- Calculate and interpret [latex]z[/latex]-scores.
standardized scores ([latex]z[/latex]-score)
A standardized score describes how far a data value is from the mean in terms of the standard deviation. To compute standardized scores, subtract the mean and then divide by the standard deviation.
[latex]\text{standardized score} = z = \frac{\text{data value }-\text{ mean}}{\text{standard deviation}}[/latex]
For example, a standardized score of [latex]-2[/latex] means that the data value is [latex]2[/latex] standard deviations below the mean.
Standardized scores are useful for deciding whether a value is unusual relative to its distribution. They are also useful for comparing values that are on different scales.