The numerical value of the standard deviation can never be
A)larger than the variance
B)zero
C)negative
D)all of these statements are correct

Question

Quizplus · Accepted Answer

The standard deviation is defined as the square root of the variance. Since the variance cannot be negative, the standard deviation cannot be negative either. It can also never be zero, unless all the data points in the sample are identical. Finally, it is possible for the variance to be zero (if all the data points are identical), but in that case the standard deviation would also be zero. Therefore, the only correct statement is that the numerical value of the standard deviation can never be negative (option C).

The Numerical Value of the Standard Deviation Can Never Be