0
$\begingroup$

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?

$\endgroup$
1
  • 1
    $\begingroup$ Is this question from a course or textbook? If so, please add the [self-study] tag & read its wiki. $\endgroup$ – gung - Reinstate Monica Apr 12 '15 at 21:15
1
$\begingroup$

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

$\endgroup$
1
  • $\begingroup$ Thank you very much indeed Dougal. If I can establish either of these variables I will get back to you. $\endgroup$ – Neil Cowling Apr 12 '15 at 21:36

Your Answer

By clicking “Post Your Answer”, you agree to our terms of service, privacy policy and cookie policy

Not the answer you're looking for? Browse other questions tagged or ask your own question.