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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 17, 16, 11, 5, 13. n USE SALT (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 7 to obtain the new data set 119, 112, 77, 35, 91. 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? O Multiplying each data value by the same constant c results in the standard deviation being |c| times smaller. O Multiplying each data value by the same constant c results in the standard deviation being |c| times as large. O Multiplying each data value by the same constant c results in the standard deviation remaining the same. O Multiplying each data value by the same constant c results in the standard deviation increasing by c units. (d) You recorded the weekly distances you bicycled in miles and computed the standard deviation to be s = 3.8 miles. Your friend wants to know the standard deviation in kilometers. Do you need to redo all the calculations? O Yes O No Given 1 mile = 1.6 kilometers, what is the standard deviation in kilometers? (Enter your answer to two decimal places.) S = km

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, 16, 11, 5, 13. n USE SALT (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 7 to obtain the new data set 119, 112, 77, 35, 91. 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? O Multiplying each data value by the same constant c results in the standard deviation being |c| times smaller. O Multiplying each data value by the same constant c results in the standard deviation being |c| times as large. O Multiplying each data value by the same constant c results in the standard deviation remaining the same. O Multiplying each data value by the same constant c results in the standard deviation increasing by c units. (d) You recorded the weekly distances you bicycled in miles and computed the standard deviation to be s = 3.8 miles. Your friend wants to know the standard deviation in kilometers. Do you need to redo all the calculations? O Yes O No Given 1 mile = 1.6 kilometers, what is the standard deviation in kilometers? (Enter your answer to two decimal places.) S = km

MATLAB: An Introduction with Applications
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 17, 16, 11, 5, 13. In USE SALT (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 7 to obtain the new data set 119, 112, 77, 35, 91. 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? O 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. 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. (d) You recorded the weekly distances you bicycled in miles and computed the standard deviation to be s = 3.8 miles. Your friend wants to know the standard deviation in kilometers. Do you need to redo all the calculations? O Yes No Given 1 mile - 1.6 kilometers, what is the standard deviation in kilometers? (Enter your answer to two decimal places.) S = km
Transcribed Image Text: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, 16, 11, 5, 13. In USE SALT (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 7 to obtain the new data set 119, 112, 77, 35, 91. 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? O 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. 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. (d) You recorded the weekly distances you bicycled in miles and computed the standard deviation to be s = 3.8 miles. Your friend wants to know the standard deviation in kilometers. Do you need to redo all the calculations? O Yes No Given 1 mile - 1.6 kilometers, what is the standard deviation in kilometers? (Enter your answer to two decimal places.) S = km
Expert Solution
Step 1

Variance: The variance (σ) is the expectation of the squared deviation of the random variable from its mean (x) value. from the variance, we can conclude that the how far set of numbers is spread out from their average value (Mean). 

The formula for sample Standard deviation:

s = ∑(xi-x)2n-1

Where,

x: Random samples.

x: Sample mean.

n: Sample size.

 

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