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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?

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    $\begingroup$ Is this question from a course or textbook? If so, please add the [self-study] tag & read its wiki. $\endgroup$
    – gung - Reinstate Monica
    Commented Apr 12, 2015 at 21:15

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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 $\mu + \frac{11}{15}\sigma$.

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  • $\begingroup$ Thank you very much indeed Dougal. If I can establish either of these variables I will get back to you. $\endgroup$
    – Neil Cowling
    Commented Apr 12, 2015 at 21:36

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