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?

1 Answer
Apr 16, 2017

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:

#(X-mu)/sigma = (75-60)/10 = 1.5#

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 #sqrt(16)=4#) is:

#(X-mu)/sigma = (36-30)/4 = 1.5#

Since both scores are the same number of standard deviations from their respective means, their relative positions are the same.