Tabular and Graphical Presentations
Statistics (exercises)
Aleksandra Pawłowska
April 7, 2020
Glossary (part 1)
Categorical data Labels or names used to identify categories of like items.
Quantitative data Numerical values that indicate how much or how many.
Frequency distribution A tabular summary of data showing the number (fre-
quency) of data values in each of several nonoverlapping classes.
Relative frequency distribution A tabular summary of data showing the fraction
or proportion of data values in each of several nonoverlapping classes.
Percent frequency distribution A tabular summary of data showing the percent-
age of data values in each of several nonoverlapping classes.
Bar chart A graphical device for depicting qualitative data that have been sum-
marized in a frequency, relative frequency, or percent frequency distribution.
Pie chart A graphical device for presenting data summaries based on subdivision
of a circle into sectors that correspond to the relative frequency for each class.
Dot plot A graphical device that summarizes data by the number of dots above
each data value on the horizontal axis.
Aleksandra Pawłowska Tabular and Graphical Presentations
Glossary (part 2)
Histogram A graphical presentation of a frequency distribution, relative frequency
distribution, or percent frequency distribution of quantitative data constructed
by placing the class intervals on the horizontal axis and the frequencies, relative
frequencies, or percent frequencies on the vertical axis.
Cumulative frequency distribution A tabular summary of quantitative data show-
ing the number of data values that are less than or equal to the upper class limit
of each class.
Cumulative relative frequency distribution A tabular summary of quantitative
data showing the fraction or proportion of data values that are less than or equal
to the upper class limit of each class.
Cumulative percent frequency distribution A tabular summary of quantitative
data showing the percentage of data values that are less than or equal to the
upper class limit of each class.
Ogive A graph of a cumulative distribution.
Scatter diagram A graphical presentation of the relationship between two quan-
titative variables. One variable is shown on the horizontal axis and the other
variable is shown on the vertical axis.
Trendline A line that provides an approximation of the relationship between two
variables.
Aleksandra Pawłowska Tabular and Graphical Presentations
Useful tips (part 1)
1 Often the number of classes in a frequency distribution is the same as the
number of categories found in the data. Most statisticians recommend
that classes with smaller frequencies be grouped into an aggregate class
called „other”. Classes with frequencies of 5% or less would most often be
treated in this fashion.
2 The sum of the frequencies in any frequency distribution always equals
the number of observations. The sum of the relative frequencies in any
relative frequency distribution.
This slides introduce the descriptive statistics and its differences with inferential statistics. It also discusses about organizing data and graphing data.
Dear students get fully solved assignments
Send your semester & Specialization name to our mail id :
help.mbaassignments@gmail.com
or
call us at : 08263069601
This slides introduce the descriptive statistics and its differences with inferential statistics. It also discusses about organizing data and graphing data.
Dear students get fully solved assignments
Send your semester & Specialization name to our mail id :
help.mbaassignments@gmail.com
or
call us at : 08263069601
TSTD 6251 Fall 2014SPSS Exercise and Assignment 120 PointsI.docxnanamonkton
TSTD 6251 Fall 2014
SPSS Exercise and Assignment 1
20 Points
In this class, we are going to study descriptive summary statistics and learn how to construct box plot. We are still working with univariate variable for this exercise.
Practice Example:
Admission receipts (in million of dollars) for a recent season are given below for the
n =
30 major league baseball teams:
19.4 26.6 22.9 44.5 24.4 19.0 27.5 19.9 22.8 19.0 16.9 15.2 25.7 19.0 15.5 17.1 15.6 10.6 16.2 15.6 15.4 18.2 15.5 14.2 9.5 9.9
10.7 11.9 26.7 17.5
Require:
a. Compute the mean, variance and standard deviation.
b. Find the sample median, first quartile, and third quartile.
c. Construct a boxplot and interpret the distribution of the data.
d. Discuss the distribution of this set of data by examining kurtosis and skewness
statistics, such as if the distribution is skewed to one side of the distribution, and if the
distribution shows a peaked/skinny curve or a spread out/flat curve.
SPSS Procedures for Computing Summary Statistics
:
Enter the 30 data values in the first column of SPSS
Data View
Tab
Variable View
and name this variable
receipts
Adjust
Decimals
to 3 decimal points
Type
Admission Receipts
($ mn)
in the
Label
column for output viewer
Return to
Data View
and click
A
nalyze
on the menu bar
Click the second menu
D
e
scriptive Statistics
Click
F
requencies …
Move
Admission Receipts
to the
Variable(s)
list by clicking the arrow button
Click
S
tatistics …
button at the top of the dialog box
Now, you can select the descriptive statistics according to what the question requires. For this practice question, it requires central tendency, dispersion, percentile and distribution statistics, so we click all the boxes
except for
P
ercentile(s): and Va
l
ues are group midpoints
.
Click
Continue
to return to the
Frequencies
dialog box
Click
OK
to generate descriptive statistic output which is pasted below:
The first table provides summary statistics and the second table lists frequencies, relative frequencies and cumulative frequencies. The statistics required for solving this problem are highlighted in red.
Statistics
Admission Receipts
N
Valid
30
Missing
0
Mean
18.76333
Std. Error of Mean
1.278590
Median
17.30000
Mode
19.000
Std. Deviation
7.003127
Variance
49.043782
Skewness
1.734
Std. Error of Skewness
.427
Kurtosis
5.160
Std. Error of Kurtosis
.833
Range
35.000
Minimum
9.500
Maximum
44.500
Sum
562.900
Percentiles
10
10.61000
20
14.40000
25
15.35000
30
15.50000
40
15.84000
50
17.30000
60
19.00000
70
19.75000
75
22.82500
80
24.10000
90
26.69000
Admission Receipts
Frequency
Percent
Valid Percent
Cumulative Percent
Valid
9.500
1
3.3
3.3
3.3
9.900
1
3.3
3.3
6.7
10.600
1
3.3
3.3
10.0
10.700
1
3.3
3.3
13.3
11.900
1
3.3
3.3
16.7
14.200
1
3.3
3.3
20.0
15.2.
Take a few moments to research the contextual elements surrounding P.docxperryk1
Take a few moments to research the contextual elements surrounding President Kennedy’s inauguration in 1961 and then critically examine this speech:
“Inaugural Address,” by John F. KennedyLinks to an external site.<
https://urldefense.com/v3/__https://nam01.safelinks.protection.outlook.com/?url=https*3A*2F*2Furldefense.com*2Fv3*2F__https*3A*2F*2Fwww.jfklibrary.org*2FAsset-Viewer*2FBqXIEM9F4024ntFl7SVAjA.aspx__*3B!!ACPuPu0!nRyVaN_vHAO7VokwK2jIluLRE3Rbgg_zTzlKs2LU0jy7JJDLOQzoLng5O9kq8Ar2xqOxu6ASoTCCAw*24&data=02*7C01*7Cs3521396*40students.fscj.edu*7C3dbff0e6302e40df260508d83ebef2dd*7C4258f8b94f8d44abb87f21ab35a63470*7C0*7C0*7C637328337145689500&sdata=rjSnrpQbmBtBYheBjJTh*2B57JapV8a8uLTbS*2BwaXQFps*3D&reserved=0__;JSUlJSUlJSUlJSUlJSUlJSUlJSUlJSU!!ACPuPu0!lzlmNESbzfxzfV0D2RFZGvC0P4JM5SVIIXnoztdLO3J83rBb44XpTJOZcRrT89Wp_du_$
> is made available by the John F. Kennedy Presidential Library and Museum. It is in the public domain.
