# Histograms

These lessons help Grade 6 students learn

• how to define a histograms,
• how to make and interpret histograms,
• the differences between histograms and bar graphs.

The following diagram shows the differences between a histogram and a bar chart. Scroll down the page for more examples and solutions on using histograms and comparing histograms with bar charts. ### Introduction to Histograms

How to define a histogram, interpret a histogram and 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 for the following data
Average gas mileage in miles/gallon:
24,17,14,22,25,26,38,42,24,12,28,19,32,21,35,28,21,31,18,19

Histograms, tally and frequency tables

Example:
Make a frequency table and histogram of the following data:
3,5,8,11,13,2,19,23,22,25,3,10,21,14,9,12,17,22,23,14

How to make a frequency histogram?

Example:
Draw a relative frequency histogram from the given data.
34,40,52,57,57,60,60,63,67,69,69,69,71,89

### Compare Bar Graphs and Histograms

Histograms are used to show distributions of variables whereas bar charts are used to compare variables. Histograms plot quantitative data with ranges of the data grouped into intervals while bar charts plot categorical data.

Note that there are no spaces between the bars of a histogram since there are no gaps between the intervals. On the other hand, there are spaces between the variables of a bar chart.

Bar graphs and Histograms
Compare bar graphs and histogram

Examples:
1 a) Describe the data in the table.
b) Make a bar graph of the data.
c) What do the horizontal and vertical axes represent?
d) Which country won the most titles? the least titles?

2 a) Describe the data in the table.
b) What does each interval represent?
c) Make a histogram of the data
d) Describe general patterns in the histogram.

What Distinguishes a Histogram From a Bar Chart?

Histograms and bar graphs are used in the mathematics world for tracking pieces of information. Learn about histograms versus bar graphs.

How to draw a bar graph and a histogram?

### Make and Interpret Histograms

Learn to make and interpret histograms

Example:

1. Use the given data to make a histogram.
2. Use the histogram and answer the following questions:
a) Are there more people who score 41-60 points or who scored 61-80 points?
b) What is the total number of people who took part in the game show?

Example:
Given a bar graph and a histogram
a) Explain which graph you would use to determine how many textbooks have less than 600 pages?
b) Explain which graph you would use to compare the size of a science book and history book?

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