Average score for the remaining people

Question

If 1000 people have an average (mean) score of 3.92, and we know that 450 people had a score of 1, how do we calculate the average score of the remaining 550 people? Can we even? My head says yes but then blocks me to working out the formula to do it.

Thanks

Answer 1

Let's say the average score you want is $A$. That means that the sum of the scores of those $550$ people must be $550A$. But then the total sum of scores is $$550A+450^*1$$ So the average of the entire group is $$3.92=\frac {550A+450}{1000}$$

It follows that $$3920-450=550A\implies A=6.30909...$$

Answer 2

By linear interpolation. We know that 450 people scored 1. if follows that the average of the remaining people must be above 3.92, but by less magnitude than 1 is below. To know how much we simply scale by percentage. (450/550)*(3.92-1)+3.92=6.30909...