Mean, Median, Mode and Range

In one line: The mean, median and mode are three ways to find a typical value in a set of numbers, and the range tells you how spread out those numbers are.

Why it works

When you have a list of numbers, called a data set, such as test scores or daily temperatures, it helps to sum it up quickly. The mean (add everything and share it equally), the median (the middle value once the numbers are in order) and the mode (the most common value) each describe a 'typical' number in a slightly different way. The range (biggest minus smallest) shows how far apart the numbers are. Together they help you compare groups, spot unusual results and understand charts in the news, sport and science.

Think of it like: Imagine a group of friends with different numbers of sweets. The mean is what each person would get if everyone put their sweets in a pile and shared them out equally. The median is how many sweets the person in the middle has when everyone lines up from fewest to most. The mode is the number of sweets that the most people happen to have. The range is the gap between the friend with the most sweets and the friend with the fewest. (Where this breaks: The sweets picture breaks down because you cannot always share sweets evenly, but the mean can be a decimal like 4.5, which is perfectly fine. Also, a real data set might have no mode at all (every value appears once) or more than one mode, which the 'most popular number' idea does not obviously suggest.)

Worked example

Seven pupils scored these marks out of 15 on a spelling quiz: 3, 8, 5, 8, 6, 12, 7. Find the mean, median, mode and range.

Put the numbers in order from smallest to largest: 3, 5, 6, 7, 8, 8, 12.
Mean: add them up (3 + 5 + 6 + 7 + 8 + 8 + 12 = 49), then divide by how many there are: 49 ÷ 7 = 7.
Median: there are 7 numbers, so the middle one is the 4th number in the ordered list, which is 7.
Mode: 8 appears twice and every other number appears once, so the mode is 8.
Range: largest minus smallest, 12 − 3 = 9.

Answer: Mean = 7, median = 7, mode = 8, range = 9.

Common mistakes

Finding the median without putting the numbers in order first gives the wrong middle value, so always sort the list from smallest to largest before you look for the middle.
When there is an even number of values, some children just pick one of the two middle numbers, but the fix is to add the two middle numbers and divide by 2.
Dividing by the wrong number when finding the mean (for example dividing by 10 out of habit) gives a wrong answer, so count how many values there are and divide the total by exactly that number.
Writing the range as two numbers like '3 to 12' is not the range, so remember the range is one number found by subtracting: largest minus smallest.

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What is the mode of these numbers: 2, 9, 4, 9, 6?

Questions parents ask

What year do kids learn mean, median, mode and range?

In the UK, children usually meet the mean in Year 6 and work with median, mode and range in Years 7 and 8. In Australia these ideas are mainly taught around Years 6 and 7, and in the US they are a key part of Grade 6 statistics, with more practice in Grades 7 and 8.

How can I help my child remember the difference between mean, median, mode and range?

Short memory tricks help: 'median' sounds like the 'medium' or middle strip of a road, 'mode' starts like 'most', and 'range' is the gap from lowest to highest. The mean is the 'share it out fairly' average.

How can I practise mean, median, mode and range at home?

Use real numbers from everyday life, such as family members' shoe sizes, goals scored in recent matches or the cost of items in a shopping basket. Ask your child to find all four values and talk about which one best describes the 'typical' result.

Which average is best to use?

It depends on the data: the mean uses every value but can be pulled a long way by one very large or very small number. The median is often better when there are unusual values, and the mode is useful for things that are not numbers, like favourite colours.