Averages and range

• Mean: add up the values and divide by how many there are.
• Median: the middle value when they're in order. With an even number of values, it's halfway between the middle two.
• Mode: the most common value.
• Range: largest − smallest. It measures how spread out the data is.

Example: find the mean, median, mode and range of 4, 8, 3, 8, 7, 5, 9.

1. In order: 3, 4, 5, 7, 8, 8, 9
2. Mean = 44 ÷ 7 = 6.29 to 2 d.p.
3. Median: the 4th value = 7
4. Mode = 8, and range = 9 − 3 = 6

So the mean is 6.29.

An outlier is a value much bigger or smaller than the rest.

Example: five salaries are £20 000, £22 000, £24 000, £25 000 and £150 000. Which average best represents them?

1. Mean = 241 000 ÷ 5 = £48 200, which is more than four of the five earn
2. Median = £24 000
3. The median, because the outlier £150 000 drags the mean up

Total = mean × number of values

1. Use the mean to find the total of all the values.
2. Subtract the values you know.

Example: five numbers have a mean of 12. Four of them are 10, 15, 9 and 16. Find the fifth.

1. Total = 12 × 5 = 60
2. 10 + 15 + 9 + 16 = 50
3. Fifth number = 60 − 50 = 10

Harder example: six numbers have a mean of 8. When a seventh number is added, the mean becomes 9. Find the seventh number.

1. Total of six: 6 × 8 = 48
2. Total of seven: 7 × 9 = 63
3. Seventh number = 63 − 48 = 15

A stem-and-leaf diagram shows the data in order. The key tells you how to read it.

Key: 2 | 3 means 23

Example: find the median, mode and range.

1. There are 12 values, so the median is halfway between the 6th and 7th
2. 6th = 23 and 7th = 27, so the median = 25
3. Mode = 23
4. Range = 42 − 12 = 30