Z-score

Last revised by Dr Ahmed Bala on 08 Apr 2020

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.

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Cases and figures

  • Figure 1: normal distribution with standard deviations
    Drag here to reorder.