In this problem, we explore the effect on the standard deviation of multiplying each data value in a data set by the same constant. Consider the data set 15, 5, 6, 14, 16.

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

*s* =

(b) Multiply each data value by 7 to obtain the new data set 105, 35, 42, 98, 112. Compute *s*. (Round your answer to four decimal places.)*s* =

(c) Compare the results of parts (a) and (b). In general, how does the standard deviation change if each data value is multiplied by a constant *c*?

– Multiplying each data value by the same constant *c* results in the standard deviation remaining the same.

– Multiplying each data value by the same constant *c* results in the standard deviation increasing by *c* units.

– Multiplying each data value by the same constant *c* results in the standard deviation being |*c*| times smaller.

– Multiplying each data value by the same constant *c* results in the standard deviation being |*c*| times as large.

Given 1 mile ≈ 1.6 kilometers, what is the standard deviation in kilometers? (Enter your answer to two decimal places.)*s* = km

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.

12, 4, 10, 4, 16

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

(b) Add 5 to each data value to get the new data set 17, 9, 15, 9, 21. 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?

- 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.

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