Choose the mean
Find 4 numbers which have a mean of 7, a median of 8 and a mode of 9.
Age
11 to 14
Challenge level
Problem
Find 4 numbers which have a mean of 7, a median of 8 and a mode of 9.
This problem is adapted from the World Mathematics Championships
Student Solutions
The median and the mean are both smaller than 9, so the other numbers must be smaller than 9.
_ _ 9 9
The median will be halfway between 9 and the next largest number, so if the median is 8, then the next largest number must be 7.
_ 7 9 9
Then 9, 9, 7 and the fourth number must have a mean of 7, so, since there are 4 of them, they must have a total of 7$\times$4 = 28.
So the numbers are:
3 7 9 9