In a short rhetorical analysis (minimum of four paragraphs in length), please answer all of the questions below. Your work should include an introduction, a body of supporting evidence, and a conclusion. Please take some time to edit your writing for punctuation, usage, and clarity prior to submission.
Questions for Analysis
1. Which important historical and social realities had an impact on this speech in 1961, and how do these contextual elements figure in President Kennedy’s organization of this speech?
2. What is President Kennedy saying about the nature of human progress (science and technology) and the challenges that we must navigate as a global community? Are these challenges unique to 1961, or relative throughout human history?
3. What are the goals of this speech? Isolate at least three aims of President Kennedy’s address, identify his strategy for supporting these goals, and critique their efficacy. Is this an effective speech? Where applicable, please include a quotation or two from the speech.
In a rhetorical analysis (minimum of eight paragraphs in length), please answer all of the questions below. Your work should include an introduction, a body of supporting evidence, and a conclusion. Please take some time to edit your writing for punctuation, usage, and clarity prior to submission.
Questions for Analysis
1. How does Jefferson organize this important document? How many subdivisions does it have, how do they operate, and how does his approach to organization impact the document’s efficacy?
2. Using at least one citation from the text, analyze Jefferson’s approach to style, voice, and tone. How does he create a sense of urgency in moving toward the conclusion of the work?
3. The complexities of this document’s reach are immense. How many different audiences was Jefferson writing to, and what were the needs of those different groups?
4. In terms of the approaches to formal rhetoric that we studied in the first learning module, which does The Declaration of Independence most closely resemble? .
Table of Contents Section 2 Improving Healthcare Quality from.docxperryk1
Table of Contents Section 2: Improving Healthcare Quality from Within Week 4
Week 4 - Assignment: Interpret Performance Measures
Week 4 - Assignment: Interpret
Performance Measures
Instructions
Course Home Content Dropbox Grades Bookshelf ePortfolio Library The Commons Calendar
You have just been appointed as the administrator of a large managed healthcare organization
with multiple facilities in your state, including facilities in city X and Y (table below). A task your
office is charged with is to reimburse facilities based on how they perform on a set of healthcare
quality measures.
Based on the information provided below, what considerations will you make in your decision-
making process? To complete this assignment, prepare a PowerPoint presentation that
highlights whether or not these two facilities (A and B) should be treated equally when
conducting your assessment. If any, what are the implications of treating these facilities as
equals for the purpose of comparison? Also, address the techniques you will use to ensure these
facilities are assessed fairly.
Measures Facility A Facility B
1
Population
characteristics
City X: Mostly people
with high economic
status and those with
more than high school
education
City Y: Mostly people
with low economic
status, minorities,
high school or less
education
2 Population served All ages
Mostly older adults
and people with
disabilities and
chronic conditions
3
Staff to patient
ratio
1:4 1:8
4
Physician and
nurses continuing
education
Required Required
5 Average number of
hours staff work
per week
50 hours 60 hours
Reflect in ePortfolio
Submissions
No submissions yet. Drag and drop to upload your assignment below.
Drop files here, or click below!
Upload Choose Existing
You can upload files up to a maximum of 1 GB.
Length: 8-10 slides (excluding title slide and references slide)
References: Include a minimum of 3-5 peer-reviewed, scholarly resources referenced on a
separate slide at the end of your presentation.
Your assignment should reflect scholarly academic writing, current APA standards,
Record
Week 4
Course Home Content Dropbox Grades Bookshelf More
Interpreting Performance Improvement Measures
and Benchmarking
As a healthcare administrator/manager, it is in your best
interest to help the facility you serve to move in the
direction charted in the National Quality Strategy (Joshi et
al., 2014). Organizations that fail to meet set standards are
known to face sanctions and sometimes required to close
shop. In consideration of this, you will want to ensure that
the facility you manage is adopting a culture of quality that
puts its patients at the center of healthcare delivery. You will
want to do this by making sure that your facility provides
quality patient care, while also keeping the facility’s
bottom-line healthy.
To ensure you are moving in the right direction, you must
measure and monitor key qual.
More Related Content
Similar to Tabular and Graphical PresentationsStatistics (exercises).docx
TSTD 6251 Fall 2014SPSS Exercise and Assignment 120 PointsI.docxnanamonkton
TSTD 6251 Fall 2014
SPSS Exercise and Assignment 1
20 Points
In this class, we are going to study descriptive summary statistics and learn how to construct box plot. We are still working with univariate variable for this exercise.
Practice Example:
Admission receipts (in million of dollars) for a recent season are given below for the
n =
30 major league baseball teams:
19.4 26.6 22.9 44.5 24.4 19.0 27.5 19.9 22.8 19.0 16.9 15.2 25.7 19.0 15.5 17.1 15.6 10.6 16.2 15.6 15.4 18.2 15.5 14.2 9.5 9.9
10.7 11.9 26.7 17.5
Require:
a. Compute the mean, variance and standard deviation.
b. Find the sample median, first quartile, and third quartile.
c. Construct a boxplot and interpret the distribution of the data.
d. Discuss the distribution of this set of data by examining kurtosis and skewness
statistics, such as if the distribution is skewed to one side of the distribution, and if the
distribution shows a peaked/skinny curve or a spread out/flat curve.
SPSS Procedures for Computing Summary Statistics
:
Enter the 30 data values in the first column of SPSS
Data View
Tab
Variable View
and name this variable
receipts
Adjust
Decimals
to 3 decimal points
Type
Admission Receipts
($ mn)
in the
Label
column for output viewer
Return to
Data View
and click
A
nalyze
on the menu bar
Click the second menu
D
e
scriptive Statistics
Click
F
requencies …
Move
Admission Receipts
to the
Variable(s)
list by clicking the arrow button
Click
S
tatistics …
button at the top of the dialog box
Now, you can select the descriptive statistics according to what the question requires. For this practice question, it requires central tendency, dispersion, percentile and distribution statistics, so we click all the boxes
except for
P
ercentile(s): and Va
l
ues are group midpoints
.
