Given that `barx` is the mean and `sigma^2` is the variance of n observations `x_1,x_2`,….,`x_n`. Prove that the mean and variance of the observations `ax_1,ax_2`, .., `ax_n`, are `abarx` and `a^2sigma^2` respectively `(a ne 0)`.

If sigma^2 is the variance of n observations x_1,x_2 ,…., x_n ,prove that the variance of n observations ax_1,ax_2 ,…, ax_n is a^2sigma^2 , where a ne 0

Given that bar x is the mean and sigma^2 is the variance of n observations x_1x_2 , ..., x_n . Prove that the mean and variance of the observations a x_1,""""a x_2 , a x_3,""""dot""""dot""""dot"""",""a x_n are a bar x and a^2sigma^2 ,

If the mean of a set of observations x_(1),x_(2), …,x_(n)" is " bar(X) , then the mean of the observations x_(i) +2i , i=1, 2, ..., n is

Mean deviation for n observation x_(1),x_(2),…..x_(n) from their mean bar x is given by

If the mean of n observations x_(1),x_(2),x_(3)...x_(n) is bar(x) then the sum of deviations of observations from mean is

If the mean and S.D. of n observations x_(1),x_(2)......x_(n) are x and ? resp,then the sum of squares of observations is

Let barx be the mean of n observations x_(1),x_(2),……..,x_(n) . If (a-b) is added to each observation, then what is the mean of new set of observations?