Z scores

Z scores are a way of standardizing scores across normal distributions.

$$Z = \frac{(observation-mean)}{SD}$$

$$Z = \frac{(observation -mean)}{\sqrt{\frac{\sum_{i=1}^{n}(x_i-\bar{x})^2}{n-1}}}$$

We could use them, for example, to compare an ACT and SAT score, both of which have nearly normal distributions.