Click
Continue
to return to the
Frequencies
dialog box
Click
OK
to generate descriptive statistic output which is pasted below:
The first table provides summary statistics and the second table lists frequencies, relative frequencies and cumulative frequencies. The statistics required for solving this problem are highlighted in red.
Statistics
Admission Receipts
N
Valid
30
Missing
0
Mean
18.76333
Std. Error of Mean
1.278590
Median
17.30000
Mode
19.000
Std. Deviation
7.003127
Variance
49.043782
Skewness
1.734
Std. Error of Skewness
.427
Kurtosis
5.160
Std. Error of Kurtosis
.833
Range
35.000
Minimum
9.500
Maximum
44.500
Sum
562.900
Percentiles
10
10.61000
20
14.40000
25
15.35000
30
15.50000
40
15.84000
50
17.30000
60
19.00000
70
19.75000
75
22.82500
80
24.10000
90
26.69000
Admission Receipts
Frequency
Percent
Valid Percent
Cumulative Percent
Valid
9.500
1
3.3
3.3
3.3
9.900
1
3.3
3.3
6.7
10.600
1
3.3
3.3
10.0
10.700
1
3.3
3.3
13.3
11.900
1
3.3
3.3
16.7
14.200
1
3.3
3.3
20.0
15.2.
Take a few moments to research the contextual elements surrounding P.docxperryk1
Take a few moments to research the contextual elements surrounding President Kennedy’s inauguration in 1961 and then critically examine this speech:
“Inaugural Address,” by John F. KennedyLinks to an external site.<
https://urldefense.com/v3/__https://nam01.safelinks.protection.outlook.com/?url=https*3A*2F*2Furldefense.com*2Fv3*2F__https*3A*2F*2Fwww.jfklibrary.org*2FAsset-Viewer*2FBqXIEM9F4024ntFl7SVAjA.aspx__*3B!!ACPuPu0!nRyVaN_vHAO7VokwK2jIluLRE3Rbgg_zTzlKs2LU0jy7JJDLOQzoLng5O9kq8Ar2xqOxu6ASoTCCAw*24&data=02*7C01*7Cs3521396*40students.fscj.edu*7C3dbff0e6302e40df260508d83ebef2dd*7C4258f8b94f8d44abb87f21ab35a63470*7C0*7C0*7C637328337145689500&sdata=rjSnrpQbmBtBYheBjJTh*2B57JapV8a8uLTbS*2BwaXQFps*3D&reserved=0__;JSUlJSUlJSUlJSUlJSUlJSUlJSUlJSU!!ACPuPu0!lzlmNESbzfxzfV0D2RFZGvC0P4JM5SVIIXnoztdLO3J83rBb44XpTJOZcRrT89Wp_du_$
> is made available by the John F. Kennedy Presidential Library and Museum. It is in the public domain.
In a short rhetorical analysis (minimum of four paragraphs in length), please answer all of the questions below. Your work should include an introduction, a body of supporting evidence, and a conclusion. Please take some time to edit your writing for punctuation, usage, and clarity prior to submission.
Questions for Analysis
1. Which important historical and social realities had an impact on this speech in 1961, and how do these contextual elements figure in President Kennedy’s organization of this speech?
2. What is President Kennedy saying about the nature of human progress (science and technology) and the challenges that we must navigate as a global community? Are these challenges unique to 1961, or relative throughout human history?
3. What are the goals of this speech? Isolate at least three aims of President Kennedy’s address, identify his strategy for supporting these goals, and critique their efficacy. Is this an effective speech? Where applicable, please include a quotation or two from the speech.
In a rhetorical analysis (minimum of eight paragraphs in length), please answer all of the questions below. Your work should include an introduction, a body of supporting evidence, and a conclusion. Please take some time to edit your writing for punctuation, usage, and clarity prior to submission.
Questions for Analysis
1. How does Jefferson organize this important document? How many subdivisions does it have, how do they operate, and how does his approach to organization impact the document’s efficacy?
2. Using at least one citation from the text, analyze Jefferson’s approach to style, voice, and tone. How does he create a sense of urgency in moving toward the conclusion of the work?
3. The complexities of this document’s reach are immense. How many different audiences was Jefferson writing to, and what were the needs of those different groups?
4. In terms of the approaches to formal rhetoric that we studied in the first learning module, which does The Declaration of Independence most closely resemble? .
Table of Contents Section 2 Improving Healthcare Quality from.docxperryk1
Table of Contents Section 2: Improving Healthcare Quality from Within Week 4
Week 4 - Assignment: Interpret Performance Measures
Week 4 - Assignment: Interpret
Performance Measures
Instructions
Course Home Content Dropbox Grades Bookshelf ePortfolio Library The Commons Calendar
You have just been appointed as the administrator of a large managed healthcare organization
with multiple facilities in your state, including facilities in city X and Y (table below). A task your
office is charged with is to reimburse facilities based on how they perform on a set of healthcare
quality measures.
Based on the information provided below, what considerations will you make in your decision-
making process? To complete this assignment, prepare a PowerPoint presentation that
highlights whether or not these two facilities (A and B) should be treated equally when
conducting your assessment. If any, what are the implications of treating these facilities as
equals for the purpose of comparison? Also, address the techniques you will use to ensure these
facilities are assessed fairly.
Measures Facility A Facility B
1
Population
characteristics
City X: Mostly people
with high economic
status and those with
more than high school
education
City Y: Mostly people
with low economic
status, minorities,
high school or less
education
2 Population served All ages
Mostly older adults
and people with
disabilities and
chronic conditions
3
Staff to patient
ratio
1:4 1:8
4
Physician and
nurses continuing
education
Required Required
5 Average number of
hours staff work
per week
50 hours 60 hours
Reflect in ePortfolio
Submissions
No submissions yet. Drag and drop to upload your assignment below.
Drop files here, or click below!
Upload Choose Existing
You can upload files up to a maximum of 1 GB.
Length: 8-10 slides (excluding title slide and references slide)
References: Include a minimum of 3-5 peer-reviewed, scholarly resources referenced on a
separate slide at the end of your presentation.
Your assignment should reflect scholarly academic writing, current APA standards,
Record
Week 4
Course Home Content Dropbox Grades Bookshelf More
Interpreting Performance Improvement Measures
and Benchmarking
As a healthcare administrator/manager, it is in your best
interest to help the facility you serve to move in the
direction charted in the National Quality Strategy (Joshi et
al., 2014). Organizations that fail to meet set standards are
known to face sanctions and sometimes required to close
shop. In consideration of this, you will want to ensure that
the facility you manage is adopting a culture of quality that
puts its patients at the center of healthcare delivery. You will
want to do this by making sure that your facility provides
quality patient care, while also keeping the facility’s
bottom-line healthy.
To ensure you are moving in the right direction, you must
measure and monitor key qual.
