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How to Find the Mode (Mathematics Lesson)

Finding the Mode

We can find the mode of a set of numbers.

Imagine a teacher wanted to find the class's average test score in mathematics.

How to Find the Mode

The mode is found by counting how often each number appears in a set and selecting the one that appears most often.

An Example Question

What is the mode of the test scores?

Step 1
List the numbers in numerical order (going from the smallest to the largest number).
6 7 7 9 10
Step 2
Count how often each number appears.
  • 6 appears 1 time.
  • 7 appears 2 times.
  • 9 appears 1 time.
  • 10 appears 1 time.
Step 3
Find the number that appears most often.



The mode of the test scores is 7.

A Real Example of How to Find the Mode

Sometimes there is more than one mode in a set of numbers.

An Example Question

What is the mode of the test scores?

Step 1
List the numbers in numerical order (going from the smallest to the largest number).
6 6 7 7 9 10
Step 2
Count how often each number appears.
  • 6 appears 1 time.
  • 7 appears 2 times.
  • 9 appears 1 time.
  • 10 appears 2 times.
Step 3
Find the number that appears most often.



The modes of the test scores are 7 and 10.

Another Real Example of How to Find the Mode

The slider below gives another example of finding the mode.

How to Find the Mode from a Frequency Table

Sometimes data is presented in frequency tables.

A frequency table representing the test scores is shown below:



It is possible to find that the mode of the test scores is 7.

Read more about finding the mode from a frequency table.

Interactive Widget
Here is an interactive widget to help you learn about the mode.
Interactive Test
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Here's a second test on finding the mode.
Here's a third test on finding the mode.
Top Tip

The Mode Is The Most

Remember, the mode is the number that appears most!

There Isn't Always a Mode

Unlike the mean and median, there isn't always a mode.

If all numbers appear equally as often, there is no mode.



Note

What Is the Mode?

The mode is an average of a set of numbers.

The mode is the number that appears most often in a set of numbers.

It is possible for a set of numbers to have no mode or multiple modes.

The Mode Can Be Used for Non-Numeric Items

The other averages (the mean and the median) only apply to numbers.

The mode can be used for items that are not numbers (non-numerica or categoric data).

Consider the list of words below:



"Dog" is the mode of this set. It appears more often than the other words.

Unimodal, Bimodal, Multimodal

  • A set of data with one mode is unimodal:



    In the set above, 1 occurs most often, more than any other number. There is only one mode.

  • A set of data with two modes is bimodal:



    In the set above, 1 and 2 both occur the same number of times, which is more than any other number. There are two modes.

  • A set of data with more than one modes is multimodal:



    In the set above, 1, 2 and 3 all occur the same number of times, which is more than any other number.

Other Types of Average

The most commonly commonly used types of average, other than the mode, are: