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 4, 11, 11, 11, 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 8, 22, 22, 22, 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 remaining the same.     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 |c| times as large.

(d) You recorded the weekly distances you bicycled in miles and computed the standard deviation to be s = 2.2 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 = km

Answer 1

Solution-A:

create a vector x1.

use sd function in R studio

x1 <- c(4, 11, 11, 11, 7)
round(sd(x1),1)

s=3.2

Solution-B:

x2 <- c(8, 22, 22, 22, 14)
round(sd(x2),1)

s=6.4

R screenhot

(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.

Solution-d:

No,we need not to redo all the calculations

NO

NO

1 mile ≈ 1.6 kilometers,

s = 2.2 miles.

s=2.2*1.6=3.52 kilometres

s =3.52 km

s =3.52 km