AQE Test Maths averages – mean, median, mode and range

There are three types of maths averages you need to understand for the AQE Test – mean, median and mode.

The range is the difference between the smallest and largest amounts in your list of data (results).

The hot topics for AQE maths are mean and range. You’re very unlikely to get a question about median or mode – it just makes sense for you to learn these averages at the same time.

Usually there is a question on mean and range in every AQE paper!

By the way, this is a really good, colourful visual to help you remember the difference between the types of average –

Transfer Test Tips averages poster amazon
Averages visual, Amazon.

(By the way, some of our posts contain affiliate links. That means we earn a small commission if you click through and buy something from a website we recommend. You don’t pay any more, and we only recommend things we really love.)


Calculating maths averages for AQE Test

Finding the mean

Usually when people say “average”, they mean the mean!

How do you work out the mean?

First, you add. Then, you divide.

You add all the data (amounts) together. Then you divide your total by the number of amounts you’ve added.

You can find the mean of any number of things. All you have to do is choose the number that you will divide your total by.


To work out median, mode and (most importantly for AQE) the range, it can really help you to write the list of results in order from smallest to largest.

Finding the median

This is the middle amount in all your data or results.

Once you have written your list of results in order from smallest to largest, you can easily pick out the median. It’s the result right in the middle.

Finding the mode

This is the result that occurs most frequently in your list of amounts.

To work out the mode, pick out the result that appears the most in your list.

Finding the range

The range is the difference between the smallest and largest amounts.

To find the range, subtract the smallest amount from the largest.

How to remember maths averages

You’ve probably learned this little rhyme about averages in school. Here’s a refresher.

Warning – this will go round and round your head once you’ve sung it to yourself a few times!

Hey diddle diddle, the median’s the middle

You add then divide for the mean

The mode is the one you can see the most

And the range is the difference between


Watch out for trickier questions on maths averages

Many AQE test questions on averages follow the same format – list of data and you must calculate the mean and range. So far, so good!

Lately there’s been a new twist on averages! The twist involves trickier questions about the range.

You might be given a list of data (with one result missing, let’s call it x) and the range. You have to work out the value of x (the missing result).

All you need to do is work your way backwards. You know that range = largest number subtract smallest number. You need to study the data you’ve been given, along with the range, and see what value makes sense for the missing result.

For example –

Four flowers have petals. The number of petals each flower has is given below. The range of the four numbers is 6.

4        2        5        x

What is the value of x?

Here’s how to work it out…

Smallest number = 2

Range is 6.

x – 2 = 6

Therefore x must be 8.


Check out more topic tips here.




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