Step by step
The question
Question: The mean of 5 numbers is 30.
Four of them are 28, 35, 22 and 31.
What is the fifth number?
1 Total needed
There are 5 numbers with a mean of 30.
So all 5 add up to 30 times 5.
That is 150.
total needed = 30 × 5 = 150
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 30 × 4 ✗
2 Total so far
Now we add the 4 numbers we know, from left to right.
total so far = 28 + 35 + 22 + 31
So far, the total is 116.
total so far = 116
3 What is missing
The total must go from 116 up to 150.
The missing part is 150 minus 116.
That is 34.
fifth number = 150 − 116 = 34
4 Check
Let's check: 116 plus 34 is 150.
And 150 divided by 5 is 30, the mean we wanted.
So it is right!
116 + 34 = 150, 150 ÷ 5 = 30
Let's look back.
First: total needed.
Then: total so far.
Then: what is missing.
Last: check.
Answer
fifth number = 150 − 116 = 34