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Mode
(KS2, Year 5)
The Lesson
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."Interactive Widget
Use this interactive widget to see the mean, median, and mode averages of your data set.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.
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:
Top Tip
The Mode Can Be Used for NonNumeric Items
The other averages (the mean and the median) only apply to numbers. The mode can be used for items that are not numbers (nonnumerica 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 aboveaverage 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%).
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