Chapter 3.2, Problem 11P

Critical Thinking: Data Transformation Using Multiplication 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 5, 9, 10, 11, 15.

(a) Use the defining formula, the computation formula, or a calculator to compute s.

(b) Multiply each data value by 5 to obtain the new data set 25, 45, 50, 55, 75. Compute s.

(c) Compare the results of pans (a) and (b). In general, how does the standard deviation change if each data value is multiplied by a constant c?

(d) You recorded the weekly distances you bicycled in miles and computed the standard deviation to be s = 3.1 miles. Your friend wants to know the standard deviation in kilometers. Do you need to redo all the calculations? Given 1 mile = 1.6 kilometers, what is the standard deviation in kilometers?