# Deriving the mean from a raw and standardized score

My son has received 52 marks in a test. This has been standardized, using a mean of 100 and a standard deviation of 15, as 102.27

What is the mean mark, and how many marks would he have needed to get to achieve a standardized score of 111?

• Is this question from a course or textbook? If so, please add the [self-study] tag & read its wiki. – gung - Reinstate Monica Apr 12 '15 at 21:15

We know that a score of $52$ is $\frac{2.27}{15}$ of a standard deviation (on the marks) above the mean (of the raw marks). That is, $$52 = \mu + \frac{2.27}{15} \sigma .$$ Unfortunately, this is a linear system with only one equation and two unknowns. You'd need another raw-standardized pair, or separate knowledge of either $\mu$ or $\sigma$, to find either $\mu$ or $\mu + \frac{11}{15}\sigma$.