Take a company and build a unique solution not currently offered. Bu.docxperryk1
Take a company and build a unique solution not currently offered. Build a
Lean Business Model Canvas.jpg
and present your idea using all 5 frameworks below:
1.Start with Why (by Simon Sinek)
2.Blue Ocean Strategy(by Chan Kim & Renee Mauborgne)
3.Being re"Markable"
4.The Tipping Point (by Malcolm Gladwell)
5.Story Brand (by Donald Miller)
.
Tackling a Crisis Head-onThis week, we will be starting our .docxperryk1
Tackling a Crisis Head-on
This week, we will be starting our work on Assignment 2. Go to
The Wall Street Journal
menu item and find an article about a crisis that occurred at a specific organization in the last year.
Considering the course materials for this week, answer the following:
Describe the crisis faced by the organization.
What communication tactics did the organization use to address its crisis? Refer to Jack and Warren's guidance for dealing with crises.
To what extent, if any, was the organization's crisis communication plan effective?
If you were a senior leader in the organization, would you have responded differently? Why or why not?
This week and next, continue to research this specific crisis so that you can better prepare for Assignment 2.
Post your initial response by Wednesday, midnight of your time zone, and reply to at least 2 of your classmates' initial posts by Sunday, midnight of your time zone.
1st response
The Bank of America Earnings Crisis
In 2020, many businesses experienced notable challenges due to the outbreak of the coronavirus. The Bank of America was no exception based on its reports of firm earnings in 2020. According to Eisen (2021), many large financial organizations in the United States withstood the recession due to COVID-19. However, the author explains that the banks have not been fully protected against the minimal rates brought about by the pandemic. For Bank of America, the outcomes of the COVID-19 outbreak have been felt in many ways, particularly the reduction of earnings by 22%. Additionally, lenders have also experienced significant challenges based on low-interest rates, and Bank of America is among them. Since the financial institution gains earnings on the difference between their lending payments and what they pay to depositors, the bank's interest rates downfall. The earnings crisis also affected the firm's operations in the last quarter of 2020 even though it made considerable profits.
Communication Tactics and Addressing the Crisis
Handling a crisis in organizations presents notable problems for managers and leaders that do not understand the proper ways of solving a crisis. Warren Buffet explains that there are four significant steps a leader can take to address a crisis. First, getting the crisis right and understanding why it happens and what can stop it will help address the crisis. The Bank of America leaders understood that the company needs to introduce measures that will increase the earnings. Secondly, according to Buffet, responding to the crisis fast is also a core step in managing a crisis. The Bank of America did not wait until the last quarter of 2020 to react to the earnings crisis. Rather, they resorted to ensuring the loan demands are stabilized by business consumers and focused more on investment activities (Eisen, 2021). The third and fourth steps based on Warren's advice involve getting the crisis out by dealing with it and getting over with. Th.
take a look at the latest Presidential Order that relates to str.docxperryk1
take a look at the latest Presidential Order that relates to strengthening cybersecurity that relates to critical infrastructure:
https://www.whitehouse.gov/presidential-actions/presidential-executive-order-strengthening-cybersecurity-federal-networks-critical-infrastructure/
Let’s look at a real-world scenario and how the Department of Homeland Security (DHS) plays into it. In the scenario, the United States will be hit by a large-scale, coordinated cyber attack organized by China. These attacks debilitate the functioning of government agencies, parts of the critical infrastructure, and commercial ventures. The IT infrastructure of several agencies are paralyzed, the electric grid in most of the country is shut down, telephone traffic is seriously limited and satellite communications are down (limiting the Department of Defense’s [DOD’s] ability to communicate with commands overseas). International commerce and financial institutions are also severely hit. Please explain how DHS should handle this situation.
please explain how DHS should handle the situation described in the preceding paragraph.
.
Take a look at the sculptures by Giacometti and Moore in your te.docxperryk1
Take a look at the sculptures by Giacometti and Moore in your text. Both pieces are good examples of the relationship between form, content, and subject matter. How do you feel the form of each sculpture expresses the content? What specific characteristics give us clues and communicate meaning?
Select a third work of art from the text and discuss how the form and content relate. Identify at least five visual elements and/or principles of design in your analysis of the third piece.
.
Table of ContentsLOCAL PEOPLE PERCEPTION TOWARDS SUSTAINABLE TOU.docxperryk1
Table of Contents
LOCAL PEOPLE PERCEPTION TOWARDS SUSTAINABLE TOURISM IN DENMARK1
Declaration:2
ACKNOWLEDGEMENT2
CHAPTER:15
Introduction5
1.1 Background of the study6
1.2 Problem Statement:7
1.3 Research Questions:8
1.4 Research Objectives:8
1.5 Thesis Structure8
CHAPTER:29
Literature review9
2.1 Attitudes of local people towards Sustainable tourism9
2.2 Practices of Sustainable tourism10
2.3 Sustainable tourism development.12
2.4 Involvement of people in Sustainability.14
2.5 Theoretical Framework.15
3.1 Introduction17
3.2 Research Design17
3.3 Sampling method18
3.4 Data collection18
3.5 Measurements and Variables18
3.6 Data analysis19
CHAPTER:1Introduction
Sustainable tourism is a form of tourism, which requires a tourist to respect the local culture, environment, preserving cultural heritage, and supporting local economies by purchasing local products which also benefits the people of that country. Sustainable tourism is a form of development, which is Social development, Economic development and Nature protection. According to the World Tourism Organization, Sustainable tourism is “Tourism that takes full account of its current and future economic, social and environmental impacts, addressing the needs of visitors, the industry, the environment, and host communities” UNWTO (2013). Denmark is more concerned about sustainable environment, for instance the Government is aiming at Copenhagen becoming the world’s first carbon-neutral capital by 2025. Government have put high taxation on vehicles, cars so Danes have to think twice before buying or using them. This could be the strategy of the nation. As they are on the way to gain something remarkable, they also have some challenges. The tourism industry has a million of turnover in Danish economy and Danish government puts a high effort in order to make it more sustainable. The big topic could be how the tourist react on it? All the government efforts could be result less if the customer and the business does not act smart. To the Danes, sustainability is a holistic approach that includes renewable energy, water management, waste recycling and green transportation including bicycle culture. Most of the local restaurants use re-usable things during their service also, practices waste deposable for take away.
Tourism is the best way to experience the culture however, damage and waste can occur due to inappropriate behavior of tourists. According to the Denmark statics (2019), every year tourist spends around 128 billion DKK in Denmark. Denmark is very responsible towards environment and most of the hotels are practicing Corporate Social Responsibility (CSR). For example, Scandic Kødbyen is one of the hotels practicing sustainability, first to implement CSR. It plays a significant support in sustainable tourism business, which includes hotel, restaurant and the service provided sectors. Visit Copenhagen states that 70% of hotels hold an official eco-certification and also known as the hap.
