Is standard deviation expressed in the same units as the data?

• A. Yes, in the same units.
• B. No, in squared units.
• C. No, in different units.
• D. Only for standardized data.

Answer: (A)

Standard deviation expresses dispersion in the same units as the data because it is the square root of variance. Variance uses squared units, so taking the square root brings the measure back to the original units. For example, if heights are measured in centimeters, the standard deviation is in centimeters. The idea of being in squared units would apply to variance, not to standard deviation. It wouldn’t be in different units either. (Note: when data are transformed to z-scores, the resulting standard deviation is 1 and unitless, but that reflects the transformed scale rather than the original data.)