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A back-to-back stem-and-leaf display on two data sets is

Applied Statistics and Probability for Engineers | 6th Edition | ISBN: 9781118539712 | Authors: Douglas C. Montgomery, George C. Runger ISBN: 9781118539712 55

Solution for problem 27E Chapter 6.2

Applied Statistics and Probability for Engineers | 6th Edition

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Applied Statistics and Probability for Engineers | 6th Edition | ISBN: 9781118539712 | Authors: Douglas C. Montgomery, George C. Runger

Applied Statistics and Probability for Engineers | 6th Edition

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Problem 27E

Problem 27E

A back-to-back stem-and-leaf display on two data sets is conducted by hanging the data on both sides of the same stems. Here is a back-to-back stem-and-leaf display for the cloud seeding data in Exercise 6-22 showing the unseeded clouds on the left and the seeded clouds on the right.

How does the back-to-back stem-and-leaf display show the differences in the data set in a way that the dotplot cannot?

6-22 Cloud seeding, a process in which chemicals such as silver iodide and frozen carbon dioxide are introduced by aircraft into clouds to promote rainfall was widely used in the 20th century. Recent research has questioned its effectiveness [Journal of Atmospheric Research (2010, Vol. 97 (2), pp. 513– 525)]. An experiment was performed by randomly assigning 52 clouds to be seeded or not. The amount of rain generated was then measured in acre-feet. Here are the data for the unseeded and seeded clouds:

Unseeded:

81.2 26.1 95.0 41.1 28.6 21.7 11.5 68.5 345.5 321.2 1202.6 1.0 4.9 163.0 372.4 244.3 47.3 87.0 26.3 24.4 830.1 4.9 36.6 147.8 17.3 29.0

Seeded:

274.7 302.8 242.5 255.0 17.5 115.3 31.4 703.4 334.1 1697.8 118.3 198.6 129.6 274.7 119.0 1656.0 7.7 430.0 40.6 92.4 200.7 32.7 4.1 978.0 489.1 2745.6 Find the sample mean, sample standard deviation, and range of rainfall for

(a) All 52 clouds

(b) The unseeded clouds

(c) The seeded clouds

Step-by-Step Solution:

Solution

Step 1 of 1

We have to explain how the back to back stem and leaf display show the the differences in the data set in a way that the dot plot can not

Here the back to back stem and leaf display compares the two data sets unseeded and seeded clouds respectively

Here the same stems are used for each data set .The leaves for 1st data set on one side and the for the 2nd data set on the other side

Back to back stem and leaf display are good way of grouping before analyzing the data

Plots from it are very sophisticated  as compared to dot plots

as we can change the increments in stem and leaf plots but not in the dot plots


Step 2 of 1

Chapter 6.2, Problem 27E is Solved
Textbook: Applied Statistics and Probability for Engineers
Edition: 6
Author: Douglas C. Montgomery, George C. Runger
ISBN: 9781118539712

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A back-to-back stem-and-leaf display on two data sets is