Finding a missing value from the mean

Difficulty Stretch · Set lbgdbf

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1
The mean of 7 numbers is 20. 6 of them are 15, 2, 15, 38, 19, 21. What is the last one?
2
The mean of 7 numbers is 14. 6 of them are 5, 20, 13, 17, 16, 1. What is the last one?
3
The mean of 7 numbers is 7. 6 of them are 11, 2, 13, 5, 1, 6. What is the last one?
4
The mean of 7 numbers is 9. 6 of them are 16, 4, 18, 2, 7, 7. What is the last one?
5
The mean of 7 numbers is 18. 6 of them are 1, 2, 26, 22, 34, 1. What is the last one?
6
The mean of 7 numbers is 10. 6 of them are 1, 16, 15, 7, 11, 8. What is the last one?
7
The mean of 7 numbers is 10. 6 of them are 12, 11, 15, 12, 8, 5. What is the last one?
8
The mean of 7 numbers is 15. 6 of them are 16, 30, 16, 15, 11, 2. What is the last one?
9
The mean of 7 numbers is 20. 6 of them are 12, 33, 22, 26, 5, 6. What is the last one?
10
The mean of 7 numbers is 14. 6 of them are 27, 28, 9, 8, 7, 2. What is the last one?
11
The mean of 7 numbers is 14. 6 of them are 24, 16, 1, 16, 6, 8. What is the last one?
12
The mean of 7 numbers is 7. 6 of them are 6, 7, 11, 9, 4, 4. What is the last one?
13
The mean of 7 numbers is 12. 6 of them are 1, 2, 21, 1, 12, 20. What is the last one?
14
The mean of 7 numbers is 9. 6 of them are 8, 18, 7, 3, 2, 2. What is the last one?
15
The mean of 7 numbers is 17. 6 of them are 25, 18, 12, 14, 2, 6. What is the last one?
16
The mean of 7 numbers is 12. 6 of them are 9, 13, 3, 19, 11, 12. What is the last one?
17
The mean of 7 numbers is 16. 6 of them are 3, 26, 26, 1, 18, 3. What is the last one?
18
The mean of 7 numbers is 7. 6 of them are 4, 14, 5, 6, 2, 8. What is the last one?
19
The mean of 7 numbers is 8. 6 of them are 15, 2, 1, 9, 9, 8. What is the last one?
20
The mean of 7 numbers is 19. 6 of them are 10, 26, 25, 4, 18, 14. What is the last one?

What is in this set

The numbers in this set run from 1 to 40.
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 240 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.