Question

Which of the following are true statements.

• A. Variance gives a better picture of dispersion or scatter compared to mean deviation
• B. For given n observation x₁, x₂, ... x_n, with mean variance will be ${\sum }_{i=1}^n$ ${(x_i-\overline{x})}^2$
• C. Variance can be zero even if all observations are not equal.
• D. Variance can be a negative quantity if all the observations are negative

Answer 1

The correct option is A

Variance gives a better picture of dispersion or scatter compared to mean deviation

Option A: As we take the square of deviations the greater deviations would be contributing more compared to the smaller deviations giving us a better picture than just adding all the deviations.
Option B: For given n observations x₁, x₂, ....x_n with mean variance about mean would be
${\sum }_{i=1}^n$$\frac{{(x_i-\overline{x})}^2}{n}$
Option C: Variance is sum of squares of deviations. The only way it can be 0 is if all deviations are 0 which implies are observations are equal.

Option D: Variance can never be negative as it is the sum of squares. The least it can get is 0 and only in the case where all observations are equal.