# Z-score

**Z-scores** are a way to translate individual data points into terms of a standard deviation.

###### Z = (X - X_{bar}) / **σ**

- X: individual data point
- X
_{bar}: 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.

#### Related articles

##### Research

- clinical trials
- descriptive studies
- statistics
- concepts
- analyses of variance
- regression
- nonparametric statistics
- bias