Instructor Manual: Ellingson and Panorska Probability and Statistics for Engineering and the Sciences, 10e, 2027, 9798214023823; Chapter 1:
Overview and Descriptive Statistics
Instructor Manual
Ellingson and Panorska Probability and Statistics for Engineering and the
Sciences, 10e, 2027, 9798214023823; Chapter 1: Overview and Descriptive Statistics
TABLE OF CONTENTS
Purpose and Perspective of the Chapter......................................................................2
Chapter Objectives........................................................................................................2
What’s New in This Chapter........................................................................................3
Chapter Outline.............................................................................................................3
© 2027 Cengage Learning, Inc. All Rights Reserved. May not be scanned, copied or duplicated, or posted to a publicly 1
accessible website, in whole or in part.
, Instructor Manual: Ellingson and Panorska Probability and Statistics for Engineering and the Sciences, 10e, 2027, 9798214023823; Chapter 1:
Overview and Descriptive Statistics
PURPOSE AND PERSPECTIVE OF THE CHAPTER
The purpose of this chapter is to provide students with the foundational principles for the field of statistics
and set the foundation for material to come in the rest of the text. Many commonly used tabular and
graphical methods and numerical measures that can help students understand and describe the information
found in a data set will be presented.
CHAPTER OBJECTIVES
The following objectives are addressed in this chapter:
1.1 Populations, Samples, and Processes:
Identify the differences between a population and a sample.
Determine whether a population is concrete or hypothetical.
List possible samples from a given population.
Explain the relationships between populations, samples, probability, and inferential statistics.
Determine whether a study is analytical or enumerative.
List possible methods for obtaining samples from a population.
1.2 Pictorial and Tabular Methods in Descriptive Statistics:
Interpret stem-and-leaf plots.
Construct a stem-and-leaf plot for a given dataset.
Interpret dotplots.
Classify quantitative data as discrete or continuous.
Interpret histograms.
Construct histograms for discrete, continuous, and categorical data.
Classify a distribution as unimodal, bimodal, or multimodal.
Classify a distribution as symmetric or nonsymmetric and determine whether a nonsymmetric
unimodal distribution is positively or negatively skewed.
1.3 Measures of Location:
Identify numerical measures for characterizing the location of a dataset.
Calculate the sample mean for a dataset.
Calculate the sample median for a dataset.
Describe the differences between the sample mean and sample median.
Calculate trimmed means for datasets with outliers.
Calculate the sample proportion for categorical data.
1.4 Measures of Variability:
Identify numerical measures for characterizing the amount of variation in a dataset.
Calculate and interpret the variance and standard deviation for a dataset.
Calculate and interpret the range and fourth spread for a dataset.
Construct a boxplot to describe the shape, location, and variability of a dataset.
Identify possible outliers using a boxplot and the five-number summary.
© 2027 Cengage Learning, Inc. All Rights Reserved. May not be scanned, copied or duplicated, or posted to a publicly 2
accessible website, in whole or in part.
, Instructor Manual: Ellingson and Panorska Probability and Statistics for Engineering and the Sciences, 10e, 2027, 9798214023823; Chapter 1:
Overview and Descriptive Statistics
Compare distributions of multiple samples by drawing comparative boxplots.
[return to top]
WHAT’S NEW IN THIS CHAPTER
R code helps students calculate numerical summaries for data and visualize data sets more quickly and
effectively to promote better understanding of how they work together to provide key information about
data.
[return to top]
CHAPTER OUTLINE
The following outline organizes activities (including any existing discussion questions in PowerPoints or
other supplements) and assessments by chapter (and therefore by topic), so that you can see how all the
content relates to the topics covered in the text.
I. Section 1.1: Populations, Sample, and Processes (1.1, PPT Slide 3)
a. Branches of Statistics
i. An investigator who has collected data may wish to summarize and describe
important features of the data simply.
(1) This entails using methods from descriptive statistics.
(2) Some of these methods are graphical in nature.
(a) Histograms
(b) Boxplots
(c) Scatter plots
(3) Other descriptive methods involve calculation of numerical summary
measures.
(a) Means
(b) Standard deviations
(c) Correlation coefficients
ii. Having obtained a sample from a population, an investigator would frequently
like to use sample information to draw some type of conclusion (make an
inference of some sort) about the population.
(1) The sample is a means to an end rather than an end in itself.
(2) Techniques for generalizing from a sample to a population are gathered
within the branch of our discipline called inferential statistics.
b. The Scope of Modern Statistics
i. Modern statistical methodology is employed by investigators in virtually all
disciplines.
(1) Molecular biology (analysis of microarray data and prediction of a
protein's biological function)
(2) Ecology (describing quantitatively how individuals in various animal and
plant populations are spatially distributed)
© 2027 Cengage Learning, Inc. All Rights Reserved. May not be scanned, copied or duplicated, or posted to a publicly 3
accessible website, in whole or in part.
