divided into sectors, each representing a proportion of the whole. The entire circle corresponds to the total data set, and the size of each sector's angle is directly proportional to the quantity it represents. The sum of all central angles is always 360°.
饼图是一种圆形统计图，被分成多个扇形，每个扇形代表整体的一部分。整个圆对应整个数据集，每个扇形的角度大小与其所代表的数量成正比。所有中心角的总和始终是 360°。
2. Why Use Pie Charts? | 为什么使用饼图？
Pie charts are excellent for showing how a total is divided into parts, especially when there are relatively few categories. They make it easy to compare proportions visually. However, they become difficult to read if there are too many slices, or if the differences between sectors are very small.
饼图非常适合展示一个总体如何被划分成各个部分，尤其是当类别较少时。它们使得比例的比较一目了然。然而，如果切片过多，或者扇形之间的差异非常小，饼图会变得难以阅读。
3. Reading a Pie Chart | 解读饼图
To read a pie chart, examine each sector and note its angle or the percentage label. You can then compare the sizes of sectors directly. For example, if one sector has a 90° angle and another has 180°, the second category represents twice as much of the total as the first.
要解读饼图，需检查每个扇形并注意其角度或百分比标签。然后，你可以直接比较各扇形的大小。例如，如果某个扇形的角度是 90°，另一个是 180°，那么第二个类别所代表的总量是第一个的两倍。
4. Calculating the Angle for Each Sector | 计算每个扇形的角度
The angle of a sector is calculated using the formula: Angle = (Category frequency ÷ Total frequency) × 360°. This works because the full circle represents 360°, and each category's share of the total is multiplied by that complete rotation.
扇形的角度计算公式为：角度 = (类别频数 ÷ 总频数) × 360°。其原理是，整个圆代表 360°，每个类别在总频数中所占的份额乘以这个完整的旋转角度。
5. Drawing a Pie Chart Step-by-Step | 逐步绘制饼图
Start by finding the total frequency. Then calculate the angle for each category using the formula. Draw a circle with a compass, and mark a starting radius. Use a protractor to measure and mark the first angle, then draw the next line. Repeat for each category, ensuring the final line returns to the starting point.
先求出总频数。然后用公式计算每个类别的角度。用圆规画一个圆，并标出起始半径。用量角器测量并标记第一个角度，然后画出下一条半径。对每个类别重复此步骤，确保最后一条半径返回到起始点。
6. Using a Protractor | 使用量角器
Place the centre point of the protractor on the centre of the circle, aligning the 0° line with the previous radius. Read the scale carefully from 0° to the required angle and make a small mark on the circumference. Then connect that mark to the centre to form the next sector boundary.
将量角器的中心点对准圆心，并将其 0° 刻度线与上一条半径对齐。小心地从 0° 到所需角度读取刻度，并在圆周上做一个标记。然后将该标记与圆心连接，形成下一个扇形边界。
7. Example with a Frequency Table | 频率表示例
72°. The sum is 144° + 96° + 48° + 72° = 360°. These angles are then drawn in a pie chart.
一项调查记录了最喜欢的颜色：红色 12 人，蓝色 8 人，绿色 4 人，黄色 6 人。总频数为 30。角度：红色 = (12/30)×360° = 144°，蓝色 = 96°，绿色 = 48°，黄色 = 72°。总和为 144° + 96° + 48° + 72° = 360°。然后用这些角度绘制饼图。
8. Interpretation – Comparing Sectors | 解读——比较扇形
s 90° and the total population is 200, the frequency for that sector is (90/360)×200 = 50.
一旦饼图绘制完成，你就可以提取有用的信息。找出哪个类别最大或最小，或者在已知总数的情况下计算实际频数。例如，如果一个扇形为 90°，而总体总量为 200，那么该扇形的频数为 (90/360)×200 = 50。
9. Pie Charts with Percentages | 带百分比的饼图
charts are labelled with percentages instead of frequencies. Since the full circle is 100%, you can convert percentages to angles by multiplying by 3.6° (because 100% × 3.6 = 360°). For example, 25% corresponds to 25 × 3.6 = 90°.
饼图常用百分比而不是频数来标注。由于整个圆是 100%，你可以通过乘以 3.6° 将百分比转换为角度（因为 100% × 3.6 = 360°）。例如，25% 对应于 25 × 3.6 = 90°。
10. Common Mistakes to Avoid | 常见错误避免
Students often forget to check that all sector angles sum to 360°. Another common error is misreading the protractor scale, especially when angles are close to 180° or when the protractor is not aligned properly. Also, ensure the compass drawing is accurate so that the centre is clearly defined.
学生经常忘记检查所有扇形角度之和是否为 360°。另一个常见错误是读错量角器刻度，尤其是当角度接近 180° 或量角器未正确对齐时。此外，要确保圆规画出的圆准确无误，使得圆心清晰明确。
11. Practice Problem | 练习题
A student spends their day: School 7 hours, Sleep 8 hours, Leisure 3 hours, Meals 2 hours, Other 4 hours. Calculate the angles for each activity, draw the pie chart, and check your sum. Then state which activity takes up the largest sector.
一个学生的一天是这样度过的：上学 7 小时，睡觉 8 小时，休闲 3 小时，用餐 2 小时，其他 4 小时。计算每项活动的角度，画出饼图，并检查角度的总和。然后指出哪项活动占的扇形最大。
12. Summary and Key Points | 总结与关键点
ngles accurately with a protractor, label sectors clearly, and verify that the sum is 360°. With practice, you will be able to both create and interpret pie charts quickly and accurately for your KS3 exams.
饼图将分类数据转化为圆形的可视切片。关键技能是使用公式 (频数 ÷ 总数) × 360° 将频数转换为角度。始终用量角器精确测量角度，清晰地标注扇形，并验证角度总和为 360°。通过练习，你将能够快速准确地绘制并解读饼图，自信应对 KS3 考试。
Published by TutorHao | Mathematics Revision Series | aleveler.com
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