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

score 3 · Accepted Answer · answered Nov 02 '15 at 14:31

3

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 $$3920-450=550A\implies A=6.30909...$$

answered Nov 02 '15 at 14:31

lulu

70,402

Thanks lulu, that makes sense. Shows I haven't had to do much maths in a long time. Rather obvious looking at it. – Jon Holland Nov 02 '15 at 14:34
Glad it helped. – lulu Nov 02 '15 at 14:36

score 1 · Answer 2 · answered Nov 02 '15 at 14:36

1

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...

answered Nov 02 '15 at 14:36

Danish

66

thanks Jordan - it is obvious looking at it. :) The brain just refused to go down the right route – Jon Holland Nov 02 '15 at 15:47

Average score for the remaining people

2 Answers2