Which statement correctly describes variance?

Which statement correctly describes variance?

• A. It is the non-squared average deviation
• B. It is the square root of the average squared deviation
• C. It is the average of squared deviations from the mean
• D. It is the maximum distance from the mean

Answer: (C)

Variance is a measure of how spread out the data are around the mean, and it does this by averaging the squared deviations from the mean. Squaring serves two purposes: it makes all deviations positive so they can be added together, and it gives more weight to larger deviations, reflecting greater spread. So the quantity you get by taking the average of those squared differences is the variance. If you take the square root of that quantity, you obtain the standard deviation, which is another common way to express spread in the same units as the data. For example, with data 2, 4, 6, the mean is 4; the deviations are −2, 0, 2; squaring gives 4, 0, 4; averaging gives 8/3 ≈ 2.67, which is the variance (and the square root of this is about 1.63, the standard deviation). The maximum distance from the mean and the mean of the absolute deviations describe other concepts, not variance. Therefore, the statement that variance is the average of squared deviations from the mean is the correct description.

Variance is a measure of how spread out the data are around the mean, and it does this by averaging the squared deviations from the mean. Squaring serves two purposes: it makes all deviations positive so they can be added together, and it gives more weight to larger deviations, reflecting greater spread. So the quantity you get by taking the average of those squared differences is the variance. If you take the square root of that quantity, you obtain the standard deviation, which is another common way to express spread in the same units as the data. For example, with data 2, 4, 6, the mean is 4; the deviations are −2, 0, 2; squaring gives 4, 0, 4; averaging gives 8/3 ≈ 2.67, which is the variance (and the square root of this is about 1.63, the standard deviation). The maximum distance from the mean and the mean of the absolute deviations describe other concepts, not variance. Therefore, the statement that variance is the average of squared deviations from the mean is the correct description.