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 17, 6, 13, 6, 7.

(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 34, 12, 26, 12, 14. 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 increasing by c units.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 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 = 2.6 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)

n = 5

x	x -	(x - )2
17	7.2	51.84
6	-3.8	14.44
13	3.2	10.24
6	-3.8	14.44
7	-2.8	7.84
Total =		98.8

Standard Deviation (s) is given by:

(b)

n = 5

x	x -	(x - )2
34	14.4	207.36
12	-7.6	57.76
26	6.4	40.96
12	-7.6	57.76
14	-5.6	31.36
Total =		395.2

Standard Deviation (s) is given by:

(c)

Correct option:

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

(d)

(i)

Correct option:

No

(ii)

s = 2.6 X 1.6 = 4.16

So,

Answer is:

s = 4.16 km