During a cold winter, the temperature stayed below zero for ten days (ranging from -20 to -5). The variance of the temperatures of the ten-day period
A) is negative since all the numbers are negative.
B) must be at least zero.
C) cannot be computed since all the numbers are negative.
D) can be either negative or positive.

Question

Quizplus · Accepted Answer

The variance is a measure of how spread out the numbers are from their mean, and it is defined as the average of the squared deviations from the mean. Since the temperatures were below zero, the mean is also below zero, but that does not affect the variance calculation. The squared deviations will always be positive, regardless of whether the temperature is negative or positive. Therefore, the variance must be at least zero, and the best choice is B.

During a Cold Winter, the Temperature Stayed Below Zero for Ten