A. z-Scores

In the previous Lesson, you saw that the area between two data values represented the amount of data (expressed as a decimal or percent) that is expected to fall between those two values. You probably also noticed that the distances the values were from the mean were measured in terms of the number of standard deviations from the mean. The number of standard deviations a data value is from the mean is called a z-score.

A normal distribution with a mean of 0 and a standard deviation of 1 is called the standard normal distribution. This distribution is useful because it shows z-scores very clearly. A z-score of 0 corresponds to the mean, a negative z-score corresponds to a data value that lies below the mean and a positive z-score corresponds to a data value that lies above the mean.

Example 1

  1. Determine the z-score for a data value of

    a. 18 if µ = 20 and s = 2.

    18 is one standard deviation below the mean of 20, so 18 has a z-score of −1.


    b. 39 if µ = 27 and s = 4.

    39 is 3 standard deviations above the mean of 27, so 39 has a z-score of 3.