Consider a data set consisting of N numbers: {21, 12, ..., Li, ..., IN-1, IN} = X. Write down the definition of the population) variance, and standard deviation. For the data set {10, 15, 20, 25, 30} = X, compute the variance and standard deviation. Next, consider the transformation Y = 32+2X. compute the variance and standard deviation of Y. Now consider transforming the general data set X = {21, 22, ..., Li, ..., IN-1, IN} into another data set Y, according to the following function y = a + Br, where a is any number and is a positive number. How are the variances of X and Y related? How are the standard deviations of X and Y related?