Step by step
The question
Question: The mean of 4 test scores is 70.
For a mean of 74, what score is needed on the next test?
1 Total needed
After the next test there will be 5 scores.
For a mean of 74, the 5 scores must add up to 74 times 5.
That is 370.
total needed = 74 × 5 = 370
The mean times how many numbers gives the total.
That is the key idea today.
mean × how many = total
Careful!
With the next test, there are 5 scores, not 4.
So we multiply by 5.
Careful: not 74 × 4 ✗
2 Total so far
4 scores with a mean of 70 add up to 70 times 4.
That is 280.
total so far = 70 × 4 = 280
3 What is missing
The total must go from 280 up to 370.
The missing part is 370 minus 280.
That is 90.
next test = 370 − 280 = 90
4 Check
Let's check: 280 plus 90 is 370.
And 370 divided by 5 is 74, the mean we wanted.
So it is right!
280 + 90 = 370, 370 ÷ 5 = 74
Let's look back.
First: total needed.
Then: total so far.
Then: what is missing.
Last: check.
Answer
next test = 370 − 280 = 90