\[\text{Mean} = \frac{\text{Sum of all values}}{\text{Number of values}}\]
The mean is the total of every value in a dataset divided by how many values there are: Mean = (sum of values) ÷ (number of values). It is the average most people mean when they just say "average", and it shares the total out equally across every data point.
Example 1 — Mean of 4, 7, 9, 2, 8
Step 1
Add all values: \(4 + 7 + 9 + 2 + 8 = 30\)
Step 2
Count the values: there are \(5\)
Step 3
Divide: \(30 \div 5 = \mathbf{6}\)
Example 2 — Mean of 12, 15, 9, 18, 11, 7
Step 1
Sum: \(12 + 15 + 9 + 18 + 11 + 7 = 72\)
Step 2
Count: \(6\) values
Step 3
\(72 \div 6 = \mathbf{12}\)
Tip: Always check your count matches the number of values listed — a common error is to count one too few.
If you know the mean and all but one value, rearrange: find the required total first, then subtract the known values.
Example 3 — Mean of 5 numbers is 8. Four are 6, 7, 10, 9. Find the missing number.
Step 1
Required total: \(8 \times 5 = 40\)
Step 2
Sum of known values: \(6 + 7 + 10 + 9 = 32\)
Step 3
Missing value: \(40 - 32 = \mathbf{8}\)
Example 4 — A class of 6 has mean test score 15. Five scores are 12, 18, 14, 16, 13. Find the sixth.
Step 1
Total needed: \(15 \times 6 = 90\)
Step 2
Known sum: \(12 + 18 + 14 + 16 + 13 = 73\)
Step 3
Sixth score: \(90 - 73 = \mathbf{17}\)
⚠ Common mistake: Students forget to multiply first. Always find the required total before subtracting.
✓ Quick Check 2 — Finding missing values given the mean
Question 1 of 10
Calculating the mean from a frequency table gets its own full lesson — see Lesson 18.5 — Averages from Frequency Tables.
Interactive — Mean Balancer
Add values to the beam. The fulcrum slides to the mean — watch the beam balance when it's exactly right.
Presets:
Add some values to begin…
✓ Balanced!
Tap a circle to remove it. Values must be 0–20.
Practice: Finding the Mean
Find the mean of each list. Type your answer, then click Check.
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Question
Answer
Result
1
Find the mean of 4, 8, 12, 16
2
Find the mean of 5, 10, 15
3
Find the mean of 2, 4, 6, 8, 10
4
Find the mean of 7, 7, 7, 7
5
Find the mean of 1, 2, 3, 4, 5, 6
6
Find the mean of 20, 30, 40
7
Find the mean of 3, 5, 9, 11
8
Find the mean of 100, 200, 300, 400, 500
9
Find the mean of 12, 18, 24
10
Find the mean of 6, 9, 12, 15, 18
⚠ Things to Watch Out For
Forgetting to divide: Adding up all the values is only half the job — you must then divide by how many values there are. Adding without dividing gives the total, not the mean.
Miscounting the values: Double-check exactly how many numbers are in the list before dividing. Missing one off (or counting one twice) throws off the whole answer.
Confusing mean with median or mode: The mean is the only one of the three averages that needs every value added together and divided — median is the middle value, mode is the most frequent.
Rounding too early: Keep full precision while adding and dividing. Round only the final answer, otherwise small errors build up.