Arithmetic Mean (Average)
The arithmetic mean — commonly called the average — is the most widely used measure of a typical value in a data set.
How to Calculate the Mean
Mean = Sum of all values ÷ Number of values
Worked Examples
Easy
Find the mean of 4, 7, 9, 6, 4. Sum = 30. Count = 5. Mean = 30 ÷ 5 = 6
Medium
Test scores: 72, 85, 91, 68, 79. Sum = 395. Mean = 395 ÷ 5 = 79
Finding a Missing Value
Five numbers have a mean of 8. Four of them are 6, 9, 7, 10. Find the fifth. Sum needed = 5 × 8 = 40. Known sum = 32. Fifth value = 40 − 32 = 8
Mean vs Median vs Mode
| Measure | What it represents | Best used when... |
|---|---|---|
| Mean | Balance point of all data | No extreme outliers |
| Median | Middle value when sorted | Data has outliers |
| Mode | Most frequent value | Categorical or repeated data |
Key Takeaways
- Mean = total ÷ count.
- Adding a value above the mean increases it; below the mean decreases it.
- The mean uses every value — outliers can pull it up or down significantly.
Practice Questions
- Find the mean of 3, 8, 5, 12, 7.
- A student scores 64, 78, 82 in three tests. What is her mean score?
- Six numbers have a mean of 12. Five of them are 10, 14, 9, 15, 11. Find the sixth.
- Find the mean temperature for a week: 18, 21, 19, 23, 20, 17, 22°C.
- Why might the mean be misleading if one data value is much larger than the rest?