Line graphs, the mean and pie charts · Usually met around P6
How a mean changes
Total = mean × how many.
How to do it
Method
Total = mean × how many
15 × 4 = 60, 60 + 25 = 85, 85 ÷ 5 = 17
Another way
Share out the extra
(25 − 15) ÷ 5 = 2, 15 + 2 = 17
In full
First get the total from the mean: total = mean × how many. Adding a number: new total = old total + the number, divided by the new count; taking one away, subtract. 4 numbers with a mean of 15 total 60; add 25 and the total is 85, 85 ÷ 5 = 17. Another way: see how much is extra and share it out: 25 is 10 more than 15, and 10 shared among 5 numbers is 2 each, 15 + 2 = 17. So adding a number above the mean raises it, below the mean lowers it, and equal to it leaves it alone. Adding 3 to every number adds 3 to the mean.
Worked examples
Have a go first, then open each one for the answer and the working.
Example 1
The mean of 4 numbers is 34. Taking away one of them, 16, what is the mean of the 3 left?
Show the answer and working
Answer: 40
Total 34 × 4 = 136; 136 − 16 = 120; 120 ÷ 3 = 40.
Example 2
The mean of 5 numbers is 34. If 54 is added, what happens to the mean?
- A. Can't tell without the numbers
- B. It goes up
- C. It goes down
- D. It stays the same
Choose the right answer
Show the answer and working
Answer: B. It goes up
A number above the mean raises it, below lowers it, equal leaves it.
Example 3
The mean of 4 numbers is 27. If 11 is added to every number, what is the new mean?
Show the answer and working
Answer: 38
The total grows by 11 × 4; divided by 4, the mean grows by 11: 27 + 11 = 38.
Practise it in the game →Line graphs, the mean and pie charts · Free to start, unlimited questions, no download