Table of Contents Title PageWELCOMETHE VAJRA.docxperryk1
Table of Contents
Title Page
WELCOME
THE VAJRACCHEDIKA PRAJÑAPARAMITA SUTRA
COMMENTARIES
PART ONE - THE DIALECTICS OF
PRAJÑAPARAMITA
Chapter 1 - THE SETTING
Chapter 2 - SUBHUTI’S QUESTION
Chapter 3 - THE FIRST FLASH OF LIGHTNING
Chapter 4 - THE GREATEST GIFT
Chapter 5 - SIGNLESSNESS
PART TWO - THE LANGUAGE OF
NONATTACHMENT
Chapter 6 - A ROSE IS NOT A ROSE
Chapter 7 - ENTERING THE OCEAN OF REALITY
Chapter 8 - NONATTACHMENT
PART THREE - THE ANSWER IS IN
THE QUESTION
Chapter 9 - DWELLING IN PEACE
Chapter 10 - CREATING A FORMLESS PURE
LAND
Chapter 11 - THE SAND IN THE GANGES
Chapter 12 - EVERY LAND IS A HOLY LAND
Chapter 13 - THE DIAMOND THAT CUTS
THROUGH ILLUSION
Chapter 14 - ABIDING IN NON-ABIDING
Chapter 15 - GREAT DETERMINATION
Chapter 16 - THE LAST EPOCH
Chapter 17 - THE ANSWER IS IN THE QUESTION
PART FOUR - MOUNTAINS AND
RIVERS ARE OUR OWN BODY
Chapter 18 - REALITY IS A STEADILY FLOWING
STREAM
Chapter 19 - GREAT HAPPINESS
Chapter 20 - THIRTY-TWO MARKS
Chapter 21 - INSIGHT-LIFE
Chapter 22 - THE SUNFLOWER
Chapter 23 - THE MOON IS JUST THE MOON
Chapter 24 - THE MOST VIRTUOUS ACT
Chapter 25 - ORGANIC LOVE
Chapter 26 - A BASKET FILLED WITH WORDS
Chapter 27 - NOT CUT OFF FROM LIFE
Chapter 28 - VIRTUE AND HAPPINESS
Chapter 29 - NEITHER COMING NOR GOING
Chapter 30 - THE INDESCRIBABLE NATURE OF
ALL THINGS
Chapter 31 - TORTOISE HAIR AND RABBIT
HORNS
Chapter 32 - TEACHING THE DHARMA
CONCLUSION
Copyright Page
WELCOME
WELCOME
BROTHERS AND SISTERS, please read The Diamond
That Cuts through Illusion with a serene mind, a mind
free from views. It’s the basic sutra for the practice of
meditation. Late at night, it’s a pleasure to recite the
Diamond Sutra alone, in complete silence. The sutra is
so deep and wonderful. It has its own language. The
first Western scholars who obtained the text thought it
was talking nonsense. Its language seems mysterious,
but when you look deeply, you can understand.
Don’t rush into the commentaries or you may be
unduly influenced by them. Please read the sutra first.
You may see things that no commentator has seen. You
can read as if you were chanting, using your clear body
and mind to be in touch with the words. Try to
understand the sutra from your own experiences and
your own suffering. It is helpful to ask, “Do these
teachings of the Buddha have anything to do with my
daily life?” Abstract ideas can be beautiful, but if they
have nothing to do with our life, of what use are they?
So please ask, “Do the words have anything to do with
eating a meal, drinking tea, cutting wood, or carrying
water?”
The sutra’s full name is The Diamond That Cuts
through Illusion, Vajracchedika Prajñaparamita in
Sanskrit. Vajracchedika means “the diamond that cuts
through afflictions, ignorance, delusion, or illusion.” In
China and Vietnam, people generally call it the Diamond
Sutra, emphasizing the word “diamond,” but, in fact,
the phrase “cutting through” is the most important.
Prajñaparamita means “per.
Take a few minutes to reflect on this course. How has your think.docxperryk1
Take a few minutes to reflect on this course. How has your thinking (e.g., worldview, knowledge, etc.) been challenged from what you thought prior to taking this course? What are your thoughts now on the significance of correctly diagnosing mental health disorders? What are your thoughts on the treatment of psychopathology? In general, what thoughts do you have about psychopathology and its impact on an individual and the family?
.
Taiwan The Tail That Wags DogsMichael McDevittAsia Po.docxperryk1
Taiwan: The Tail That Wags Dogs
Michael McDevitt
Asia Policy, Number 1, January 2006, pp. 69-93 (Article)
Published by National Bureau of Asian Research
DOI: 10.1353/asp.2006.0011
For additional information about this article
Access provided by Florida International University (9 Sep 2013 16:14 GMT)
http://muse.jhu.edu/journals/asp/summary/v001/1.mcdevitt.html
http://muse.jhu.edu/journals/asp/summary/v001/1.mcdevitt.html
asia p olicy, number 1 (january 2006 ), 69–93
Michael McDevitt (Rear Admiral, retired) is Vice President and Director
of the Center for Naval Analyses at the CNA Corporation. These views are his
own and do not represent the views of the CNA Corporation. He can be reached
at <[email protected]>.
keywords: taiwan; china; united states; japan; foreign relations
Taiwan: The Tail That Wags Dogs
Michael McDevitt
[ 70 ]
execu tive summary
asia p olicy
This essay explores how Taiwan has been able to seize the political initiative
from China, Japan, and the United States.
main argument
Taiwan has attained this leverage due to the interrelationship of four factors:
• Strategic considerations stemming from Taiwan’s geographic position lead
Tokyo and Washington to prefer the status quo, while leading China to
strive for reunification. China’s increasing military power, however, may
suggest a Chinese intention to change the status quo.
• Shared democratic values and the fact that the “democracy issue” has great-
ly prolonged the timetable for reunification give Taipei political influence
in both Washington and Tokyo.
• China’s constant threats of force actually empower Taipei in its relationship
with Washington, and cause the United States to plan for the worst.
• Taiwan is a litmus test of U.S. credibility as an ally, a condition that in turn
creates a perception on the island that U.S. military backing is uncondi-
tional.
policy implications
• Taipei’s high-risk diplomatic approach carries with it the very real possibil-
ity of miscalculation, which could easily lead to great power conflict.
• The United States would benefit from exploring with Beijing ways in which
to demilitarize the issue of Taiwan independence so that the threat of great
power conflict over Taiwan is greatly moderated.
• Tensions may eventually lessen substantially if Beijing can be encouraged to
substitute political deterrence for military deterrence.
• In order to ensure that the U.S. position in the region would survive a
Taipei-provoked conflict should the United States choose not to become
directly involved, Washington can undertake extensive talks with Japan de-
signed to ensure that Japan does not lose confidence in Washington.
organization of the essay
The first four sections of the essay respectively explore the four factors of the
complex U.S.-Taiwan-Japan-China relationship outlined above:
Geostrategic Issues and Considerations . . . . . . . . . . . . . . . . . ..
