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, 5, 10, 9, 4.

(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 3 to obtain the new data set 51, 15, 30, 27, 12. 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? Possible answers are as follows... 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 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 results in the standard deviation being |c| times smaller.

(d) You recorded the weekly distances you bicycled in miles and computed the standard deviation to be s = 2.8 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

26. 1 points BBUnderStal12 3.2.011. 0/100 Submissions Used My Ask You 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, 5, 10, 9, 4. (a) Use the defining formula, the computation formula, or a calculator to compute s. (Round your answer to one decimal place.) (b) Multiply each data value by 3 to obtain the new data set 51, 15, 30, 27, 12: Compute s. (Round your answer to ore decimai place.) (c) Compare the results of parts (a) and (b). In gerneral, how does the standard devlation change if each data value is multiplied by a constant c? Multiplying each data value by the same constant c results in the standard deviatian remaining the same. Multiplying each data value by the same constant c results in the standard deviation being ici times as large. Multiplying each data value by the same constant c results in the standard devlatian increasing by c units. Multiplyin g each data value by the same constant c results in the standard deviation being Icl times smaller. devlation in 2.8 miles. Your friend wants to know the standard cled in miles and computed the standard devlation to be s d) You recorded the weekly distances you bicy kilometers. Do you need to redo all the calculations? Yes No Given 1 mlle 1.6 kilometers, what is the standard deviation in kilometers? (Enter your answer to two decimal places.) krr Need Help? Read ItWatch t

Answer 1

a)

std deviation =5.1

b)

Multiply each data value by 3 ; new std deviation =15.4 ( please try 15.3 if this comes wrong)

c)

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

d)

No

std deviation in kilometers =1.6*2.8=4.48