What is the average?
We explain what the term average means in maths, how to find the average of a set of data (and how children are taught to do it in primary school), and what a mean average is.
What is the average?
In maths, the average value in a set of numbers is the middle value, calculated by dividing the total of all the values by the number of values.
When we need to find the average of a set of data, we add up all the values and then divide this total by the number of values.
When we need to find the average of a set of data, we add up all the values and then divide this total by the number of values.
Finding the average: the process explained step by step
Here is an example:
This is the amount Mrs Mansell has spent on food shopping in the last month:
Week 1 £67
Week 2 £92
Week 3 £52
Week 4 £38
Week 5 £73
Week 6 £86
To find out the average amount Mrs Mansell spends on food every week:
This is the amount Mrs Mansell has spent on food shopping in the last month:
Week 1 £67
Week 2 £92
Week 3 £52
Week 4 £38
Week 5 £73
Week 6 £86
To find out the average amount Mrs Mansell spends on food every week:
- Add up all the values: 67 + 92 + 52 + 38 + 73 + 86 = 408
- We would then divide 408 by the number of values (6) using short division. This would give us the answer 68. We therefore know that Mrs Mansell's average spend was £68.
This can also be called finding the 'mean average' of a set of data and is learnt by children in Year 6. In the “old” (pre-2014) national curriculum children were also taught how to find the mode, range and median of a number of values. Since September 2015, children in Year 6 have only been required to learn about the mean average.
A simpler problem that could be solved mentally could be:
Keiran wrote down the score he got for his spelling test for the first six weeks of term:
Week 1 - 8
Week 2 - 6
Week 3 - 9
Week 4 - 8
Week 5 - 10
Week 6 - 7
Here, the total is 48, which is then be divided mentally by 6 to make an average score of 8.
It is important for children to understand why we would take the trouble to find an average value.
Finding an average gives us an idea as to an overall behaviour or trend – Mrs Mansell's average spend on shopping gives us an idea as to whether she usually spends a lot or a little money and Keiran's average spelling score gives us an idea as to how good he usually is at spelling. If we were given just one value to judge Mrs Mansell or Keiran by, this might not be representative of their overall behaviour.
Keiran wrote down the score he got for his spelling test for the first six weeks of term:
Week 1 - 8
Week 2 - 6
Week 3 - 9
Week 4 - 8
Week 5 - 10
Week 6 - 7
Here, the total is 48, which is then be divided mentally by 6 to make an average score of 8.
It is important for children to understand why we would take the trouble to find an average value.
Finding an average gives us an idea as to an overall behaviour or trend – Mrs Mansell's average spend on shopping gives us an idea as to whether she usually spends a lot or a little money and Keiran's average spelling score gives us an idea as to how good he usually is at spelling. If we were given just one value to judge Mrs Mansell or Keiran by, this might not be representative of their overall behaviour.
