What is variance?

• A. The average value.
• B. A measure of skewness.
• C. The maximum value.
• D. The square of standard deviation.

Answer: (D)

Variance measures how spread out values are around the mean. It is defined as the average of the squared differences between each data point and the mean, so each deviation contributes positively and larger deviations are weighted more heavily, giving a summary of dispersion. Since the standard deviation is the square root of the variance, the variance is the square of the standard deviation. In other words, variance and standard deviation are two ways of expressing the same spread, just on different scales. For contrast, the mean is about central tendency, skewness describes asymmetry in the distribution, and the maximum value simply reflects the largest observation. For example, with values 1, 2, 3, the mean is 2; the squared deviations are 1, 0, 1; the average of those is 2/3, so the variance is 2/3 and the standard deviation is sqrt(2/3).