Concept 9 of 9
Mean (Average): The Fair-Share Number
Today's big idea
The mean is the level every value reaches once the total is shared out equally.
Values gathered into one total, then divided by how many there are.
How it works
👀 What's going on?
Four friends have 3, 5, 6 and 6 stickers. Push the lot into one pile and deal them back out, one at a time, until everybody holds the same number. Every one of them ends with 5.
💡 Here's the trick
The mean is the level everything would sit at if the total were shared out equally. Picture a row of cube towers at different heights. Take bricks off the tall ones to fill the short ones until every tower stands level. That level is the mean.
🪄 How to do it
- 1.Add up every value in the picture above to get the total.
- 2.Count how many values there are.
- 3.Divide the total by that count.
✍️ Try it
Three towers hold 2, 6 and 7 cubes. What is the mean? And if the mean of four numbers is 12, with three of them being 10, 14 and 11, what is the fourth?
The towers total 15 across 3 towers, so the mean is 5. For the second, four numbers with a mean of 12 must total 48, the three known ones make 35, so the missing one is 13.
⚠️ Watch out
The mean always lands somewhere between the smallest value and the largest. An answer outside that range is wrong before you check anything else. A set running from 2 to 7 can never have a mean of 9.
🌟 Why this matters
Sharing out equally is something you already do without calling it maths. Splitting a bill, dividing sweets so nobody complains, working out a typical week of pocket money.
Exam tip: For a missing-value question, go through the total. Mean times count gives the total, and the total take away what you know gives the answer.
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. Find the MEAN.”
- 1
Sum the values
7 + 8 + 6 + 9 + 10 = 40
- 2
Count the values
5
- 3
Divide
40 ÷ 5 = 8
- 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
Four numbers are 12, 15, 9 and 8. What is the MEAN?
⚡ Finish the activity above first to answer.
Keep going!