Question

During a cold winter, the temperature stayed below zero for ten days (ranging from -20 to -5). The variance of the temperature of the ten day period

a. is negative since all the numbers are negative
b. must be at least zero
c. can not be computed since all the numbers are negative
d. can be either negative or positive

Answer 1

Variance measures how far a set of numbers are spread out from their average value. Since it involves squaring the differences from the mean, the variance of temperatures, even if they are negative, must be at least zero because squares of real numbers are non-negative.

Step-by-step explanation:

The question addresses the concept of variance in a statistical context. Variance is a measure of the spread between numbers in a data set. It calculates the average of the squared differences from the mean. Now, even though the temperatures are negative because they are below zero, when we compute variance, the squared differences will always result in non-negative values.

Therefore, the correct answer is: the variance must be at least zero. Variance cannot be negative because the squaring process turns negative differences into positive values. The fact that all the numbers are negative does not affect the non-negativity of the variance.