###
5.3: *z* Scores and Unusual Values

The *z* score is one of the three measures of relative standing. It describes the location of a value in a dataset relative to the mean. *z* scores are obtained after the standardization of the values in a dataset. The *z *score for the mean is 0.

This score indicates how far a value is from the mean in terms of standard deviation. For example, if a data value has a *z s*core of +1, the researcher can infer that the particular data value is one standard deviation above the mean. If another data value displays a *z *score of -2, one can conclude that the data value is two standard deviations below the mean.

Most values in any distribution have *z *scores ranging from -2 to +2. The values with *z *scores beyond this range are considered unusual or outliers. These values lie far from other data points in a distribution. Outliers can occur due to experimental errors and variations in measurement.

For instance, consider a distribution of student heights in a class. After standardization, it is found that one particular student had a *z *score of +3.3. This means that the student is unusually tall compared to other students in the class.

*This text is adapted from* *Openstax, Introductory Statistics, **6.1 The Standard Normal Distribution*