, Instructor Manual: Ellingson and Panorska Probability and Statistics for Engineering and the Sciences, 10e, 2027, 9798214023823; Chapter 1:
Overview and Descriptive Statistics
(3) Medical imaging (modeling the variation in appearance or brain waves of
the portion of a brain affected by a neurological condition)
(4) Materials engineering (studying properties of various treatments to slow
down corrosion)
(5) Marketing (developing market surveys and strategies for marketing new
products)
(6) Public health (identifying sources of diseases and ways to treat them)
(7) Civil engineering (assessing the effects of stress on structural elements
and the impacts of traffic flows on communities)
ii. As you progress through the book, you’ll encounter a wide spectrum of scenarios
in the examples and exercises that illustrate the application of techniques from
probability and statistics.
(1) Many of these scenarios involve data or other material extracted from
articles in engineering and science journals.
(2) The methods presented herein have become established and trusted tools
in the arsenal of those who work with data.
(3) Statisticians continue to develop new models for describing randomness
and uncertainty, and new methodology for analyzing data.
c. Enumerative Versus Analytic Studies
i. In an enumerative study, interest is focused on a finite, identifiable, unchanging
collection of individuals or objects that make up a population.
(1) A sampling frame—that is, a listing of the individuals or objects to be
sampled—is either available to an investigator or else can be constructed.
(a) The frame might consist of all signatures on a petition to qualify
a certain initiative for the ballot in an upcoming election.
(i) A sample is usually selected to ascertain whether the
number of valid signatures exceeds a specified value.
(b) The frame may contain serial numbers of all furnaces
manufactured by a particular company during a certain time
period.
(i) A sample may be selected to infer something about the
average lifetime of these units.
ii. An analytic study is broadly defined as one that is not enumerative in nature.
(1) Such studies are often carried out with the objective of improving a
future product by taking action on a process of some sort.
(a) Recalibrating equipment
(b) Adjusting the level of some input such as the amount of a
catalyst
(2) Data can often be obtained only on an existing process, one that may
differ in important respects from the future process.
(a) There is thus no sampling frame listing the individuals or objects
of interest.
(i) A sample of five turbines with a new design may be
experimentally manufactured and tested to investigate
efficiency.
© 2027 Cengage Learning, Inc. All Rights Reserved. May not be scanned, copied or duplicated, or posted to a publicly 4
accessible website, in whole or in part.
Overview and Descriptive Statistics
Instructor Manual
Ellingson and Panorska Probability and Statistics for Engineering and the
Sciences, 10e, 2027, 9798214023823; Chapter 1: Overview and Descriptive Statistics
TABLE OF CONTENTS
Purpose and Perspective of the Chapter......................................................................2
Chapter Objectives........................................................................................................2
What’s New in This Chapter........................................................................................3
Chapter Outline.............................................................................................................3
© 2027 Cengage Learning, Inc. All Rights Reserved. May not be scanned, copied or duplicated, or posted to a publicly 1
accessible website, in whole or in part.
, Instructor Manual: Ellingson and Panorska Probability and Statistics for Engineering and the Sciences, 10e, 2027, 9798214023823; Chapter 1:
Overview and Descriptive Statistics
PURPOSE AND PERSPECTIVE OF THE CHAPTER
The purpose of this chapter is to provide students with the foundational principles for the field of statistics
and set the foundation for material to come in the rest of the text. Many commonly used tabular and
graphical methods and numerical measures that can help students understand and describe the information
found in a data set will be presented.
CHAPTER OBJECTIVES
The following objectives are addressed in this chapter:
1.1 Populations, Samples, and Processes:
Identify the differences between a population and a sample.
Determine whether a population is concrete or hypothetical.
List possible samples from a given population.
Explain the relationships between populations, samples, probability, and inferential statistics.
Determine whether a study is analytical or enumerative.
List possible methods for obtaining samples from a population.
1.2 Pictorial and Tabular Methods in Descriptive Statistics:
Interpret stem-and-leaf plots.
Construct a stem-and-leaf plot for a given dataset.
Interpret dotplots.
Classify quantitative data as discrete or continuous.
Interpret histograms.
Construct histograms for discrete, continuous, and categorical data.
Classify a distribution as unimodal, bimodal, or multimodal.
Classify a distribution as symmetric or nonsymmetric and determine whether a nonsymmetric
unimodal distribution is positively or negatively skewed.
1.3 Measures of Location:
Identify numerical measures for characterizing the location of a dataset.
Calculate the sample mean for a dataset.
Calculate the sample median for a dataset.
Describe the differences between the sample mean and sample median.
Calculate trimmed means for datasets with outliers.
Calculate the sample proportion for categorical data.
