Step by step
The question
Question: The mean of 5 numbers is 12.
Four of them are 10, 8, 15 and 11.
What is the fifth number?
1 Total needed
There are 5 numbers with a mean of 12.
So all 5 add up to 12 times 5.
That is 60.
total needed = 12 × 5 = 60
The mean times how many numbers gives the total.
That is the key idea today.
mean × how many = total
Careful!
The mean is of all 5 numbers, not just the 4 we know.
So we multiply by 5.
Careful: not 12 × 4 ✗
2 Total so far
Now we add the 4 numbers we know, from left to right.
total so far = 10 + 8 + 15 + 11
So far, the total is 44.
total so far = 44
3 What is missing
The total must go from 44 up to 60.
The missing part is 60 minus 44.
That is 16.
fifth number = 60 − 44 = 16
4 Check
Let's check: 44 plus 16 is 60.
And 60 divided by 5 is 12, the mean we wanted.
So it is right!
44 + 16 = 60, 60 ÷ 5 = 12
Let's look back.
First: total needed.
Then: total so far.
Then: what is missing.
Last: check.
Answer
fifth number = 60 − 44 = 16