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
14, 6, 9, 7, 17. (a) Use the defining formula, the computation formula, or a calculator to compute 5. (Round your answer to one decimal place.) (b) Multiply each data value by 7 to obtain the new data set 98, 42, 63, 49, 119. Compute 5. (Round your answer to one decimal place.) (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?
A Multiplying each data value by the same constant c results in the standard deviation increasing by c units. (7 Multiplying each data value by the same constant c results in the standard deviation being |c| times smaller.
ﬂ Multiplying each data value by the same constant c results in the standard deviation being |c| times as large. (T, Multiplying each data value by the same constant c results in the standard deviation remaining the same. (d) You recorded the weekly distances you bicycled in miles and computed the standard deviation to be 5 = 2.9 miles. Your friend wants to know
the standard deviation in kilometers. Do you need to redo all the calculations?
(j Yes (7N0 Given 1 mile 5 1.6 kilometers, what is the standard deviation in kilometers? (Enter your answer to two decimal places.) 5: km