How to Find the Average: An 11+ Maths Guide

What Does Average Mean?

In 11+ maths, the word average usually means the mean: a single number that represents the typical or central value in a set of data.

For example, if several children receive different scores in a test, the average score gives a useful overall picture of how the group performed. It does not tell us every individual score, but it condenses the information into one meaningful number.

The method is always the same:

1. Add all the values together.
2. Count how many values there are.
3. Divide the total by the number of values.

In short:

Step	What to Do	Why It Matters
1	Add all values	Finds the total amount
2	Count the values	Tells you how many equal shares are needed
3	Divide total by count	Finds the mean average

Tip: Encourage your child to say the rule aloud: “Add them all, then divide by how many.” This simple reminder helps prevent many avoidable errors.

A Simple Worked Example

Imagine a child records the number of pages they read over five days:

Day	Pages Read
Monday	12
Tuesday	9
Wednesday	15
Thursday	10
Friday	14

First, add the values:

12 + 9 + 15 + 10 + 14 = 60

There are 5 values, so divide 60 by 5:

60 ÷ 5 = 12

The average number of pages read was 12 pages per day.

It is worth pausing here to make the idea concrete. If the 60 pages were shared equally across the five days, each day would have 12 pages. That is exactly what the mean average represents.

Finding an Average When the Answer Is a Whole Number

Some average questions work out neatly as whole numbers. For instance, find the average of:

8, 6, 11, 7, 9, 10, 5, 8, 8

Add the numbers:

8 + 6 + 11 + 7 + 9 + 10 + 5 + 8 + 8 = 72

Count the numbers. There are 9.

Now divide:

72 ÷ 9 = 8

So the average is 8.

A sensible check is to look at the original values. Most of them are close to 8, so an average of 8 is believable. Estimation is a valuable exam habit: it will not replace working, but it can alert a child if they accidentally enter 72 ÷ 8 or miss a number from the total.

What If the Average Is a Decimal?

Averages do not have to be whole numbers. In fact, decimal answers are very common in 11+ questions.

Consider the values:

7, 9, 12, 14

The total is:

7 + 9 + 12 + 14 = 42

There are 4 values:

42 ÷ 4 = 10.5

The average is 10.5.

This makes perfect sense: 10.5 sits between the values in the set. Children should not worry if they get a decimal. They should only round if the question tells them to do so.

Did you know? An average can be a value that does not appear anywhere in the original data. A group may have an average score of 10.5 even though no child scored exactly 10.5.

Common Average Mistakes to Avoid

Average questions are straightforward once the method is secure, but they can be lost through rushed arithmetic. Watch for these common pitfalls.

Mistake	How It Happens	How to Prevent It
Missing out a value	A number is skipped while adding	Cross off or tick each value as it is used
Dividing by the wrong number	The child counts incorrectly	Count the values separately before dividing
Dividing by the total	The total is used as the divisor	Write “total ÷ number of values” before calculating
Rounding too early	A decimal is changed before the final answer	Keep the exact answer unless told to round
Forgetting the context	An answer has no unit	Write “minutes”, “marks”, “pence” or another suitable unit

For more general approaches to accuracy, timing and multi-step questions, our guide on how to improve your child’s 11+ maths score is a helpful next read.

Average Questions in an 11+ Test

In a real 11+ paper, averages are not always presented as a simple list of numbers. Your child may need to extract the relevant figures first, then apply the same method.

They may see averages in questions involving:

• test scores;
• weekly spending or pocket money;
• distances travelled;
• temperatures;
• lengths and weights;
• tables and bar charts;
• missing values;
• comparison problems.

For example, a question may say that four quiz scores have an average of 18 and ask for a missing fifth score. The key is to work backwards.

If the average of five scores is 18, their total must be:

5 × 18 = 90

If four known scores add up to 71, the missing score is:

90 − 71 = 19

These reverse questions are a little more demanding because children need to understand what an average means, rather than merely follow a memorised procedure.

Tip: In missing-value questions, find the required total first: average × number of values. Then compare it with the total of the known values.

Mean, Median and Mode: Know the Difference

Although “average” often means the mean, some 11+ materials may also refer to the median and mode. Children should recognise the distinction.

Type	Meaning	Example for 3, 5, 5, 7, 10
Mean	Total divided by number of values	6
Median	Middle value when values are ordered	5
Mode	Most frequent value	5

The mean is the focus of most introductory average questions. Still, understanding the vocabulary will help a child read questions carefully and avoid using the wrong method.

Data handling is one of several core areas that need regular, calm practice. Our 11+ Maths Test Questions and Answers guide explains how topic knowledge and exam technique work together.

A Short Practice Routine

Averages are ideal for short, frequent practice sessions because each question reinforces addition, division and careful reading.

Day	Activity	Time
Monday	Calculate averages from short lists of whole numbers	10 mins
Tuesday	Practise checking totals with estimation	10 mins
Wednesday	Find averages with decimal answers	10 mins
Thursday	Solve one missing-value average problem	10 mins
Friday	Complete a mixed data-handling quiz	15 mins
Weekend	Review mistakes and explain one method aloud	10 mins

The most useful question to ask is not simply, “What is the answer?” Try asking, “Why did you divide by that number?” If your child can explain that they divided by the number of values, they are building the understanding needed for unfamiliar exam questions.

Build Confidence with 11+ Maths Practice

Averages sit within the wider data-handling skills children need for the 11+. The 11+ Maths Learn & Test app provides 1,280 questions across 32 topics, with detailed study notes covering shapes, algebra, fractions, data handling, time, money, and more. It is a strong place to learn the method, practise it in manageable steps and revisit areas that need more confidence.

Once the foundations feel secure, the 11+ Maths Practice Papers app helps children apply their knowledge under more realistic conditions, with 1,200 maths questions across 24 full practice papers covering all 11+ maths topics with detailed explanations.

Together, they make it easier to move from “I know the rule” to “I can use it confidently in a timed question”. They are part of the full 11+ Apps suite, offering 8100+ questions across 7 apps for focused grammar-school preparation.