how many $\sigma$ (standard deviation) away from the mean from a normal distribution ? $$ z = \frac{x-\mu}{\sigma}$$
usage
comparing 2 distribution for example Juwan took LSAT and MCAT with score: 172 on the LSAT and 37 on the MCAT. summary stats of LSAT and MCAT:
| Exam | mean $\mu$ | std $\sigma$ |
|---|---|---|
| LSAT | 151 | 10 |
| MCAT | 25.1 | 6.4 |
which exam did he do relatively better on? LSAT z-score = $\frac{172 - 151}{10}$ = 2.1 MCAT z-score = $\frac{37 - 25.1}{6.4}$ = 1.86 Juwan did relatively better on LSAT as his score is around 2.1 $\sigma$ away from the mean (higher than 1.86)
References
https://www.khanacademy.org/math/statistics-probability/modeling-distributions-of-data#z-scores