Calculate without technology and show your work. (a) The following data represents inches of rain in San Diego over the last 10 years. Calculate the mean, standard deviation, and coefficient of variation. x: 1069 11 17 8 10 19 11 9 (b) Prove mathematically, that when data is re-scaled, i.e. zi= kxi, where k is a constant, then the mean of the re-scaled data is, = kx, the standard deviation is oz - kox, and the coefficient of variation remains the same. (c) Suppose we want to re-scale the data from inches to feet. Calculate the mean, standard deviation, and coefficient of variation of the re-scaled data set. Note: Show your work for each option a, b and c.