Mean, Median, Mode and Range
Learn the four types of average — mean, median, mode and range — with worked examples using real data like test scores, prices and salaries.
When someone says "average", they usually mean the mean. But there are actually three types of average plus the range. Each one tells you something different.
Mean — The "Add Up and Share" Average
Worked Example 1 — Test scores: 6, 8, 7, 9, 5
- Add them up: 6 + 8 + 7 + 9 + 5 = 35
- Count them: 5 values
- Mean = 35 ÷ 5 = 7
Median — The Middle Value
Step 1: Line the numbers up in order from smallest to biggest.
Step 2: Find the middle one. If there are two middle values, find their mean.
Worked Example 2 — Finding the Median
Data: 12, 3, 7, 9, 5, 8, 11
- Order: 3, 5, 7, 8, 9, 11, 12
- 7 values → middle one is the 4th
- Median = 8
Mode — The Most Common Value
The mode is simply the value that appears most often. There can be more than one mode, or no mode at all.
Example: 2, 3, 3, 5, 7, 3, 8 → Mode = 3 (appears 3 times).
Range — How Spread Out the Data Is
Example: data goes from 3 to 12 → Range = 12 − 3 = 9.
When to Use Which One?
| Average | Best when… | Watch out for… |
|---|---|---|
| Mean | Data is evenly spread | Extreme values (outliers) pull it up or down |
| Median | There are outliers (e.g. salaries) | Ignores actual values |
| Mode | Data is categorical (e.g. shoe sizes, colours) | May not exist or may have multiple |
Salary example: If 9 workers earn £25k and the boss earns £250k, the mean salary is £47,500 — which makes it look like everyone earns loads. The median is £25k, which is much more realistic.
Worked Example 3 — Supermarket Prices
Prices of milk (per pint): £0.80, £0.85, £0.80, £0.90, £1.20, £0.80
- Mean: (0.80+0.85+0.80+0.90+1.20+0.80) ÷ 6 = £5.35 ÷ 6 = £0.89
- Median: Ordered: 0.80, 0.80, 0.80, 0.85, 0.90, 1.20 → middle of 3rd and 4th = (0.80+0.85)÷2 = £0.825
- Mode: £0.80 (appears 3 times)
- Range: £1.20 − £0.80 = £0.40
Try It Yourself
- Find the mean of 4, 7, 9, 12, 8. (Answer: 8)
- Find the median of 15, 3, 9, 7, 12, 5. (Answer: 8 — the mean of 7 and 9)
- A data set has values from 2 to 19. What is the range? (Answer: 17)