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.

4, 16, 12, 4, 16

(a)Use the defining formula, the computation formula, or a calculator to compute s. (Enter your answer to four decimal places.)

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(b)Add 3 to each data value to get the new data set 7, 19, 15, 7, 19. Compute s. (Enter your answer to four decimal places.)

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(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?

a- Adding the same constant c to each data value results in the standard deviation remaining the same.

b- Adding the same constant c to each data value results in the standard deviation increasing by c units.

c- Adding the same constant c to each data value results in the standard deviation decreasing by c units.

d- There is no distinct pattern when the same constant is added to each data value in a set.