If x₁, x₂, ……, x_n are n values of a variable X and y₁, y₂, ……., y_n are n values of variable Y such that y_i = ax_i + b, i = 1,2, ……, n, then write Var(Y) in terms of Var(X).

Write the variance of first n natural numbers.

If the sum of the squares of deviations for 10 observations taken from their mean is 2.5, then write the value of standard deviation.

If X and Y are two variates connected by the relation and , then write the expression for the standard deviation of Y.

In a series of 20 observations, 10 observations are each equal t k, and each of the remaining halves is equal to –k. If the standard deviation of the observation is 2, then write the value of k.