  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, ... xn, with mean  variance will be    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  Solution

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, ....xn with mean variance about mean would be                            ∑ni=1(xi−¯x)2n             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.  Mathematics

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