What is a z-score?

• A. The value of an observation expressed in standard deviation units.
• B. The distance of the observation from the mean in original units.
• C. The probability of observing that value under the distribution.
• D. The median of the distribution.

Answer: (A)

A z-score expresses how far an observation is from the mean in terms of standard deviation units. It’s found by subtracting the mean from the value and dividing by the standard deviation: z = (X − μ) / σ. This standardizes different distributions so scores can be compared on the same scale. A positive z-score means the value is above the mean, a negative one means it’s below, and a z-score of zero indicates the value is exactly at the mean. Because it’s measured in standard deviation units, you can use the standard normal framework to judge how typical or extreme a value is across different datasets. The distance from the mean in original units, X − μ, doesn’t account for variability, so it isn’t the standardized score. The probability of observing that value under the distribution relates to a p-value or density, not the z-score itself. The median is a different measure of central tendency, unrelated to standardizing values by dispersion.