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:
8,
12,
10,
12,
14
(a) Use the defining formula, the computation formula, or a calculator to compute s. (Enter your answer to four decimal places.)
(b) Add 2 to each data value to get the new data set: 10, 14, 12, 14, 16. Compute s. (Enter your answer to four decimal places.)
(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 remaining the same.
- 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 decreasing by c units.
- There is no distinct pattern when the same constant is added to each data value in a set.
