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.

7, 7, 7, 10, 15

(a) Compute the value of s. (Enter your answer to two decimal places.)

s=

(b) Add 5 to each data value to get the new data set 12, 12, 12, 15, 20. Compute s. (Enter your answer to two 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.
• There is no distinct pattern when the same constant is added to each data value in a set.
• 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.