at alll 70% 4:48 PM
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 6, 7, 4, 7, 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 6 to obtain the
new data set 36, 42, 24, 42, 42. 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 smaller.
Multiplying each data value by the same constant c results in the standard deviation being jof 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 re
viation remaining the same.
(d) You recorded the weekly distances you
bicycled in miles and computed the standard
deviation to be s = 3.3 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=
3.36
* km