📚 Interpreting Histograms | 解读直方图
Histograms are one of the most important graphical tools in statistics for displaying grouped continuous data. Unlike bar charts, histograms use area to represent frequency, which makes them especially powerful when class intervals have unequal widths. In this article, we will explore everything you need to know about interpreting histograms for your IGCSE Edexcel Mathematics examination.
直方图是统计学中展示分组连续数据最重要的图形工具之一。与条形图不同，直方图使用面积来表示频数，这使得它在组距不等时尤为强大。在本文中，我们将全面讲解IGCSE Edexcel数学考试中解读直方图所需的全部知识。
1. What is a Histogram | 什么是直方图
A histogram is a type of chart used to show the distribution of continuous data that has been grouped into class intervals. The horizontal axis represents the variable being measured, while the vertical axis represents the frequency density. In a histogram, there are no gaps between bars because the data is continuous.
直方图是一种用于展示分组连续数据分布的图表类型。水平轴表示被测量的变量，垂直轴表示频率密度。在直方图中，条形之间没有空隙，因为数据是连续的。
Key features of a histogram:
直方图的关键特征：
Bars are drawn adjacent to each other with no gaps.
条形彼此相邻，没有任何间隙。
The area of each bar is proportional to the frequency of that class interval.
每个条形的面积与该组距的频数成正比。
The horizontal axis shows continuous data values in class intervals.
水平轴以组距的形式显示连续数据值。
The vertical axis shows frequency density, not frequency itself.
垂直轴显示的是频率密度，而不是频数本身。
2. Histograms vs Bar Charts | 直方图与条形图的区别
Many students confuse histograms with bar charts, but the two are fundamentally different. Understanding the distinction is essential for choosing the correct graph and for interpreting exam questions correctly.
许多学生将直方图与条形图混淆，但两者有本质区别。理解这一区别对于选择正确的图表以及正确解读考题至关重要。
| Feature | Histogram | Bar Chart |
|---|---|---|
| Data type | Continuous | Discrete or categorical |
| Gaps between bars | No gaps | Gaps present |
| Vertical axis | Frequency density | Frequency |
| Area of bar | Represents frequency | Not meaningful |
In an exam, if you see a graph with no gaps between bars and a vertical axis labelled 'frequency density', it is a histogram. If the data is discrete and the bars are separated, it is a bar chart.
在考试中，如果你看到条形之间无空隙且纵轴标注为"频率密度"的图形，那就是直方图。如果数据是离散的且条形之间有间隔，那就是条形图。
3. Frequency Density | 频率密度
The frequency density is the height of each bar in a histogram. It tells us how concentrated the data is within each class interval. Without it, we could not compare classes of different widths fairly.
频率密度是直方图中每个条形的高度。它告诉我们数据在每个组距内的集中程度。没有它，我们就无法公平地比较不同组距宽度的组别。
The formula for frequency density is:
频率密度的公式为：
Frequency Density = Frequency ÷ Class Width
For example, consider the following frequency table for the times taken by students to complete a puzzle:
例如，考虑以下关于学生完成拼图所需时间的频数表：
| Time (min) | Frequency | Class Width | Frequency Density |
|---|---|---|---|
| 0 – 10 | 20 | 10 | 2 |
| 10 – 20 | 30 | Published by TutorHao | IGCSE Mathematics Revision Series | aleveler.com
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