What is a Histogram in Math? - Definition & Examples

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  • 0:05 What Is a Histogram?
  • 0:41 When to Use
  • 3:19 How to Read
  • 4:03 Lesson Summary
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Lesson Transcript
Instructor: Yuanxin (Amy) Yang Alcocer

Amy has a master's degree in secondary education and has taught math at a public charter high school.

Watch this video lesson to see how useful a histogram can be when you need to show a bunch of data in an easy to read format. Also, learn how you can easily gather the information you need from looking at a histogram.

What is a Histogram?

In math, a histogram is a visual way to display frequency data using bars. A feature of histograms is that they show the frequency of continuous data, such as the number of trees at various heights from 3 feet to 8 feet. They are not used to show categorical data, such as the population of dogs in Norway, Finland, and Sweden. Another feature of histograms is that the data can be grouped into ranges. For example, the height of the trees can be grouped into 3 to 4 feet, 5 to 6 feet, and 7 to 8 feet.

When to Use a Histogram

How do you know when to use a histogram? You can decide this by looking at your data. Ask yourself, 'Is the data continuous, or can I group the data into ranges?'

What you are looking for is a group of data that is continuous. What this means is that the data covers a range of values that does not jump. For example, the range of tree heights is 3 to 8 feet. The data does not jump from 4 to 6 feet. There is no gap. The countries of Norway, Finland, and Sweden, though, do jump. There is no continuity between the countries. They are separate entities. For histograms, you need continuous information and not just categories that jump.

Histograms are great at showing results, such as the frequency of the number of trees at various heights from 3 to 8 feet. So, if you have a set of continuous data, then you can use a histogram to show the results visually.

So, let's say that I surveyed a hill by my house, and I counted the number of trees at various heights. I found that at 3 feet, my hill only had 2 trees. At 4 feet, my hill had 4 trees. At 5 feet, I only had 1 tree. At 6 feet, I had 7 trees. At 7 feet, it was 8 trees. Then at 8 feet, I had 2 trees. The histogram for this information would have the x-axis showing the range of heights from 3 to 8 feet. Then, the y-axis would have the number of trees.

Then, I have several options for showing the data. I can show the data for each height separately, or I can group them into ranges, such as 3 to 4 feet, 5 to 6 feet, and then 7 to 8 feet.

There are different options for showing data on a histogram.
image showing histogram data

I can combine the data into any number of different ranges. I can also group them into ranges, such as 3 to 5 feet and 6 to 8 feet. It is your choice based on the kind of information you want to show. If you want to be specific, then use smaller ranges or don't use ranges at all. If you want to be more general with your data and just show an overview, then you can use larger ranges to group your data.

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