Looking at a dot plot, we often want one number that says what is typical. The mean is one such number, and you already know how to compute it with division.
Key idea
The mean is the sum of the values divided by how many values there are. It is the fair share: the amount each would get if the total were shared out evenly.
Why it works
Picture four stacks of cubes, 3, 7, 5 and 9 tall. Move cubes from the tall stacks to the short ones until every stack is the same height. No cubes are added or lost, so the total is still $3 + 7 + 5 + 9 = 24$, now in 4 equal stacks: $24 \div 4 = 6$ each. That leveled height is the mean. The mean is also the balance point of a dot plot: the values above it and below it pull equally.
Worked example: Find the mean
Find the mean of 3, 7, 5 and 9.
- Add: $3 + 7 + 5 + 9 = 24$.
- Divide by the count, 4: $24 \div 4 = 6$.
Answer: 6
Worked example: Test scores
Find the mean of the scores 85, 90, 78, 92 and 80.
- Sum: $85 + 90 + 78 + 92 + 80 = 425$.
- $425 \div 5 = 85$.
Answer: 85
Worked example: A missing value
The mean of four numbers is 7. Three of them are 5, 9 and 6. What is the fourth?
- Mean 7 for 4 numbers means the total is $4 \times 7 = 28$.
- The three known numbers add to 20.
- The fourth is $28 - 20 = 8$.
Answer: 8
Common mistake
Dividing by the wrong count, especially when some values are 0. The data 0, 4, 5 has three values, so the mean is $9 \div 3 = 3$, not $9 \div 2$. Quick check: the mean must lie between the smallest and the largest value.