Concept 5 of 7
Mean (Average): The Fair-Share Number
Today's big idea
Mean = sum ÷ count, and a missing value = mean × count − the known sum.
Mean usually is not one of the values in the list, so do not go hunting for it.
How it works
👀 What's going on?
Five friends pool their pocket money, then split it back out equally. Nobody counts who brought what any more. That equal share is the mean.
💡 Here's the trick
Look at the working above. Add every value to get the total, then divide by how many values there are. The mean always sits somewhere between the smallest value and the largest.
🪄 How to do it
- 1.Add all the values, as the working above does.
- 2.Divide that total by how many values there are.
- 3.To find a missing value, use mean × count, then take away what you know.
✍️ Try it
Four bags weigh 12 kg, 15 kg, 9 kg and 16 kg. What is the mean mass? Then: five boys average 30 kg, and four of them are 28, 31, 29 and 27 kg. Find the fifth.
The bags total 52 kg, and 52 ÷ 4 = 13 kg. Five boys at 30 kg average 150 kg in all, the four known weigh 115 kg, so the fifth is 35 kg.
⚠️ Watch out
You might be thinking the mean must be one of the numbers in the list. It usually is not. The mean of 4 and 7 is 5.5, a value that never appears at all.
🌟 Why this matters
A cricketer's batting average, the average rainfall for June and your family's monthly spend all use this one calculation. It turns a long messy list into a single fair number.
Exam tip: When a mean is given, turn it into a total straight away, because the total is what you work with.
Watch me solve one
Quanta solves it
“Watch how I think through one of these — then you try.”
THE PROBLEM
“Five test scores: 7, 8, 6, 9, 10. What is the MEAN?”
- 1
Add them up
7 + 8 + 6 + 9 + 10 = 40. ⚖️
- 2
Count them
5 scores.
- 3
Divide
40 ÷ 5
- 4
Answer ✓
Mean = 8.
Now you try one — same steps, different story 👇
See it in action
⚡ Time to play!
Mean = Sum ÷ Count. Reverse: Sum = Mean × Count. Take it one tap at a time.
MEAN · ROUND 1 OF 3
Data: 2, 4, 6, 8, 10
Step 1 — add them all: 2 + 4 + 6 + 8 + 10 = ?
Quick check
✅ VERIFICATION
A cricketer scores 32, 45, 28 and 55 in four innings. What is his MEAN score?
⚡ Finish the activity above first to answer.
Keep going!
Up next: Mode & Median
Mean = sum ÷ count. Use the right tool.