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, 11, 15, 14, 16. (a) Use the defining formula, the computation formula, or a calculator to compute s. (Round your answer to one decimal place.)
s = 1(b) Multiply each data value by 4 to obtain the new data set 68, 44, 60, 56, 64. Compute s. (Round your answer to one decimal place.)
s = 2
(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 being |c| times as large. 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 remaining the same.
(d) You recorded the weekly distances you bicycled in miles and computed the standard deviation to be s = 2.1 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? (Enter your answer to two decimal places.)
s = 5 km