How are z-scores calculated?

Z-scores are a statistical measurement that describe a value's relation to the mean of a group of values. Specifically, a z-score indicates how many standard deviations an element is from the mean. The calculation of a z-score involves the following formula:

[ z = \frac{(X - \mu)}{\sigma} ]

where ( X ) is the raw score, ( \mu ) is the mean of the distribution, and ( \sigma ) is the standard deviation.

The correct answer highlights that z-scores are commonly standardized to have a mean of 0 and a standard deviation of 1. This standardization allows for easier comparison of scores from different distributions. When data are standardized in this manner, it makes interpretation straightforward; a z-score of 0 indicates that the data point is exactly at the mean, positive values indicate scores above the mean, and negative values indicate scores below the mean.

While other options present various means and standard deviations, they do not reflect the standard approach used for calculating and interpreting z-scores, which is rooted in a mean of 0 and a standard deviation of 1. Thus, the choice of a mean of 0 and a standard deviation of 1 is essential for achieving