Step by step
The question
Question: The mean of 6 numbers is 20.
Five of them are 18, 25, 14, 22 and 19.
What is the sixth number?
1 Total needed
There are 6 numbers with a mean of 20.
So all 6 add up to 20 times 6.
That is 120.
total needed = 20 × 6 = 120
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 6 numbers, not just the 5 we know.
So we multiply by 6.
Careful: not 20 × 5 ✗
2 Total so far
Now we add the 5 numbers we know, from left to right.
total so far = 18 + 25 + 14 + 22 + 19
So far, the total is 98.
total so far = 98
3 What is missing
The total must go from 98 up to 120.
The missing part is 120 minus 98.
That is 22.
sixth number = 120 − 98 = 22
4 Check
Let's check: 98 plus 22 is 120.
And 120 divided by 6 is 20, the mean we wanted.
So it is right!
98 + 22 = 120, 120 ÷ 6 = 20
Let's look back.
First: total needed.
Then: total so far.
Then: what is missing.
Last: check.
Answer
sixth number = 120 − 98 = 22