# Find the Average Score Given the Standard Deviation

I think I'm supposed to use $z = (X - \bar X)/S$ but I'm not sure how to apply it properly to this problem.

Kyle got an 8.25 on his previous test while the average score was a 7.2 and the standard deviation was 0.8.

On another test he got a 7.25 and the standard devation was also 0.8. What was the average score for the second test?

I assume it's the same sample size but I'm not sure if that would matter. So attempting to use the equation I listed I tried doing the following:

$$z = \frac{8.25-7.2}{.8} = 1.3125$$

Then using that apply it to the second test (after shifting around the equation to solve for the average):

$$\bar X = -((.8 \times 1.3125)-7.25) = 6.2$$

So my guess is that the average would be 6.2 but I haven't done this is a long time and don't recall if what I did is correct.

• On the assumption that Kyle's performance is always the same number of standard deviation units from the mean, the calculation is correct. The assumption is not necessarily reasonable. But without some assumption of this type, one cannot solve the problem. – André Nicolas May 26 '16 at 23:04
• This is all that was given so I made that assumption as well as there wasn't anything else to go off of. Thanks! – canpan14 May 26 '16 at 23:15