Question

In a particular set of data,if you multiply each data value by 3 and then add 5, what effect will this have on the mean and standard deviation of the data set?

Answer 1

if `Y = a + bX`

then `E(Y) = a + bE(X)`

and `Var(Y) = b^2Var(X)`

Thus if `color(red)(Y = 5 + 3X)`

Then `color(red)( E(Y) = 5 + 3E(X))`

and `color(red)(Var(Y) = 3^2Var(X))`