Which statistic is the square root of the variance?

Which statistic is the square root of the variance?

• A. Variance
• B. Mode
• C. Mean
• D. Standard deviation

Answer: (D)

The standard deviation is the square root of the variance, and that link is why it’s the go-to measure of dispersion in the same units as the data. Variance computes dispersion by averaging the squared deviations from the mean, so the units become squared (for example, square inches). By taking the square root, those squared units are converted back to the original units, giving a sense of how far typical data points lie from the mean in the same scale you’re working with. This makes interpretation straightforward and intuitive. The mean and mode describe central tendencies or the most frequent value, not how spread out the data are, so they don’t fit the relationship to the square root of dispersion. And while the variance is itself a measure of spread, it’s defined with squared deviations; its square root, not the variance itself, provides the standard deviation.

The standard deviation is the square root of the variance, and that link is why it’s the go-to measure of dispersion in the same units as the data. Variance computes dispersion by averaging the squared deviations from the mean, so the units become squared (for example, square inches). By taking the square root, those squared units are converted back to the original units, giving a sense of how far typical data points lie from the mean in the same scale you’re working with. This makes interpretation straightforward and intuitive.

The mean and mode describe central tendencies or the most frequent value, not how spread out the data are, so they don’t fit the relationship to the square root of dispersion. And while the variance is itself a measure of spread, it’s defined with squared deviations; its square root, not the variance itself, provides the standard deviation.