What does a child have to do to calculate an arithmetic mean in the 11+?

Find the mean of a short supplied data set. It is one of 55 named maths skills in the 11+, in the data strand, and this page carries 2 interactive exercises that practise it.

What is the trap in an 11+ calculate an arithmetic mean question?

The middle of the largest and smallest values is the range midpoint, not the mean. The wrong answers on this skill are built out of that, not out of random numbers, so it is worth naming out loud before your child meets it under time pressure.

What can I say if my child is stuck on calculate an arithmetic mean?

Point at the next move rather than explaining the whole rule. Add every number in the Saturday cups column first, then share that total equally between the 4 rows.

What is not part of calculate an arithmetic mean in the 11+?

The skill map draws the line here: Excludes median and mode. A question past that line is testing a different named maths skill, which is worth knowing before you spend a week practising the wrong one.

Which other 11+ skills should we practise alongside calculate an arithmetic mean?

The data strand holds 9 skills that are tested together, and the pages next to calculate an arithmetic mean are compare bar-chart values, compare line-graph change and compare table values. Each has its own exercise and its own link, and none of them needs an account.

How can my child practise calculate an arithmetic mean for free?

Use Fair Share Machine and Average Showdown, embedded on this page. They are the exercises the skill map attaches to calculate an arithmetic mean, they run in the browser with no account to make, nothing is scored, and nothing a child does here is recorded or sent anywhere. Each also has its own link, so you can send one to a child without sending them anywhere else first.

Maths · Data

Calculate an arithmetic mean

Find the mean of a short supplied data set.

Free to use and free to share. There is no sign-up, no score, and nothing a child does here is recorded or sent anywhere.

Practise it now

5 classmates stacked up their reading tokens into towers. Time to make sense of the piles.

It covers most of this skill rather than all of it.

Loading the interactive exercise. Nothing you do here is saved or scored.

A worked example

One question of the kind this skill is tested with, worked all the way through: the reasoning, and what the wrong answers are there to catch.

Working out a mean from a table

What is the mean of the Saturday cups column?

Drinks poured at the park cafe.

Drink	Saturday cups	Sunday cups
Cocoa	46	48
Lemonade	67	25
Cordial	61	8
Milkshake	46	56

220
55
46
67

Answer: 55

How you get there

The Saturday cups column adds up to 220 across 4 rows, and 220 shared between 4 is 55, which means the mean is not any single row's figure.

Why the other answers tempt

The middle of the largest and smallest values is the range midpoint, not the mean.

If they are stuck, say this

Add every number in the Saturday cups column first, then share that total equally between the 4 rows.

Now do it live in Fair Share Machine

How each of these 2 exercises teaches it

Fair Share Machine

5 classmates stacked up their reading tokens into towers. Time to make sense of the piles.

Sharing the blocks out equally leaves every tower at 5 - that levelled height IS the mean $(8 + 5 + 6 + 3 + 3 = 25$ , shared between 5). The height that appears most often is 3: that is the mode.

Step 1. Share it out. Move blocks between the towers until every tower is the same height.
Step 2. Find the crowd. Tap every tower that shares the most common height.

What to say if they get stuck

Nothing is added or taken away - blocks only ever move from one tower to another.
The mean is the height every tower reaches once the sharing is fair.
Median means middle, mode means most, range means the gap from shortest to tallest.

Open Fair Share Machine on its own page to share it

Average Showdown

Only one of the two claims is true about these block towers. Tap the true one.

Mean, median and mode are three different questions, so they usually give three different answers. The mean shares every block out equally, so add the towers up and divide by how many towers there are. The median is about position, not size: sort the towers, then point at the middle one. The mode is about how often, so look for the height that repeats. When a claim looks wrong, work out the statistic it names before you decide, because most mistakes come from checking the wrong one.

What to say if they get stuck

The median is the middle tower once you put them in order from smallest to tallest.
The mean is what every tower would be if you shared all the blocks out equally.
The mode is the height that turns up more often than any other.

Open Average Showdown on its own page to share it

Related maths skills

All maths 11+ skills

Questions parents ask about calculate an arithmetic mean

Answered from what the skill map records about this skill, not from a template. Every answer here is on the page, and the same questions are the page's FAQ structured data.

: Find the mean of a short supplied data set. It is one of 55 named maths skills in the 11+, in the data strand, and this page carries 2 interactive exercises that practise it.
: The middle of the largest and smallest values is the range midpoint, not the mean. The wrong answers on this skill are built out of that, not out of random numbers, so it is worth naming out loud before your child meets it under time pressure.
: Point at the next move rather than explaining the whole rule. Add every number in the Saturday cups column first, then share that total equally between the 4 rows.
: The skill map draws the line here: Excludes median and mode. A question past that line is testing a different named maths skill, which is worth knowing before you spend a week practising the wrong one.
: The data strand holds 9 skills that are tested together, and the pages next to calculate an arithmetic mean are compare bar-chart values, compare line-graph change and compare table values. Each has its own exercise and its own link, and none of them needs an account.
: Use Fair Share Machine and Average Showdown, embedded on this page. They are the exercises the skill map attaches to calculate an arithmetic mean, they run in the browser with no account to make, nothing is scored, and nothing a child does here is recorded or sent anywhere. Each also has its own link, so you can send one to a child without sending them anywhere else first.

Knowing which maths topic to practise is most of the work

A free diagnostic covers arithmetic, fractions, geometry, measure and data handling, and comes back with the topics to spend the next few weeks on.

Start the free 11+ diagnostic