Question

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, 16, 13, 7, 8.

(a) Use the defining formula, the computation formula, or a calculator to compute s. (Round your answer to one decimal place.)
s =

(b) Multiply each data value by 7 to obtain the new data set 98, 112, 91, 49, 56. Compute s. (Round your answer to one decimal place.)
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 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 remaining the same.Multiplying each data value by the same constant c results in the standard deviation being |c| times smaller.

(d) You recorded the weekly distances you bicycled in miles and computed the standard deviation to be s = 2.9 miles. Your friend wants to know the standard deviation in kilometers. Do you need to redo all the calculations?

YesNo    

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

Answer 1