Question

In this problem, we explore the effect on the standard deviation of multiplying each data value...

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

Homework Answers

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

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