A **histogram** is a vertical bar chart in which the frequency corresponding to a class is represented by the **area** of a bar (or rectangle) whose base is the class width.

Note that the histogram differs from a bar chart in that it is the area of the bar that denotes the value, not the height. However, if the widths of the bars are uniform then only the height need to be considered.

In this lesson, we will look at histograms with uniform (equal width).

In another lesson, we will look at histograms with non-uniform widths

In a histogram:

There are no gaps between the rectangles

The

y-axis is the frequency and always starts at 0.

*Example*

The following table shows the frequency distribution of the masses, in kg, of 21 members of a sports club.

Mass (kg) |
53 – 55 |
56 – 58 |
59 – 61 |
62 – 64 |
65 – 67 |

Frequency |
2 |
6 |
8 |
4 |
1 |

A histogram of the above frequency table is as follows:

Define a histogram.

Interpret a histogram.

Create a histogram from data.

A histogram is a bar graph that represents a frequency distribution. The width represents the interval and the height represents the corresponding frequency. There are no spaces between the bars.

Example:

Create a histogram from the following data:

Average Gas Mileage: 24,17,14,22,25,26,38,42,24,12,28,19,32,21,35,28,21,31,18,19

If there are no breaks in the data, then normally the last data value of a bin is the first value in the next bin.

This video will show you step by step on how to create a histogram from data.

Properties of Histograms

1. Quantitative Data

2. No gaps

3. Bar Width (Bin size or Class size)

4. Y-axis corresponds to the frequency

Example:

Here are the grades of 15 students

88,48,60,51,57,85,69,75,97,72,71,79,65,63,73

Build a histogram from the data.

Rotate to landscape screen format on a mobile phone or small tablet to use the **Mathway** widget, a free math problem solver that **answers your questions with step-by-step explanations**.

You can use the free Mathway calculator and problem solver below to practice Algebra or other math topics. Try the given examples, or type in your own problem and check your answer with the step-by-step explanations.

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