Essentials of Mathematical Probability and StatisticsA First Course For the Mathematically Inclined

Section 5.5 Standard Units

Any distribution variable can be converted to “standard units” using the linear translation \(\displaystyle z = \frac{x-\mu}{\sigma}\text{.}\) In doing so, then values of z will always represent the number of standard deviations x is from the mean and will provide “dimensionless” comparisons.