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 16, 11, 11, 12, 6.

(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 2 to obtain the new data set 32, 22, 22, 24, 12. 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 remaining the same.

-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.

(d) You recorded the weekly distances you bicycled in miles and computed the standard deviation to be s = 3.4 miles. Your friend wants to know the standard deviation in kilometers. Do you need to redo all the calculations?

-Yes or No?

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

Answer 1

a) = (16 + 11 + 11 + 12 + 6)/5 = 11.2

s = sqrt(((16 - 11.2)^2 + (11 - 11.2)^2 + (11 - 11.2)^2 + (12 - 11.2)^2 + (6 - 11.2)^2)/4) = 3.6

b) = (32 + 22 + 22 + 24 + 12)/5 = 22.4

s = sqrt(((32 - 22.4)^2 + (22 - 22.4)^2 + (22 - 22.4)^2 + (24 - 22.4)^2 + (12 - 22.4)^2)/4) = 7.1

c) Option - a) Multiplying each data value by the same constant results in the standard deviation being |c| times as large.

d) No, we do not need to redo all the calculations.

s = 3.4 * 1.6 = 5.44 km