Z-Scores

Z-score

The z-score represents the number of standard deviations a data point is from the mean of its distribution:

$$z = \frac{x - \mu}{\sigma}$$

A positive z-score means the point is above the mean; negative means below. A z-score of zero means exactly at the mean. Z-scores assume your data is normally distributed and are sensitive to outliers (which inflate $sigma$, deflating everything's z-score).

When the assumptions hold, z-scores enable probability statements: a z-score of 2 corresponds to roughly the 97.5th percentile in a standard normal distribution.