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The following data on distilled alcohol content (%) for a

Probability and Statistics for Engineers and the Scientists | 9th Edition | ISBN: 9780321629111 | Authors: Ronald E. Walpole; Raymond H. Myers; Sharon L. Myers; Keying E. Ye ISBN: 9780321629111 32

Solution for problem 56E Chapter 1

Probability and Statistics for Engineers and the Scientists | 9th Edition

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Probability and Statistics for Engineers and the Scientists | 9th Edition | ISBN: 9780321629111 | Authors: Ronald E. Walpole; Raymond H. Myers; Sharon L. Myers; Keying E. Ye

Probability and Statistics for Engineers and the Scientists | 9th Edition

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Problem 56E

The following data on distilled alcohol content (%) for a sample of 35 port wines was extracted from the article “A Method for the Estimation of Alcohol in Fortified Wines Using Hydrometer Baumé and Refractometer Brix” (?Amer. J. Enol. Vitic.,? 006: 486–490). Each value is an average of two duplicate measurements. Use methods from this chapter, including a boxplot that shows outliers, to describe and summarize the data.

Step-by-Step Solution:

Solution : Step 1 The given data is on distilled alcohol content (%) for a sample of 35 port wines.,to find the alcohol content in the wines. It is also given that each value is an average of two duplicate measurements. We have to make a boxplot based on the given data and we have to summarize and interpret the data. Step2 : By arranging the data into ascending order we will get 15.3 16.2 16.35 17.15 17.48 17.73 17.75 17.85 18 18.68 18.82 18.85 19.03 19.07 19.08 19.17 19.2 19.2 19.33 19.37 19.45 19.48 19.5 19.58 19.6 19.62 19.9 19.97 20 20.05 21.22 22.25 22.75 23.25 23.78 From the arrangement it is clear that the median median= 18th observation = 19.20 Smallest value= 15.3 Largest value= 23.78 By using R code we can make a boxplot for the given data. As Boxplot(variable,main=” boxplot”, xlab=”alcohol content”) The alcohol content distribution of this sample of 35 port wines is roughly symmetric except for four high outliers and two low outliers . The median alcohol content is 19.2% and the fourth spread is 1.42%. upper fourth (upper quartile) = median of observation after 19.20 = (19.90 + 19.62)/2 = 19.76 lower fourth( Lower quartile) = median of observations before 19.20 = (18.00 + 18.68)/2 = 18.34. The six outliers were 22.25%,22.75%,23.25% ,23.78%, and in the lower part 15.3% and 16.2%indicating six port wines with unusually high and low alcohol content.

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Chapter 1, Problem 56E is Solved
Textbook: Probability and Statistics for Engineers and the Scientists
Edition: 9
Author: Ronald E. Walpole; Raymond H. Myers; Sharon L. Myers; Keying E. Ye
ISBN: 9780321629111

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The following data on distilled alcohol content (%) for a