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Question

Which of the following are true statements.


A

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

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B

For given n observation x1, x2, ... xn, with mean variance will be

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C

Variance can be zero even if all observations are not equal.

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D

Variance can be a negative quantity if all the observations are negative

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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.


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