When you initially learn about averages, four topics are normally learnt together: mean, median, mode and range.

While the first three are averages and give one number to represent the set of data, **range is a measure of spread.**

The range doesn't give a number to represent the others, it gives a measure of how** **consistent** **the data is - the **smaller the range**, the **more consistent the data.**

**How to find the range**

The range is found by subtracting the smallest piece of data from the largest:

**range = largest - smallest**

**Example 1:**

**Find the range of 4, 8, 7, 5, 9, 4, 8, 3**

The largest value in the list is 9.

The smallest value in the list is 3.

**Range = 9 - 3 = 6**

**Example 2:**

I collect the shoe sizes of a group of people and put the data into a frequency table.

**What is the range of the shoe sizes?**

Shoe size | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 | 11 | 12 |

Number of people | 5 | 7 | 9 | 14 | 21 | 28 | 16 | 6 | 5 | 1 |

We need to be careful here, the largest number that appears in the table is 28, but this is a frequency, not a shoe size. We never use frequency when we are finding the range.

The** largest shoe size **that appears is 12.

The** smallest** **shoe size** that appears is 3.

The range of shoe sizes is **12 - 3 = 9**

Let's move on to the questions now.