Which statistic is the square root of the sample variance?

Which statistic is the square root of the sample variance?

• A. Population variance
• B. Sample value
• C. Property value
• D. Standard deviation

Answer: (D)

The measure of spread that matches the data in its original units is the standard deviation. The sample variance s^2 captures how far sample values deviate from the sample mean, but it does so using squared deviations. Taking the square root brings those deviations back to the same units as the data, giving the sample standard deviation s. This statistic describes, on average, how far individual sample observations lie from the mean. The other options don’t describe dispersion in the sample: the population variance pertains to the entire population, not the sample; a single sample value is just one data point; and a property value isn’t a standard measure of spread.

The measure of spread that matches the data in its original units is the standard deviation. The sample variance s^2 captures how far sample values deviate from the sample mean, but it does so using squared deviations. Taking the square root brings those deviations back to the same units as the data, giving the sample standard deviation s. This statistic describes, on average, how far individual sample observations lie from the mean.

The other options don’t describe dispersion in the sample: the population variance pertains to the entire population, not the sample; a single sample value is just one data point; and a property value isn’t a standard measure of spread.