Arithmetic mean

Question

The average of 8 scores is Q. If the average of 3 of the scores is Z, what is the average of the other 5 scores?

Answer 1

8Q gives you the total of all the scores.

3Z  gives you the total of three of the scores

8Q-3Z gives you the sum of the remaining five scores.

The average of the remaining 5 scores will be (8Q-3Z)/5.

Answer 2

This is an application of the weighted arithmetic mean.  Let x = the average of the "other 5 scores":

 

(3/8)Z + (5/8)x = Q

 

(5/8)x = Q - (3/8)Z

 

x = (8/5)Q - (3/5)Z

 

Check:

(3/8)Z + (5/8)x = Q

(3/8)Z + (5/8){(8/5)Q - (3/5)Z} = Q       [Plug in (8/5)Q-(3/5)Z in place of x]

(3/8)Z + Q - (3/8)Z = Q

Q = Q

Check!!