The Mean

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Add All Values, Divide by Count

\[\text{Mean} = \frac{\text{Sum of all values}}{\text{Number of values}}\]

The mean is the most common type of average. You share the total equally across every data value.

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.

✓ Quick Check 1 — Add all values, divide by count

Question 1 of 10

Finding a Missing Value Given the Mean

\[\text{Sum} = \text{Mean} \times \text{Count}\quad\Rightarrow\quad\text{Missing} = \text{Sum} - \text{Known total}\]

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.

Practice: Finding the Mean

Find the mean of each list. Type your answer, then click Check.

#	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.

Learning Objectives

Real-World Applications

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Example 1 — Mean of 4, 7, 9, 2, 8

Example 2 — Mean of 12, 15, 9, 18, 11, 7

Example 3 — Mean of 5 numbers is 8. Four are 6, 7, 10, 9. Find the missing number.

Example 4 — A class of 6 has mean test score 15. Five scores are 12, 18, 14, 16, 13. Find the sixth.

Interactive — Mean Balancer

Practice: Finding the Mean

⚠ Things to Watch Out For