TABLE 1-1 Milestones of Medicine and Medical Education 1700–2015 ■.docxperryk1
TABLE 1-1 Milestones of Medicine and Medical Education 1700–2015 ■ 1700s: Training and apprenticeship under one physician was common until hospitals were founded in the mid-1700s. In 1765, the first medical school was established at the University of Pennsylvania. ■ 1800s: Medical training was provided through internships with existing physicians who often were poorly trained themselves. In the United States, there were only four medical schools, which graduated only a handful of students. There was no formal tuition with no mandatory testing. ■ 1847: The AMA was established as a membership organization for physicians to protect the interests of its members. It did not become powerful until the 1900s when it organized its physician members by county and state medical societies. The AMA wanted to ensure these local societies were protecting physicians’ financial well-being. It also began to focus on standardizing medical education. ■ 1900s–1930s: The medical profession was represented by general or family practitioners who operated in solo practices. A small percentage of physicians were women. Total expenditures for medical care were less than 4% of the gross domestic product. ■ 1904: The AMA created the Council on Medical Education to establish standards for medical education. ■ 1910: Formal medical education was attributed to Abraham Flexner, who wrote an evaluation of medical schools in the United States and Canada indicating many schools were substandard. The Flexner Report led to standardized admissions testing for students called the Medical College Admission Test (MCAT), which is still used as part of the admissions process today. ■ 1930s: The healthcare industry was dominated by male physicians and hospitals. Relationships between patients and physicians were sacred. Payments for physician care were personal. ■ 1940s–1960s: When group health insurance was offered, the relationship between patient and physician changed because of third-party payers (insurance). In the 1950s, federal grants supported medical school operations and teaching hospitals. In the 1960s, the Regional Medical Programs provided research grants and emphasized service innovation and provider networking. As a result of the Medicare and Medicaid enactment in 1965, the responsibilities of teaching faculty also included clinical responsibilities. ■ 1970s–1990s: Patient care dollars surpassed research dollars as the largest source of medical school funding. During the 1980s, third-party payers reimbursed academic medical centers with no restrictions. In the 1990s with the advent of managed care, reimbursement was restricted. ■ 2014: According to the 2014 Association of American Medical Colleges (AAMAC) annual survey, over 70% of medical schools have or will be implementing policies and programs to encourage primary care specialties for medical school students. TABLE 1-2 Milestones of the Hospital and Healthcare Systems 1820–2015 ■ 1820s: Almshouses or poorhouses, the pr.
Tackling wicked problems A public policy perspective Ple.docxperryk1
Tackling wicked problems : A
public policy perspective
Please note - this is an archived publication.
Commissioner’s foreword
The Australian Public Service (APS) is increasingly being tasked with solving very
complex policy problems. Some of these policy issues are so complex they have
been called ‘wicked’ problems. The term ‘wicked’ in this context is used, not in the
sense of evil, but rather as an issue highly resistant to resolution.
Successfully solving or at least managing these wicked policy problems requires
a reassessment of some of the traditional ways of working and solving problems
in the APS. They challenge our governance structures, our skills base and our
organisational capacity.
It is important, as a first step, that wicked problems be recognised as such.
Successfully tackling wicked problems requires a broad recognition and
understanding, including from governments and Ministers, that there are no quick
fixes and simple solutions.
Tackling wicked problems is an evolving art. They require thinking that is capable
of grasping the big picture, including the interrelationships among the full range of
causal factors underlying them. They often require broader, more collaborative
and innovative approaches. This may result in the occasional failure or need for
policy change or adjustment.
Wicked problems highlight the fundamental importance of the APS building on the
progress that has been made with working across organisational boundaries both
within and outside the APS. The APS needs to continue to focus on effectively
engaging stakeholders and citizens in understanding the relevant issues and in
involving them in identifying possible solutions.
The purpose of this publication is more to stimulate debate around what is
needed for the successful tackling of wicked problems than to provide all the
answers. Such a debate is a necessary precursor to reassessing our current
systems, frameworks and ways of working to ensure they are capable of
responding to the complex issues facing the APS.
I hope that this publication will encourage public service managers to reflect on
these issues, and to look for ways to improve the capacity of the APS to deal
effectively with the complex policy problems confronting us.
Lynelle Briggs
Australian Public Service Commissioner
1. Introduction
Many of the most pressing policy challenges for the APS involve dealing with very
complex problems. These problems share a range of characteristics—they go
beyond the capacity of any one organisation to understand and respond to, and
there is often disagreement about the causes of the problems and the best way to
tackle them. These complex policy problems are sometimes called ‘wicked’
problems.
Usually, part of the solution to wicked problems involves changing the behaviour
of groups of citizens or all citizens. Other key ingredients in solving or at least
managing complex policy problems include successfu.
Tahira Longus Week 2 Discussion PostThe Public Administration.docxperryk1
Tahira Longus Week 2 Discussion Post:
The Public Administrations may entrust the development of collective bargaining activities to bodies created by them, of a strictly technical nature, which will hold their representation in collective bargaining before the corresponding political instructions and without prejudice to the ratification of the agreements reached by the bodies. Government or administrative with competence for it. In addition, public bargaining involves the process of resolving labor-management conflicts. It alsoensuresboth the employee and the employer fair treatment during the negotiation process. The Tables will be validly constituted when, in addition to the representation of the corresponding Administration, and without prejudice to the right of all legitimate trade union organizations to participate in them in proportion to their representatives, such union organizations represent, at least, the absolute majority of the members of the unitary representative bodies in the area in question.
www.ilo.org ›
The Public Administrations may entrust the development of collective bargaining activities to bodies created by them, of a strictly technical nature, which will hold their representation in collective bargaining before the corresponding political instructions and without prejudice to the ratification of the agreements reached by the bodies. Government or administrative with competence for it. In addition, public bargaining involves the process of resolving labor-management conflicts. It also assures both the employee and the employer fair treatment during the negotiation process. The Tables will be validly constituted when, in addition to the representation of the corresponding Administration, and without prejudice to the right of all legitimate trade union organizations to participate in them in proportion to their representatives, such union organizations represent, at least, the absolute majority of the members of the unitary representative bodies in the area in question.
Tara St Laurent Post
.
