If an entire population of N = 20 scores is transformed into z-scores,the set of 20 z-scores will have SX = 0.

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Quizplus · Accepted Answer

When transforming a set of scores into z-scores, the mean of the resulting distribution of z-scores will always be 0 (by definition), regardless of the sample size. Therefore, if an entire population of N = 20 scores is transformed into z-scores, the set of 20 z-scores will indeed have SX (i.e., the standard deviation of the z-scores) equal to 0, since this is the only way for the set to have a mean of 0.

If an Entire Population of N = 20 Scores Is