Variance is defined as the square of which quantity?

Variance is defined as the square of which quantity?

• A. Standard deviation squared
• B. Mean squared
• C. Variance equals the standard deviation
• D. The variance is the square of the mean

Answer: (A)

Variance is a measure of how spread out values are, defined as the average of the squared deviations from the mean. The standard deviation is the positive square root of that spread. Because taking the square root reverses squaring, variance equals the square of the standard deviation. The other statements mix up dispersion with central tendency or misstate the relationship: squaring the mean reflects location, not spread; saying variance equals the standard deviation would imply they are the same, which they are not; and squaring the mean is not how dispersion is defined.

Variance is a measure of how spread out values are, defined as the average of the squared deviations from the mean. The standard deviation is the positive square root of that spread. Because taking the square root reverses squaring, variance equals the square of the standard deviation. The other statements mix up dispersion with central tendency or misstate the relationship: squaring the mean reflects location, not spread; saying variance equals the standard deviation would imply they are the same, which they are not; and squaring the mean is not how dispersion is defined.