Which has a better relative position: a score of 75 on stats test with a mean of 60 and a standard deviation of 10 or a score of 36 on an accounting test with a mean of 30 and a variance of 16?
They have the same relative position.
You can think of the position of a score as "how many standard deviations the score is from the mean."
A score of X=75 from a distribution with mean 60 and s.d. 10 has a position of:
So this score is 1.5 s.d.'s above the mean.
Similarly, a score of X=36 from a distribution with mean 30 and variance 16 (and thus s.d. of
Since both scores are the same number of standard deviations from their respective means, their relative positions are the same.