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Line Plots and Dot Plots | 线图与点图

2026-08-21 17:38 · 本文部分内容由AI辅助创作

📚 Line Plots and Dot Plots | 线图与点图

In IGCSE Mathematics, data handling questions often ask you to read, make and interpret line plots, which are also called dot plots. A line plot shows individual data points as marks above a number line. It is useful for small sets of data because you can quickly see the frequency, mode, gaps and range.

在 IGCSE 数学中，数据处理题经常要求你阅读、绘制和解释线图，线图也叫点图。线图用数轴上方的标记表示每个数据点。它适合用于较小的数据集，因为你可以快速看出频数、众数、空缺和全距。

1. What Is a Line Plot? | 什么是线图？

A line plot is a simple statistical diagram. It uses a horizontal number line and a mark, usually an X or a dot, above each value. Each mark represents one data value. If the same value occurs several times, the marks are stacked vertically above that number.

线图是一种简单的统计图。它使用一条水平的数轴，并在每个数值上方画一个标记，通常是 X 或圆点。每个标记代表一个数据值。如果同一个数值出现多次，标记就会垂直堆叠在该数字上方。

Line plots are especially helpful when the data set is small or when you need to see the shape of the data quickly. They are common in school surveys, sports results and quick experiments.

线图在数据集较小或需要快速观察数据分布时特别有用。它们常见于学校调查、体育成绩和快速实验。

2. Key Parts of a Line Plot | 线图的主要组成部分

A clear line plot must have a title, a number line with equal intervals, and one mark above the number line for each data value. The number line must cover the smallest and largest values in the data set.

清晰的线图必须有标题、间隔相等的数轴，以及数轴上方每个数据值对应的标记。数轴必须覆盖数据集中的最小值和最大值。

PartWhat it does
TitleTells the reader what the data is about
Number lineShows the values being measured
X or dot marksRepresent individual data points

这些部分必须一起配合：标题说明数据内容，数轴显示被测量的数值，X 或圆点标记表示每个数据点。缺失任何一部分都会让线图不易理解。

3. Reading a Line Plot | 读取线图

To read a line plot, look at the number under each stack of marks. The number of marks above that value is the frequency of that value. For example, if the number 4 has six X marks above it, then the value 4 occurred six times.

读取线图时，先看每堆标记下方的数字。该数值上方的标记数量就是该数值的频数。例如，如果数字 4 上方有六个 X 标记，那么数值 4 出现了六次。

Here is a simple example. A class recorded the number of books read in one month:

下面是一个简单例子。一个班级记录了每个学生一个月读的书的数量：

Number of booksFrequency
21
34
46
53
61

udents read at least 4 books, add the frequencies for 4, 5 and 6: 6 + 3 + 1 = 10 students.

要找出有多少学生至少读了 4 本书，就把 4、5 和 6 的频数相加：6 + 3 + 1 = 10 名学生。

4. Making a Line Plot from Data | 根据数据绘制线图

Follow these steps to make a line plot: first, identify the smallest and largest values. Second, draw a horizontal number line that includes all values from the smallest to the largest with equal spacing. Third, place one X or dot above the number line for each data value. If a value repeats, stack the marks vertically. Finally, add a title that describes the data.

按照以下步骤绘制线图：首先，找出最小值和最大值。其次，画一条水平的数轴，包含从最小值到最大值的所有数值，并且间距相等。第三，在数轴上方为每个数据值画一个 X 或圆点。如果数值重复，就把标记垂直堆叠。最后，加上一个描述数据的标题。

For example, the data 5, 6, 6, 7, 8, 8, 8, 9, 10 has values from 5 to 10. Draw a number line from 5 to 10 with equal intervals. Above 5 place one X, above 6 place two X marks, above 7 place one X, above 8 place three X marks, above 9 place one X, and above 10 place one X.

例如，数据 5, 6, 6, 7, 8, 8, 8, 9, 10 的值从 5 到 10。画一条从 5 到 10 的等距数轴。在 5 上方画一个 X，在 6 上方画两个 X，在 7 上方画一个 X，在 8 上方画三个 X，在 9 上方画一个 X，在 10 上方画一个 X。

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5. Frequency and Mode from a Line Plot | 线图中的频数与众数

The frequency of a value is the number of marks above that value. The mode is the value with the greatest frequency, meaning it has the tallest stack of marks. In the books example above, the value 4 has frequency 6, so the mode is 4 books.

某个数值的频数就是该数值上方的标记数量。众数是频数最大的数值，也就是标记堆叠最高的数值。在上面的读书例子中，数值 4 的频数是 6，所以众数是 4 本书。

If two values have the same highest frequency, the data set can have two modes and is called bimodal. If every value appears the same number of times, there is no mode.

如果两个数值的最高频数相同，数据集可以有两个众数，称为双众数。如果每个数值出现的次数相同，则没有众数。

6. Range and Gaps from a Line Plot | 线图中的全距与空缺

ks example, the largest value is 6 and the smallest is 2, so the range is 6 − 2 = 4 books.

全距是最大值与最小值之间的差。计算方法是：用线图上的最大值减去最小值。在读书例子中，最大值是 6，最小值是 2，所以全距是 6 − 2 = 4 本书。

A gap is a value on the number line that has no marks above it. Gaps can be important because they show that no data value fell on that number. They also help you see where the data is concentrated or spread out.

空缺是数轴上没有标记的数值。空缺很重要，因为它们表明没有数据落在该数值上。它们还能帮助你看出数据集中或分散的位置。

7. Comparing Two Line Plots | 比较两个线图

Line plots are useful for comparing two small data sets. Place the two number lines with the same scale one above the other, or compare the frequencies side by side. Look at the modes, ranges and gaps for each set.

线图很适合比较两个较小的数据集。将两条刻度相同的数轴上下放置，或并排比较它们的频数。观察每个数据集的众数、全距和空缺。

For example, Class A recorded goals scored in matches as follows: 0:2, 1:5, 2:4, 3:3, 4:1. Class B recorded goals scored as: 0:0, 1:3, 2:6, 3:5, 4:2. Class A has a mode of 1 goal, while Class B has a mode of 2 goals. Class B also has a larger frequency of higher scores, so Class B scored more goals overall in this comparison.

例如，A 班记录比赛进球数如下：0:2，1:5，2:4，3:3，4:1。B 班记录进球数如下：0:0，1:3，2:6，3:5，4:2。A 班的众数是 1 球，而 B 班的众数是 2 球。B 班在较高分数上的频数也更大，因此在此比较中 B 班的进球总数更多。

8. Common Errors and How to Avoid Them | 常见错误及如何避免

Students often lose marks on line plot questions for a few simple reasons. Knowing these errors will help you avoid them in an exam.

学生在回答线图问题时经常因为几个简单的原因而失分。了解这些错误能帮助你在考试中避免它们。