A *z*-score tells you the distance of the score from the arithmetic mean of a set of scores that are normally distributed.

The *z*-score represents standard deviation units thus, a *z*-score of 1 means it is one standard deviation above the mean of the set of scores. A *z*-score of minus one (-1) means the score is one standard deviation below the mean of the set of scores.

The *z*-scores are often plotted along the *x*-axis of a normal distribution, which is sometimes called the bell curve.

Use lower case italics when reporting *z*-scores in APA style. The upper case *Z* is a different score.

You can calculate a *z*-score by subtracting a raw score from the mean and dividing by the standard deviation of the set of scores.

Example: A raw score on a test = 60. If the mean = 50 and the standard deviation = 10 then (60-50) = 10 and 10 divided by 10 = 1.0. The *z* score is 1.0, it is one standard deviation above the mean.

Most *z*- scores fall between -3.0 and +3.0 but it is possible to have scores beyond - 3or + 3.

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