Which statement correctly describes the standard deviation?

Which statement correctly describes the standard deviation?

• A. It is the sum of squared deviations
• B. It is the square of the variance
• C. It is the mean of the data
• D. It is the square root of the variance

Answer: (D)

The standard deviation measures how spread out the data are around the mean. It is defined as the square root of the variance—the variance being the average of the squared deviations from the mean. Taking the square root brings the measure back to the same units as the data, making it easier to interpret the typical distance from the mean. The sum of squared deviations is part of the variance calculation, but the standard deviation is not simply that sum. The mean describes central location, not spread. Squaring the variance would describe a different quantity with a different interpretation. So the standard deviation is best described as the square root of the variance.

The standard deviation measures how spread out the data are around the mean. It is defined as the square root of the variance—the variance being the average of the squared deviations from the mean. Taking the square root brings the measure back to the same units as the data, making it easier to interpret the typical distance from the mean. The sum of squared deviations is part of the variance calculation, but the standard deviation is not simply that sum. The mean describes central location, not spread. Squaring the variance would describe a different quantity with a different interpretation. So the standard deviation is best described as the square root of the variance.