Average (Mean)

If four friends shared all their stickers out so everyone had the same amount, how many would each get? That equal share is the average — also called the mean. It's one of the most useful ideas in P6 maths, and once you know its one formula and its three forms, average questions become quick, reliable marks.

Parents: let your child predict before they reveal each step. The blue dotted words are tappable definitions, and the "Method tip" boxes name exactly what a marker rewards — writing the average formula before plugging in numbers.

By the end you'll be able to find an average, work backwards to the total or the number of items, and solve word problems where a new value changes the average. Let's level the stacks.

What an average is

The average is what each item would be if the whole amount were shared out equally. The one formula to remember is:

average = total ÷ number of items

Imagine three boxes holding 4, 7 and 7 sweets. Altogether that's 4 + 7 + 7 = 18 sweets. Shared equally between 3 boxes, each would hold 18 ÷ 3 = 6. So the average is 6 — even though no single box actually has 6. The average is the "fair share", not a real count.

Working backwards to the total

Here is what makes average so powerful: you can rearrange the formula. If you know the average and the number of items, you can find the total:

total = average × number of items

Say 5 children have an average of 12 stickers each. You don't know any single child's count, but the total must be 12 × 5 = 60 stickers. This "average times number" step unlocks almost every harder average problem, because once you have the total you can add to or take away from it.

Working backwards to the number of items

The third form lets you find how many items there are when you know the average and the total:

number of items = total ÷ average

Suppose a class collected 84 cans for recycling and the average per pupil was 12 cans. How many pupils are there? Divide the total by the average: 84 ÷ 12 = 7 pupils. Notice all three forms come from the same formula — you just rearrange to find the part that is missing.

When a new value changes the average

The trickiest P6 average questions add a new value and ask for the new average. The safe method is always: go through the total. Find the old total, change it, then divide by the new number of items.

Try this. Sara's first 4 tests have an average of 70 marks. She scores 80 on her 5th test. What is her new average over all 5 tests? First find the old total: 70 × 4 = 280. Add the new mark: 280 + 80 = 360. Now divide by the new number of tests: 360 ÷ 5 = 72. Her new average is 72.

Watch out — these are easily mixed up

Quick recap

🎯 Mastery check

Answer all 6 — your progress is saved on this device.

1. The average of 4 numbers is 15. What is their total?

   601911

2. A shop sold 84 cakes in a week, with an average of 12 cakes per day. How many days did it sell cakes?

   7672

3. Four boxes weigh 50, 60, 70 and 60 grams. What is their average mass?

   60 grams240 grams55 grams

4. The average of 4 test scores is 70. A fifth test scores 80. What is the new average over all 5 tests?

   727570

5. Five numbers have an average of 18. What is the total of all five numbers?

   90233.6

6. Three parcels have an average mass of 8 kg. One parcel weighing 6 kg is removed. What is the average mass of the 2 parcels left?

   9 kg8 kg7 kg

See my score