Unimodal & Bimodal Distributions: Definition & Examples

Unimodal & Bimodal Distributions: Definition & Examples
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Lesson Transcript
Instructor: Cathryn Jackson

Cat has taught a variety of subjects, including communications, mathematics, and technology. Cat has a master's degree in education and is currently working on her Ph.D.

Sometimes a single mode does not accurately describe a data set. In this lesson, learn the differences between and the uses of unimodal and bimodal distribution. When you are finished, test your knowledge with a quiz!

Unimodal and Bimodal Distributions

Professor Greenfield is looking at the grades for his latest math test. He notices that his morning class has scored pretty well, with most of the students scoring a B on the test. Greenfield's second class is a little different. He notices that the grades are spread really far apart, with equal amounts of students scoring D's and B's. Professor Greenfield is looking at an example of unimodal and bimodal distribution.

You're probably familiar with the concept of mode in statistics. The mode of a data set is the value that appears the most frequently in the data set. For example, if the data set was 3, 4, 5, 3, 7, 3, 10, the value that appears the most frequently would be 3. Therefore 3 is our mode. So, what do unimodal and bimodal mean?

Take a look at our data set again: 3, 4, 5, 3, 7, 3, 10. Are there any other numbers that appear frequently in the data set? No, 3 appears the most and is the only number that is repeated. Because this data set only has one number that repeats, it is considered a unimodal distribution. Unimodal distribution is when the data set has a single mode. Professor Greenfield's first class, the one that scored primarily B's on the math test, would be considered a unimodal distribution.

Sometimes, a single mode doesn't describe the data properly. Take Professor Greenfield's second class for example. It wouldn't be fair to the people that scored the B's to say that most of the people in the class scored a D. Likewise, it wouldn't be an accurate representation of the data to say that most of the people in the class scored a B. So, what do we do? This class is a great example of a bimodal distribution, where the data set has two different modes.

Unimodal Distribution

Let's look at another data set. Professor Greenfield surveyed his students to see how many hours each student studied for the math test. Professor Greenfield came up with the following numbers: 1, 3, 2, 1, 5, 1, 4, 3, 2, 1, 1. Each number represents the number of hours each student spent studying. Look at this chart to see how the information is organized:

# of Study Hours # of Students
1 5
2 2
3 2
4 1
5 1
6 0
7 0

Notice that five of the students spent an hour studying for the math test. That's more than any other number of hours. We can also see this data represented in a histogram.

This is a histogram, a graphical representation of the distribution of data.

A histrogram can help determine whether a data set is unimodal or bimodal
histogram of the example data

Bimodal Distribution

Now Professor Greenfield wants to know the breakdown of the math test. He reviews each test and figures out how many students got each answer right. Then, he creates a histogram to represent this data.

Two peaks on a histogram prove a bimodal distribution
histogram of example data

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