The Mean Problem
Can you work out the four unknown numbers from the clues about their means?
Age
11 to 14
Challenge level
Problem
Image
There are four unknown numbers.
The mean of the first two numbers is 4.
The mean of the first three numbers is 9.
The mean of all four numbers is 15.
If one of the four numbers is 2, what are the others?
Getting Started
Student Solutions
If the first two numbers have a mean of 4, then they have to add up to 8.
If the first three numbers have a mean of 9, they have to add up to 27.
Therefore the third number has to be 27 $-$ 8 = 19
The sum of the four numbers has to be 15 $\times$ 4 = 60
Therefore the fourth number had to be 60 $-$ 27 = 33
If one of the numbers is 2, and the sum of the first two numbers is eight, the second number must be 6.So alongside 2, the other three numbers are 6, 19 and 33.