If a student in the class gets a raw score equal to 53, what would their standard score be?

Question

Say that you have a distribution of exam scores with a mean m = 67 and a standard deviation s = 8.

Answer 1

(53-67)/8 = -1.75
(to get a data set with mean 0 and sd 1)
(i.e. If you did this calculation to all of the marks, then the mean of the whole set of marks would be 0 and the sd would be 1. This is the mathematical definition of 'standardising' a set of data)

You can then adjust this figure according to what mean and sd you want your 'standardised' score to have, if different from 0 and 1.

For example, if you want your standardised data set to have mean 50 and sd 10,
then the score would be (-1.75 x 10) + 50

'Standardise' not 'standardize' because I'm English!

Answer 2

I THINK, but will happily give way to more knowledgeable folk, that from your mean + or - 8, which implies the range from 59 to 75, would capture about 68 per cent of your testing population(34% above and 34% below mean), assuming they are a "normal sample."

53 is below that range, so I would infer that that raw score would imply something less than 16th percentile (somewhere below the 34% below the mean).

Answer 3

SS = (53-67)/8 = - 1.75