Topics · Primary Maths · Average
Average: levelling out
The average is what everyone would have if the total were shared out equally. One formula, three ways of using it — and the hard questions all come from working it backwards.
- 170 exam papers analysed
- appears in 86% of P6 Maths papers
- ~3 min read
02 The three questions
Every average question gives you two of the three quantities and asks for the third. Recognising which is missing is the whole job.
- Average missing: total ÷ how many. 20 ÷ 4 = 5.
- Total missing: average × how many. If 4 children average 5, the total is 20. This is the step most often skipped.
- One value missing: find the total from the average, then subtract the ones you know. If 4 children average 5, the total is 20; three of them have 3, 7 and 5, so the fourth has 20 − 15 = 5.
- A value changes: work out the old total and the new total. The difference is the change.
03 Why the total is the way in
The harder P6 questions never give you the total directly, and getting to it is always the first move.
The average of 5 numbers is 12. A sixth number is added and the average becomes 13. What is the sixth number?
Five numbers averaging 12 total 60. Six averaging 13 total 78. The sixth number is 78 − 60 = 18 — not 13, and not 1.
Notice it is much bigger than the new average, which is what pulled the average up in the first place.
04 How to say them
These are words most children have never said out loud, and a word you cannot say is a word you avoid using. Capitals mark the syllable you lean on. Tap the speaker to hear it.
- averagesayAV-uh-rijmore than oneaverages
The total shared equally: total divided by how many things there are.
- totalsayTOH-tuhlmore than onetotals
Everything added together. The bridge between an average and the individual values.
- meanmore than onemeans
Another word for this kind of average. Secondary school uses it more than primary does.
05 What each level is tested on
The same topic, asked differently as it goes up. The percentage is the share of papers at that level in which it appears.
- P5
Finding an average from a set of numbers, and finding a total from an average.
Practise P5 Average — 10 questions →39% of P5 papers
- P6
Missing values, averages that change when a value is added or removed, and averages inside word problems.
Practise P6 Average — 10 questions →86% of P6 papers
06 Mistakes worth knowing about
Each of these is wrong. Decide why before you open it.
“The average must be one of the numbers.”
It usually is not. Three children with 1, 2 and 6 average 3, and nobody has 3.
“Six numbers average 13, so the new number is 13.”
Work through the totals: 5 × 12 = 60 and 6 × 13 = 78, so the new number is 18. It has to be above the average to pull it up.
“To find the total I divided by the average.”
Multiply. Average × how many = total. Dividing goes the other way.
“The average of 4, 6 and 8 is 6, so the average of their doubles is still 6.”
Double everything and the average doubles too, to 12.
“I averaged the two averages.”
Only works when the groups are the same size. Otherwise add the real totals and divide by the real number of things.
Now try it
20 questions across 2 levels, marked as you go with the working shown.