Variance equals?

Variance equals?

• A. The square root of the mean squared deviation.
• B. The sum of squared deviations from the mean.
• C. The mean squared deviation, or the average squared distance from the mean.
• D. The absolute deviation from the mean.

Answer: (C)

Variance is defined as the average of the squared deviations from the mean. In other words, you take each observation, subtract the mean, square those differences, and then average them. This measures how spread out the data are around the mean, with the result in squared units. That’s why the correct description is "the mean squared deviation, or the average squared distance from the mean." Why other descriptions don’t fit: taking the square root of that average would give a root-mean-square deviation, not the variance. Summing the squared deviations gives the total (not averaged) squared distance. Using absolute deviations yields the mean absolute deviation, another dispersion measure. If you’re dealing with a sample rather than a population, variance is still the same idea, but you divide by n–1 instead of n to get an unbiased estimate.

Variance is defined as the average of the squared deviations from the mean. In other words, you take each observation, subtract the mean, square those differences, and then average them. This measures how spread out the data are around the mean, with the result in squared units. That’s why the correct description is "the mean squared deviation, or the average squared distance from the mean."

Why other descriptions don’t fit: taking the square root of that average would give a root-mean-square deviation, not the variance. Summing the squared deviations gives the total (not averaged) squared distance. Using absolute deviations yields the mean absolute deviation, another dispersion measure. If you’re dealing with a sample rather than a population, variance is still the same idea, but you divide by n–1 instead of n to get an unbiased estimate.