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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 17 4 13 8 16 USE SALT 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 119 28 91 56 112 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 being Icl times smaller Multiplying each data value by the same constant c results in the standard deviation being Icl times as large Multiplying each data value by the same constant c results in the standard deviation increasing by c units d You recorded the weekly distances you bicycled in miles and computed the standard deviation to be s 2 6 miles Your friend wants to know the standard deviation in kilometers Do you need to redo all the calculations Yes No Given 1 mile 1 6 kilometers what is the standard deviation in kilometers

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