1.8: Introduction to z Scores

The z score, or standardized score, is the number of standard deviations that a given value is away from the mean. It is one of the commonly used measures of relative standing.

Using the standardization formula, data can be converted into corresponding z scores. The standardization formula for a population and a sample differ in the mean and standard deviation notations.

z scores provide the relative position of a data point. A positive z score means the data point is above the mean and a negative z indicates below the mean. The mean value always has a zero z score.

The z score is also used to compare data measured on different scales, such as comparing a student's height and weight with classmates. Since data are measured on different scales, they are standardized into z scores.

A z score of 1.5 indicates that the student is taller than most of his classmates, while a zscore of minus 0.5 suggests that his weight is close to the class average.