The answer to both questions is yes.
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The mean deviation for any distribution is always 0 and so conveys no information whatsoever. The standard deviation is the square root of the variance. The variance of a set of values is the sum of the probability of each value multiplied by the square of its difference from the mean for the set. A simpler way to calculate the variance is Expected value of squares - Square of Expected value.
You cannot prove it because it is not true.The expected value of the sample variance is the population variance but that is not the same as the two measures being the same.
It means that the variance remains the same across the range of values of the variable.
A non favourable variance Eg: adverse revenue means the company earned less revenue than expected.
the variance