Question

The variance of a variable 'x' having 50 observations is 25. If a new variable is defined as u=x+10, the variance of the new variable is

Answer 1

Answer:

If u = a + by, where a and b are constants, then mean of u = a + b x (mean of y) and var(u) = var(a+by) = b^2 x var(y). [ Can you prove this? If not, get back to me through comment box. I may help you.]

Accordingly, if var(x) = 10, var(50+ 5x) = 25 x var(x) = 250. So, standard deviation = square root of variance = sqrt(250) = 5 x sqrt(10)