When we find averages, we end up with one number that describes a set of data (this is properly called a **distribution**).

The reason we do this is so that we are able to compare two distributions.

**How do we compare?**

To compare distributions, we need to find an average (this is normally **the mean)** and a measure of spread (for a small data set, this is normally the **range**).

When a question comes up in the exam, you need to make a comment on the average and a comment on the range.

**Example 1:**

Dan can catch either the number 1 or number 2 bus to school. He records how many minutes late they are over the course of 10 days:

Number 1: 4, 2, 0, 6, 4, 8, 8, 6, 3, 9

Number 2: 3, 4, 0, 10, 3, 5, 13, 1, 0, 1

**By comparing the mean and range for each, which bus should Dan catch if he wants to be at school on time?**

**Bus number 1: **

Mean = 50 ÷ 10 = 5

Range = 9 - 0 = 9

**Bus number 2: **

Mean = 40 ÷ 10 = 4

Range = 13 - 0 = 13

You could argue in favour of either bus:

The mean is lower for bus number 2, meaning that it is late less often.

The range is lower for bus number 1, meaning that bus 1 is more consistent and reliable.

Let's try some questions now.