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 x 1 , x 2 , . . . x n , with mean variance will be ∑ i = 1 n ( x i − 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

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       x    1    ,      x    2    ,  .  .  .      x    n  , with mean  variance will be       ∑          i      =      1        n    (      x    i    −      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

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The right option is A Variance gives a better picture of dispersion or scatter compared to mean deviationOption A: The higher deviations would be contributing more as we take the square of deviations compared to the lesser deviations, providing us a better picture than simply adding all the deviations.Option B: For given n observations       x    1    ,      x    2    ,  .  .  .  .      x    n   with mean variance about mean would be       ∑          i      =      1        n    (                    x        i            −              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: Since variance is the sum of squares, it can never be negative. The least it can get is 0 and only in the case where all observations are equal.

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