Definition of Bimodal in Statistics

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A data set is bimodal if it has two modes. This means that there is not a single data value that occurs with the highest frequency. Instead, there are two data values that tie for having the highest frequency.

Example of a Bimodal Data Set

To help to make sense of this definition, we will look at an example of a set with one mode, and then contrast this with a bimodal data set. Suppose we have the following set of data:

1, 1, 1, 2, 2, 2, 2, 3, 4, 5, 5, 6, 6, 6, 7, 7, 7, 8, 10, 10

We count the frequency of each number in the set of data:

  • 1 occurs in the set three times
  • 2 occurs in the set four times
  • 3 occurs in the set one time
  • 4 occurs in the set one time
  • 5 occurs in the set two times
  • 6 occurs in the set three times
  • 7 occurs in the set three times
  • 8 occurs in the set one time
  • 9 occurs in the set zero times
  • 10 occurs in the set two times

Here we see that 2 occurs most often, and so it is the mode of the data set. 

We contrast this example to the following

1, 1, 1, 2, 2, 2, 2, 3, 4, 5, 5, 6, 6, 6, 7, 7, 7, 7, 7, 8, 10, 10, 10, 10, 10

We count the frequency of each number in the set of data:

  • 1 occurs in the set three times
  • 2 occurs in the set four times
  • 3 occurs in the set one time
  • 4 occurs in the set one time
  • 5 occurs in the set two times
  • 6 occurs in the set three times
  • 7 occurs in the set five times
  • 8 occurs in the set one time
  • 9 occurs in the set zero times
  • 10 occurs in the set five times

Here 7 and 10 occur five times. This is higher than any of the other data values. Thus we say that the data set is bimodal, meaning that it has two modes. Any example of a bimodal dataset will be similar to this.

Implications of a Bimodal Distribution

The mode is one way to measure the center of a set of data.

Sometimes the average value of a variable is the one that occurs most often.  For this reason, it is important to see if a data set is bimodal. Instead of a single mode, we would have two.

One major implication of a bimodal data set is that it can reveal to us that there are two different types of individuals represented in a data set. A histogram of a bimodal data set will exhibit two peaks or humps.

For example, a histogram of test scores that are bimodal will have two peaks. These peaks will correspond to where the highest frequency of students scored. If there are two modes, then this could show that there are two types of students: those who were prepared for the test and those who were not prepared.