Question

A sample of n = 5 scores has a mean of m = 8. one new score is added to the sample and the new mean is calculated to be m = 9. what is the value of new score?

Answer 1

If the 5 scores have a mean of 8, then their total sum would be 8*5 = 40

Now if one score if added (let's call this score x), there are 6 scores and the mean changes to 9, thus:
(40 + x)/6 = 9
40 + x = 54
x = 14

Answer 2

When = n = 5, m = 8 , total = 5 x 8 = 40

When n = 6, m = 9, total = 6 x 5 = 54

The new number = 54 - 40 = 14


Answer: The new value is 14.