Which statement about z-scores is true?

Which statement about z-scores is true?

• A. Converting to z-scores changes the shape of the distribution.
• B. A z-score of -1 is always more than the mean.
• C. Z-scores help locate a score within the distribution.
• D. Z-scores are measured in percent units.

Answer: (C)

Z-scores describe where a score sits relative to the mean, in units of standard deviation. When you convert raw scores to z-scores, you recenter the distribution at zero and rescale by its spread, but you do not change the shape of the distribution. Because of this, z-scores are ideal for comparing positions across different distributions. This is why the statement that z-scores help locate a score within the distribution is true. For example, a score with z = +2 is two standard deviations above the mean, while z = -1 is one standard deviation below the mean. The other ideas don’t fit: standardizing doesn’t alter the distribution's shape, a z-score of -1 is not above the mean, and z-scores are not measured in percent units.

Z-scores describe where a score sits relative to the mean, in units of standard deviation. When you convert raw scores to z-scores, you recenter the distribution at zero and rescale by its spread, but you do not change the shape of the distribution. Because of this, z-scores are ideal for comparing positions across different distributions.

This is why the statement that z-scores help locate a score within the distribution is true. For example, a score with z = +2 is two standard deviations above the mean, while z = -1 is one standard deviation below the mean.

The other ideas don’t fit: standardizing doesn’t alter the distribution's shape, a z-score of -1 is not above the mean, and z-scores are not measured in percent units.