When we find averages is to find one number that describes a set of data (this is properly called a distribution).
The reason we do this is so we are able to compare two distributions.
How do we compare?
To compare distributions, we need to find an average (this 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
Mean = 50 ÷ 10 = 5.
Range = 8 - 0 = 8
Mean = 40 ÷ 10 = 4
Range = 13 - 0 = 13
You could argue for either bus.
The number 2 bus is less late so he should catch that one (the mean is lower for number 2)
The number 1 bus is more consistent so he should catch that one (the range is lower for number 1)