Table 4-5 CSFs for ERP ImplementationCritical Success Fact.docxperryk1
Table 4-5 CSFs for ERP Implementation
Critical Success Factors
Description
Management Support
Top management advocacy, provision of adequate resources, and commitment to project
Release of Full-Time Subject Matter Experts (SME)
Release full time on to the project of relevant business experts who provide assistance to the project
Empowered Decision Makers
The members of the project team(s) must be empowered to make quick decisions
Deliverable Dates
At planning stage, set realistic milestones and end date
Champion
Advocate for system who is unswerving in promoting the benefits of the new system
Vanilla ERP
Minimal customization and uncomplicated option selection
Smaller Scope
Fewer modules and less functionality implemented, smaller user group, and fewer site(s)
Definition of Scope and Goals
The steering committee determines the scope and objectives of the project in advance and then adheres to it
Balanced Team
Right mix of business analysts, technical experts, and users from within the implementation company and consultants from external companies
Commitment to Change
Perseverance and determination in the face of inevitable problems with implementation
Question 11 pts
The melody of a piece of music is
the harmony
the rhythm
the tune
the chords
Flag this Question
Question 21 pts
Chords are an element of
melody
rhythm
all of the above
harmony
Flag this Question
Question 31 pts
The distance between pitches is called
a space
an interval
a beat
all of the above
Flag this Question
Question 41 pts
Rhythmic organization in pre-Conquest Native American music was
divisive
in duple meter
in triple meter
additive
Flag this Question
Question 51 pts
Pan-Indian music often uses:
all of the above
the Navajo language
vocables
English
Flag this Question
Question 61 pts
Pre-conquest Native American musicians were primarily valued for their expertise in spiritual matters.
True
False
Flag this Question
Question 71 pts
Traditional Native American melodies have a wide melodic range
True
False
Flag this Question
Question 81 pts
Early Native American music features intervals that are:
rhythmically longer
rhythmically shorter
farther apart than what we have in the western system
closer together than what we have in the western system
Flag this Question
Question 91 pts
In the early New England colonies folk songs were:
derived from Irish melodies
derived from English melodies
all of the above
usually sung without accompaniment
Flag this Question
Question 101 pts
Early Anglo - American folks songs were:
often in polymeters
often in triple meter
often in duple meter
often in free meter
Flag this Question
Question 111 pts
Of the following, which is not a form of early Anglo-American folk songs?
ballads
lyric songs
work songs
jubilees
Flag this Question
Question 121 pts
Of the following which instrument was not brought to the Americas by European colonists?
clavichord
recorder
viol
banjo
Flag this Question
Quest.
TableOfContentsTable of contents with hyperlinks for this document.docxperryk1
TableOfContentsTable of contents with hyperlinks for this documentExcluding standard worksheets that come with the original dataSheet namePurposeNotesOnDataPrep!A1Tips and tricks for students in doing data analysis in ExcelSalaryPivotTable!A1Using a histogram of salary to compare other variables in terms of chunks of salaryDescriptiveStatsForFrequency!A1Example of producing descriptive stats for chunks of a numeric variable (grouping, frequency table as 'categories')VariableDescriptiveStatsPHStat!A1Example of descriptive stats produced by PHStat and then edited, items removed that are not neededCorrelations!A1Instructor reference for how all variables are inter-relatedRegressionAge!A1Example of regression output highighting output to pay attention toSPSSRegressionAllEnter!A1Instructor reference - regressing salary on all independent variables to discern stongest, independent predictorsPivotTableCreatePercentPolygon!A1Example of comparing distributions between two categories with different number of cases or different scales, i.e., version of percent polygonAnalysis resultsGender univariate descriptive statisticsGenderAnalysis!A1Gender/Salary; Gender/Job Grade Classification analysis; Gender/other independent variables Salary histogram, distributionCompare gender/salary descriptive statisticsGenderCompareDescriptives!A1Comparison Table gender descriptive statistics in terms of all variables. This might be something worth doing.EthnicitySalaryAnalysis!A1Ethnicity/Salary analysisOptionalEthnicitySalaryAnalysis!A1Optional ethnicity/salary analysis - distribution of ethnicity over chunks of salary, percent polygonEthnicityJGClassAnalysis!A1Ethnicity/Job Grade Classification analysisAgeSalaryAnalysis!A1Age/Salary analysisAgeJobGradeClassAnalysis!A1Age/Job grade classification analysisYearsWorkedSalaryAnalysis!A1Years worked/Salary analysisYears worked/Job grade classification analysisRelationship between endogenous variablesJob grade classification/Salary analysisRelationship between independent variablesPercentPolygonGenderYearsWorked!A1Compare years worked distribution by gender; Example of comparing distributions between two categories with different number of cases or different scales, i.e., version of percent polygon Standard sheets that come with the dataVariable INFO'!A1Information on variablesHuman Resources DATA'!A1DataCross-Class-Table'!A1Summary Table'!A1Histogram!A1% Polygons 2 Groups'!A1Freq. & % Distribution'!A1
Variable INFOTableOfContents!A1The data are a random sample of 120 responses to a survey conducted by the VP of Human Resources at a large company.Source:INFO 501 class at Montclair State UniversityVariablesSalaryin thousands of dollars (K)Age in years YrsWorkin years JGClassjob-grade classification of 1, 3, 5, 7, 9, 11 (lowest skill job to highest skill job)Ethnicity1=Minority0=Not MinorityGender(Male, Female)Named ranges created in this worksheet - use these names to address the data more quickly then manually selecting dat.
Tajfel and Turner (in chapter two of our reader) give us the followi.docxperryk1
Tajfel and Turner (in chapter two of our reader) give us the following definition of Social Identity Theory: "SIT proposes that individuals make sense of their social environment by categorizing themselves and others into groups that can be contrasted with others" (Oksanen et al., 2014). SIT brings order to chaos, you might say, in that individuals define themselves as being different from everyone else.
Considering what we have read about the perpetrators of group violence, how do you suppose that it is that people make the leap from their own social identity to group violence? What social and psychological mechanisms are at work that would go from simple categorization to overt violence?
.
Tableau Homework 3 – Exploring Chart Types with QVC Data .docxperryk1
Tableau Homework 3 – Exploring Chart Types with QVC Data
Getting familiar with the data
You will focus on five dimensions as you start to explore the QVC data:
• order date (Order Dt)
• merchandise department (Merchandise Dept)
• region of the country (Region)
• customer state (Ship To State)
• location of the originating warehouse (Warehouse Zip).
You will use five measures:
• price (Total Line Amt)
• number of orders (Number of Records)
• average order value (AOV to be calculated)
• delivery time ([Days Shipped] to be calculated)
Create two calculated fields:
AOV = SUM([Total Line Amt])/SUM([Number of Records]). On the Data Pane, change the number
format to Currency with 2 decimal places.
Days Shipped = CEILING( [Delivery Confirmation Dt]-[Shipped Dt])
In the next homework, we will explore additional measures to address the QVC analytics challenge more
explicitly. In this homework, the primary goal is to continue to build basic Tableau skills for creating
tables, maps, and charts.
Change the label in the Region dimension for Alaska and Hawaii:
Alaska and Hawaii were not assigned a region in the input data, but we are going to change the Null
label to AK/HI. Depending on the context, we may filter out these states.
