Z-scores are a way to translate individual data points into terms of a standard deviation.
Z = (X - Xbar) / σ
- X: individual data point
- Xbar: the arithmetic mean
- σ: the standard deviation
The purpose of the Z-score is to allow comparison between values in different normal distributions. Two values from two different data sets may have quite a large absolute difference, but their Z-scores may be similar, meaning that they are at roughly the same distance from the mean in their respective distributions.
For instance, a value of 7.75 in one normal distribution may correspond with a value of 1077 in a different normal distribution if their Z-scores are both the same.
Z-scores are often encountered in DXA bone densitometry.