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 set15,4,5,13,4.

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

(b) Multiply each data value by3to obtain the new data set45,12,15,39,12. Computes. (Round your answer to four decimal places.)

(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 constantc?

• A. Multiplying each data value by the same constantcresults in the standard deviation being |c| times as large.
• B. Multiplying each data value by the same constantcresults in the standard deviation increasing bycunits.
• C. Multiplying each data value by the same constantcresults in the standard deviation being |c| times smaller.
• D. Multiplying each data value by the same constantcresults in the standard deviation remaining the same.

(d) You recorded the weekly distances you bicycled in miles and computed the standard deviation to bes=3.4miles. Your friend wants to know the standard deviation in kilometers. Do you need to redo all the calculations?

• Yes
• No

Given 1 mile1.6 kilometers, what is the standard deviation in kilometers? (Enter your answer to two decimal places.)