Variance is defined as what?

Variance is defined as what?

• A. The square of the standard deviation
• B. The square root of the standard deviation
• C. The average of the absolute deviations
• D. The difference between max and min

Answer: (A)

Variance measures how spread out data are around the mean. It is defined as the average of the squared deviations from the mean, which is exactly why it equals the square of the standard deviation—standard deviation is the square root of variance. This pairing helps explain dispersion with all deviations treated as positive and emphasizes larger gaps more strongly. The other ideas describe different measures: the square root of the standard deviation isn’t a standard way to define dispersion; the average of the absolute deviations is a separate measure called the mean absolute deviation; and the difference between the maximum and minimum is simply the range, a rough spread indicator.

Variance measures how spread out data are around the mean. It is defined as the average of the squared deviations from the mean, which is exactly why it equals the square of the standard deviation—standard deviation is the square root of variance. This pairing helps explain dispersion with all deviations treated as positive and emphasizes larger gaps more strongly. The other ideas describe different measures: the square root of the standard deviation isn’t a standard way to define dispersion; the average of the absolute deviations is a separate measure called the mean absolute deviation; and the difference between the maximum and minimum is simply the range, a rough spread indicator.