Finding a missing value from the mean

Difficulty Starter · Set fp7g2h

Fill in what you can and press Check. Nothing you type is sent anywhere.

1
The mean of 4 numbers is 14. 3 of them are 1, 8, 12. What is the last one?
2
The mean of 4 numbers is 7. 3 of them are 5, 8, 6. What is the last one?
3
The mean of 4 numbers is 12. 3 of them are 22, 7, 6. What is the last one?
4
The mean of 4 numbers is 13. 3 of them are 18, 15, 3. What is the last one?
5
The mean of 4 numbers is 13. 3 of them are 23, 4, 3. What is the last one?
6
The mean of 4 numbers is 16. 3 of them are 28, 12, 4. What is the last one?
7
The mean of 4 numbers is 8. 3 of them are 4, 5, 10. What is the last one?
8
The mean of 4 numbers is 13. 3 of them are 13, 17, 1. What is the last one?
9
The mean of 4 numbers is 19. 3 of them are 12, 13, 14. What is the last one?
10
The mean of 4 numbers is 14. 3 of them are 13, 8, 1. What is the last one?
11
The mean of 4 numbers is 15. 3 of them are 5, 13, 1. What is the last one?
12
The mean of 4 numbers is 13. 3 of them are 14, 4, 13. What is the last one?
13
The mean of 4 numbers is 11. 3 of them are 18, 7, 5. What is the last one?
14
The mean of 4 numbers is 8. 3 of them are 11, 7, 1. What is the last one?
15
The mean of 4 numbers is 18. 3 of them are 34, 3, 11. What is the last one?
16
The mean of 4 numbers is 13. 3 of them are 1, 4, 17. What is the last one?
17
The mean of 4 numbers is 5. 3 of them are 6, 3, 3. What is the last one?
18
The mean of 4 numbers is 13. 3 of them are 3, 7, 9. What is the last one?
19
The mean of 4 numbers is 7. 3 of them are 7, 8, 1. What is the last one?
20
The mean of 4 numbers is 6. 3 of them are 8, 2, 5. What is the last one?

What is in this set

The numbers in this set run from 1 to 36.
A careful solution takes 3 written steps on average.
The mistake this set invites most often, in 97% of the problems: the mean was written down again; the missing number is the total the mean implies, less what is already there.
Answers are a whole number.

Drawing 240 problems from this page produced 239 different ones, 100% — so a sheet of 20 is a new sheet almost every time.

The same skill, harder or easier

We would put this in front of a grade 7 class. That is our judgement, not a standard, and it is printed here so you can disagree with it. Everything else we put in that year.