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 score 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
