Which dispersion measure equals the square of the standard deviation?

Which dispersion measure equals the square of the standard deviation?

• A. Variance
• B. Standard deviation
• C. Range
• D. Variation ratio

Answer: (A)

Variance is the dispersion measure that equals the square of the standard deviation. The standard deviation tells you, on average, how far observations lie from the mean. To obtain the variance, you square those deviations and average them across all data points. Since the standard deviation is defined as the square root of the variance, squaring the standard deviation brings you back to the variance. The other options don’t fit this relationship: the range is simply max minus min, and the variation ratio relates to how concentrated observations are in the modal category for nominal data. For example, with data 2, 4, 6, the mean is 4, deviations are -2, 0, 2, their squares sum to 8, and the average is 8/3, which is the variance; the standard deviation is the square root of that, about 1.63, and squaring it returns 8/3.

Variance is the dispersion measure that equals the square of the standard deviation. The standard deviation tells you, on average, how far observations lie from the mean. To obtain the variance, you square those deviations and average them across all data points. Since the standard deviation is defined as the square root of the variance, squaring the standard deviation brings you back to the variance. The other options don’t fit this relationship: the range is simply max minus min, and the variation ratio relates to how concentrated observations are in the modal category for nominal data. For example, with data 2, 4, 6, the mean is 4, deviations are -2, 0, 2, their squares sum to 8, and the average is 8/3, which is the variance; the standard deviation is the square root of that, about 1.63, and squaring it returns 8/3.