The value of the sum of the squared deviations from the mean, i.e., $\Sigma ( x - \bar { x } ) ^ { 2 }$ must always be _____.
A) less than the mean
B) negative
C) either positive or negative, depending on whether the mean is negative or positive
D) at least zero

Question

Quizplus · Accepted Answer

The sum of the squared deviations from the mean, $\Sigma ( x - \bar { x } ) ^ { 2 }$, involves squaring each deviation, which ensures that each term in the sum is non-negative. Therefore, the total sum must be at least zero, as it cannot be negative.

The Value of the Sum of the Squared Deviations from the Mean