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, 6, 7, 4, 6.   (a) Use the defining formula, the computation formula, or a calculator to compute s. (Round your answer to four decimal places.) s =  (b) Multiply each data value by 8 to obtain the new data set 32, 48, 56, 32, 48. Compute s. (Round your answer to four decimal places.) 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 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.Multiplying each data value by the same constant c results in the standard deviation remaining the same. (d) You recorded the weekly distances you bicycled in miles and computed the standard deviation to be s = 2.5 miles. Your friend wants to know the standard deviation in kilometers. Do you need to redo all the calculations? YesNo     Given 1 mile ≈ 1.6 kilometers, what is the standard deviation in kilometers? (Enter your answer to two decimal places.) s =  km

Glencoe Algebra 1, Student Edition, 9780079039897, 0079039898, 2018
18th Edition
ISBN:9780079039897
Author:Carter
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Chapter10: Statistics
Section10.4: Distributions Of Data
Problem 19PFA
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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, 6, 7, 4, 6.

 
(a) Use the defining formula, the computation formula, or a calculator to compute s. (Round your answer to four decimal places.)
s = 

(b) Multiply each data value by 8 to obtain the new data set 32, 48, 56, 32, 48. Compute s. (Round your answer to four decimal places.)
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 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.Multiplying each data value by the same constant c results in the standard deviation remaining the same.

(d) You recorded the weekly distances you bicycled in miles and computed the standard deviation to be s = 2.5 miles. Your friend wants to know the standard deviation in kilometers. Do you need to redo all the calculations?
YesNo    

Given 1 mile ≈ 1.6 kilometers, what is the standard deviation in kilometers? (Enter your answer to two decimal places.)
s =  km
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