The variance of n observations is `sigma^2`. Show that if each observation is increased by a, then the variance of the new set of observations remains `sigma^2`.

If each observation of the data is increased by 5, then their mean

The variance of 20 observations is 5. If each observation is multiplied by 2, find the new variance of the resulting observations.

If each observation of a data is increased by 3, then what about the new man?

The mean of n observations x_1,x_2,…………..x_n is barx . If (p+q) is added to each observations then prove that the mean of the new set of observations is barx+(p+q) .

If the mean of 8 observations be 15 and 2 be added to each observation, then the mean of new set of observations will be .

The mean of 5 observation is 4.4 and their variance is 8.24 . If three of the observations are 1,2 and 6, find the other two observations

The mean and variance of 7 observations are 8 and 16 respectively. If five observations are 2, 4, 10, 12, 14, find the remaining two observations.

Given that bar x 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 a bar x and a^2 sigma^2 respectively (a ne 0) .