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 9, 5, 10, 5, 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 5 to obtain the new data set 45, 25, 50, 25, 35. 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 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.

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 = 3.5 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

a)

given data : 9, 5, 10, 5, 7.

Sample mean :

standard deviation :

b)

Multiply each data value by 5 to obtain the new data set 45, 25, 50, 25, 35.

sample mean

sample standard deviation s :

c)

Compare the results of parts (a) and (b) it is observed that ,

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

D)

No, Bucause using previous result we can directly calculate standard deviation in  kilometers.

1 mile ≈ 1.6 kilometers ,   s = 3.5 miles

To get standard deviation in kilometers multiply by 1.6 to given standard deviation.

So, s = 1.6*3.5 = 5.6 kilometers