If the mean and standard deviation of a set of data are 60 and 5 respectively, then the values 50 and 70 have $z$-scores which are equal in magnitude, but opposite in sign.

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Quizplus · Accepted Answer

The $z$-score of a value is calculated as $z = \frac{(X - \mu)}{\sigma}$, where $X$ is the value, $\mu$ is the mean, and $\sigma$ is the standard deviation. For $X = 50$, $z = \frac{(50 - 60)}{5} = -2$, and for $X = 70$, $z = \frac{(70 - 60)}{5} = 2$. Thus, the $z$-scores are equal in magnitude but opposite in sign.

If the Mean and Standard Deviation of a Set of Data