In this problem, we explore the effect on the standard deviation of adding the same constant to each data value in a data set. Consider the data set 5, 9, 10, 11, 15.
(a) Use the defining formula, the computation formula, or a calculator to compute s.
(b) Add 5 to each data value to get the new data set 10, 14, 15, 16, 20.
Compute s.
(c) Compare the results of parts (a) and (b). In general, how do you think the standard deviation of a data set changes if the same constant is added to each data value?