5.2: Introduction to z Scores
A z score (or standardized value) is measured in units of the standard deviation. It tells you how many standard deviations the value x is above (to the right of) or below (to the left of) the mean, μ. Values of x that are larger than the mean have positive z scores, and values of x that are smaller than the mean have negative z scores. If x equals the mean, then x has a zero z score. It is important to note that the mean of the z scores is zero, and the standard deviation is one.
z scores help to find the outliers or unusual values from any data distribution. According to the range rule of thumb, outliers or unusual values have z scores less than -2 or greater than +2.
This text is adapted from Openstax, Introductory Statistics, 6.1 The Standard Normal Distribution