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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