The numerical value of the varianceA) is always larger than the numerical value of the standard deviation.B) is always smaller than the numerical value of the standard deviation.C) is negative if the mean is negative.D) can be larger or smaller than the numerical value of the standard deviation.

Question

The numerical value of the varianceA)  is always larger than the numerical value of the standard deviation.B)  is always smaller than the numerical value of the standard deviation.C)  is negative if the mean is negative.D)  can be larger or smaller than the numerical value of the standard deviation.

Louis Magnien · Accepted Answer

Final Answer : D, Explanation :  The variance is the average of the squared differences between each data point and the mean. The standard deviation is the square root of the variance. Since the variance includes the squared differences, it can be larger than the standard deviation. However, in some cases, the standard deviation may be larger than the variance if the data points are relatively close to the mean. Therefore, D is the best choice. A and B are incorrect because the relationship between the variance and the standard deviation depends on the data distribution. C is incorrect because the variance is always non-negative, regardless of the mean value.

Definitions

Learning Objectives

Learning Objectives

Related questions