1.4 Measures of Variability:
Identify numerical measures for characterizing the amount of variation in a dataset.
Calculate and interpret the variance and standard deviation for a dataset.
Calculate and interpret the range and fourth spread for a dataset.
Construct a boxplot to describe the shape, location, and variability of a dataset.
Identify possible outliers using a boxplot and the five-number summary.
© 2027 Cengage Learning, Inc. All Rights Reserved. May not be scanned, copied or duplicated, or posted to a publicly 2
accessible website, in whole or in part.
, Instructor Manual: Ellingson and Panorska Probability and Statistics for Engineering and the Sciences, 10e, 2027, 9798214023823; Chapter 1:
Overview and Descriptive Statistics
Compare distributions of multiple samples by drawing comparative boxplots.
[return to top]
WHAT’S NEW IN THIS CHAPTER
R code helps students calculate numerical summaries for data and visualize data sets more quickly and
effectively to promote better understanding of how they work together to provide key information about
data.
[return to top]
CHAPTER OUTLINE
The following outline organizes activities (including any existing discussion questions in PowerPoints or
other supplements) and assessments by chapter (and therefore by topic), so that you can see how all the
content relates to the topics covered in the text.
I. Section 1.1: Populations, Sample, and Processes (1.1, PPT Slide 3)
a. Branches of Statistics
i. An investigator who has collected data may wish to summarize and describe
important features of the data simply.
(1) This entails using methods from descriptive statistics.
(2) Some of these methods are graphical in nature.
(a) Histograms
(b) Boxplots
(c) Scatter plots
(3) Other descriptive methods involve calculation of numerical summary
measures.
(a) Means
(b) Standard deviations
(c) Correlation coefficients
ii. Having obtained a sample from a population, an investigator would frequently
like to use sample information to draw some type of conclusion (make an
inference of some sort) about the population.
(1) The sample is a means to an end rather than an end in itself.
(2) Techniques for generalizing from a sample to a population are gathered
within the branch of our discipline called inferential statistics.
b. The Scope of Modern Statistics
i. Modern statistical methodology is employed by investigators in virtually all
disciplines.
(1) Molecular biology (analysis of microarray data and prediction of a
protein's biological function)
(2) Ecology (describing quantitatively how individuals in various animal and
plant populations are spatially distributed)
© 2027 Cengage Learning, Inc. All Rights Reserved. May not be scanned, copied or duplicated, or posted to a publicly 3
accessible website, in whole or in part.
, Instructor Manual: Ellingson and Panorska Probability and Statistics for Engineering and the Sciences, 10e, 2027, 9798214023823; Chapter 1:
Overview and Descriptive Statistics
(3) Medical imaging (modeling the variation in appearance or brain waves of
the portion of a brain affected by a neurological condition)
(4) Materials engineering (studying properties of various treatments to slow
down corrosion)
(5) Marketing (developing market surveys and strategies for marketing new
products)
(6) Public health (identifying sources of diseases and ways to treat them)
(7) Civil engineering (assessing the effects of stress on structural elements
and the impacts of traffic flows on communities)
ii. As you progress through the book, you’ll encounter a wide spectrum of scenarios
in the examples and exercises that illustrate the application of techniques from
probability and statistics.
(1) Many of these scenarios involve data or other material extracted from
articles in engineering and science journals.
(2) The methods presented herein have become established and trusted tools
in the arsenal of those who work with data.
(3) Statisticians continue to develop new models for describing randomness
and uncertainty, and new methodology for analyzing data.
c. Enumerative Versus Analytic Studies
i. In an enumerative study, interest is focused on a finite, identifiable, unchanging
collection of individuals or objects that make up a population.
(1) A sampling frame—that is, a listing of the individuals or objects to be
sampled—is either available to an investigator or else can be constructed.
(a) The frame might consist of all signatures on a petition to qualify
a certain initiative for the ballot in an upcoming election.
(i) A sample is usually selected to ascertain whether the
number of valid signatures exceeds a specified value.
(b) The frame may contain serial numbers of all furnaces
manufactured by a particular company during a certain time
period.
(i) A sample may be selected to infer something about the
average lifetime of these units.
ii. An analytic study is broadly defined as one that is not enumerative in nature.
(1) Such studies are often carried out with the objective of improving a
future product by taking action on a process of some sort.
(a) Recalibrating equipment
(b) Adjusting the level of some input such as the amount of a
catalyst
(2) Data can often be obtained only on an existing process, one that may
differ in important respects from the future process.
(a) There is thus no sampling frame listing the individuals or objects
of interest.
(i) A sample of five turbines with a new design may be
experimentally manufactured and tested to investigate
efficiency.
© 2027 Cengage Learning, Inc. All Rights Reserved. May not be scanned, copied or duplicated, or posted to a publicly 4
accessible website, in whole or in part.
