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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Description: 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

MATLAB: An Introduction with Applications

6th Edition

ISBN:9781119256830

Author:Amos Gilat

Publisher:Amos Gilat

Chapter1: Starting With Matlab

Section: Chapter Questions

Problem 1P

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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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