# Histograms

Videos, worksheets, and solutions to help Grade 6 students learn how to make and interpret histograms.

In this lesson, we will learn
• how to define a histograms
• how to make and interpret histograms
• the differences between histograms and bar graphs
Related Topics: More Statistics Lessons

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

### 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?
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
Frequency histogram
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.

Learn to compare bar graphs and histograms.
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? 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?

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.