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Mode (Mathematics Glossary)

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.

Dictionary Definition

The Oxford English Dictionary defines the mode as "the value, or range of values, of a variable which occurs most frequently in a set of data."

Finding the Mode

Imagine we wanted to find the mode of the numbers given below:



To find the mode, find the number that appears most often.
  • 1 appears 2 times.
  • 2 appears 4 times.
  • 3 appears 1 time.
2 appears most often.

The mode is 2.

Read more about how to find the mode

Understanding the Mode

Imagine several candidates are standing for election. The candidate with the most votes would win the election.

The winning candidate would be the mode. Their name would appear most in the ballot box.

Different Numbers of Modes

For a set of numbers, there is only one mean and one median (the other types of average).

However, there can be different numbers of modes: none, one or more than one.
  • If there are no repeated numbers in a set there is no mode. The set of numbers below has no mode:


  • If there is one number that apears more often that the others, there is one mode (this is called unimodal). The set of numbers below has one mode:


  • If there is more than one number that appear more often than the others, there is more than one mode (this is called multimodal).

    The set of numbers below has two modes (1 and 2). This is called bimodal. 1 and 2 appear more often than the other numbers but equally often as each other:

Other Types of Average

Along with the mode, there are other types of average. The most commonly used are: Read more about the mean
Read more about the median

Interactive Widget
Here is an interactive widget to help you learn about averages.

Interactive Test
  show
 


Here's a second test on the mode.
Here's a third test on the mode.
Top Tip

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). In the example used on this page, the politician that wins an election is the one with the most votes. Their name (with a voter's cross next to) appears most in the ballot box.

Beware

The Mode is a Bad Measure of Central Tendency

An average is a measure of central tendency.

Although a set of numbers will have different values, their average should give you an idea of where the middle of the numbers is (where the numbers tend to center around).

The mean and median do this, but the mode can do a very bad job of being in the middle.

For example, consider the numbers below:
1, 1, 20, 25, 30, 35, 40
1 is the mode, although it does a very bad job of describing a middle or a typical number. The mean (21.7) and the median (25) are nearer the middle of the numbers.

The Mode Can Be Misleading

Look at these test results:
8%, 8%, 9%, 50%, 70%, 75%, 80%, 85%, 90%, 95%
The mode is 8%.

If you got 9% in the test, you could claim you got an above-average score because 9% is greater than the mode of 8%.

9% is a very low score and much worse than most students got. It is much lower than the mean score (57%) and the median score (72.5%).