Which of the following statements is true?
A) The sum of the deviations from the mean is always zero.
B) The sum of the squared deviations from the mean is always zero.
C) The standard deviation is always smaller than the variance.
D) The distance between the first and third quartiles is twice the distance between the first and second quartiles.
E) None of these is true.

Question

Quizplus · Accepted Answer

The sum of the deviations from the mean is always zero because for every point that is above the mean, there is a corresponding point below the mean with the same distance from the mean. Therefore, when we sum up all deviations, the positives and the negatives cancel each other out and we are left with zero.

Which of the Following Statements Is True