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 following data set.
13, 9, 17, 15, 3
(a)
Use the defining formula, the computation formula, or a calculator to compute s. (Round your answer to four decimal places.)
s =
(b)
Add 3 to each data value to get the new data set 16, 12, 20, 18, 6. Compute s. (Round your answer to four decimal places.)
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?
Adding the same constant c to each data value results in the standard deviation decreasing by c units.
Adding the same constant c to each data value results in the standard deviation increasing by c units.
Adding the same constant c to each data value results in the standard deviation remaining the same.
There is no distinct pattern when the same constant is added to each data value in a set.