# 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?

Apr 16, 2017

They have the same relative position.

#### Explanation:

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:

$\frac{X - \mu}{\sigma} = \frac{75 - 60}{10} = 1.5$

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:

$\frac{X - \mu}{\sigma} = \frac{36 - 30}{4} = 1.5$

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