Which statistic is the mean of the squared deviations?

Which statistic is the mean of the squared deviations?

• A. Variance
• B. Sum of Squares
• C. Standard Deviation
• D. Range

Answer: (A)

The mean of the squared deviations from the mean is the variance. You compute, for each data point, how far it is from the mean, square that distance to avoid cancellations and to emphasize larger differences, and then average those squared distances. That average quantifies how far observations tend to lie from the center. If you’re working with a population, you divide by the number of observations; for a sample, you divide by one less than that, to make it an unbiased estimator. The standard deviation is the square root of the variance, so it’s not the mean of squared deviations itself but the typical distance in the original units. The sum of squares is just the total of those squared deviations without averaging, and the range is the difference between the maximum and minimum values, which does not involve squaring deviations.

The mean of the squared deviations from the mean is the variance. You compute, for each data point, how far it is from the mean, square that distance to avoid cancellations and to emphasize larger differences, and then average those squared distances. That average quantifies how far observations tend to lie from the center. If you’re working with a population, you divide by the number of observations; for a sample, you divide by one less than that, to make it an unbiased estimator. The standard deviation is the square root of the variance, so it’s not the mean of squared deviations itself but the typical distance in the original units. The sum of squares is just the total of those squared deviations without averaging, and the range is the difference between the maximum and minimum values, which does not involve squaring deviations.