To change the label, go to the blue pill for Region and right-click (or click on the down arrow) to get the
menu of actions. Select Aliases…. In the pop-up box, change the alias for Null to AK/HI.
For the rest of the course, you are expected to have complete titles on every worksheet you complete. I
will guide you through this process for the first few worksheets.
Chapter 19 – Highlight Tables
1. Create a text table with merchandise departments for rows and the sum of sales (Total Line Amt) in
the table. Sort in descending order by sales.
Add Region to the Columns Shelf. You should have a crosstab table with 5 columns and 11 rows of data.
Drag the Total Line Amt to the Color marks card. Change the mark type to Square. Note that the East
region has highest sales overall and the ordering within region is similar. Name the sheet Highlight
Table.
Edit the title (double-click on the Highlight Table text and type over <Sheet Name>) to be something like
‘Total sales by region and merchandise department’.
Chapter 22 – Scatter Plot
2. Open a new worksheet. Create a scatter plot of average Days Shipped (Columns Shelf) and average
order value AOV (Row Shelf). Make sure you change the default SUM aggregate function to AVG for
Days Shipped. Drag Merchandise Dept to the Detail marks card. Drag Total Line Amt to the Size marks
card.
At this point, you will want to change the axis settings so they do not include 0. Right-click on each axis,
select Edit Axis, and uncheck the Include zero box.
Add an average line for each measure. This plot highlights that the jewelry department has high average
ship times, though is a small revenue department. .
Ethnobotany and Ethnopharmacology:
Ethnobotany in herbal drug evaluation,
Impact of Ethnobotany in traditional medicine,
New development in herbals,
Bio-prospecting tools for drug discovery,
Role of Ethnopharmacology in drug evaluation,
Reverse Pharmacology.
This is a presentation by Dada Robert in a Your Skill Boost masterclass organised by the Excellence Foundation for South Sudan (EFSS) on Saturday, the 25th and Sunday, the 26th of May 2024.
He discussed the concept of quality improvement, emphasizing its applicability to various aspects of life, including personal, project, and program improvements. He defined quality as doing the right thing at the right time in the right way to achieve the best possible results and discussed the concept of the "gap" between what we know and what we do, and how this gap represents the areas we need to improve. He explained the scientific approach to quality improvement, which involves systematic performance analysis, testing and learning, and implementing change ideas. He also highlighted the importance of client focus and a team approach to quality improvement.
Unit 8 - Information and Communication Technology (Paper I).pdfThiyagu K
This slides describes the basic concepts of ICT, basics of Email, Emerging Technology and Digital Initiatives in Education. This presentations aligns with the UGC Paper I syllabus.
The Roman Empire A Historical Colossus.pdfkaushalkr1407
The Roman Empire, a vast and enduring power, stands as one of history's most remarkable civilizations, leaving an indelible imprint on the world. It emerged from the Roman Republic, transitioning into an imperial powerhouse under the leadership of Augustus Caesar in 27 BCE. This transformation marked the beginning of an era defined by unprecedented territorial expansion, architectural marvels, and profound cultural influence.
The empire's roots lie in the city of Rome, founded, according to legend, by Romulus in 753 BCE. Over centuries, Rome evolved from a small settlement to a formidable republic, characterized by a complex political system with elected officials and checks on power. However, internal strife, class conflicts, and military ambitions paved the way for the end of the Republic. Julius Caesar’s dictatorship and subsequent assassination in 44 BCE created a power vacuum, leading to a civil war. Octavian, later Augustus, emerged victorious, heralding the Roman Empire’s birth.
Under Augustus, the empire experienced the Pax Romana, a 200-year period of relative peace and stability. Augustus reformed the military, established efficient administrative systems, and initiated grand construction projects. The empire's borders expanded, encompassing territories from Britain to Egypt and from Spain to the Euphrates. Roman legions, renowned for their discipline and engineering prowess, secured and maintained these vast territories, building roads, fortifications, and cities that facilitated control and integration.
The Roman Empire’s society was hierarchical, with a rigid class system. At the top were the patricians, wealthy elites who held significant political power. Below them were the plebeians, free citizens with limited political influence, and the vast numbers of slaves who formed the backbone of the economy. The family unit was central, governed by the paterfamilias, the male head who held absolute authority.
Culturally, the Romans were eclectic, absorbing and adapting elements from the civilizations they encountered, particularly the Greeks. Roman art, literature, and philosophy reflected this synthesis, creating a rich cultural tapestry. Latin, the Roman language, became the lingua franca of the Western world, influencing numerous modern languages.
Roman architecture and engineering achievements were monumental. They perfected the arch, vault, and dome, constructing enduring structures like the Colosseum, Pantheon, and aqueducts. These engineering marvels not only showcased Roman ingenuity but also served practical purposes, from public entertainment to water supply.
How to Create Map Views in the Odoo 17 ERPCeline George
The map views are useful for providing a geographical representation of data. They allow users to visualize and analyze the data in a more intuitive manner.
Palestine last event orientationfvgnh .pptxRaedMohamed3
An EFL lesson about the current events in Palestine. It is intended to be for intermediate students who wish to increase their listening skills through a short lesson in power point.
1.4 modern child centered education - mahatma gandhi-2.pptx
Tabular and Graphical PresentationsStatistics (exercises).docx
1. Tabular and Graphical Presentations
Statistics (exercises)
Aleksandra Pawłowska
April 7, 2020
Glossary (part 1)
Categorical data Labels or names used to identify categories of
like items.
Quantitative data Numerical values that indicate how much or
how many.
Frequency distribution A tabular summary of data showing the
number (fre-
quency) of data values in each of several nonoverlapping
classes.
Relative frequency distribution A tabular summary of data
showing the fraction
or proportion of data values in each of several nonoverlapping
classes.
Percent frequency distribution A tabular summary of data
showing the percent-
age of data values in each of several nonoverlapping classes.
Bar chart A graphical device for depicting qualitative data that
have been sum-
marized in a frequency, relative frequency, or percent frequency
distribution.
Pie chart A graphical device for presenting data summaries
based on subdivision
2. of a circle into sectors that correspond to the relative frequency
for each class.
Dot plot A graphical device that summarizes data by the number
of dots above
each data value on the horizontal axis.
Aleksandra Pawłowska Tabular and Graphical Presentations
Glossary (part 2)
Histogram A graphical presentation of a frequency distribution,
relative frequency
distribution, or percent frequency distribution of quantitative
data constructed
by placing the class intervals on the horizontal axis and the
frequencies, relative
frequencies, or percent frequencies on the vertical axis.
Cumulative frequency distribution A tabular summary of
quantitative data show-
ing the number of data values that are less than or equal to the
upper class limit
of each class.
Cumulative relative frequency distribution A tabular summary
of quantitative
data showing the fraction or proportion of data values that are
less than or equal
to the upper class limit of each class.
Cumulative percent frequency distribution A tabular summary
of quantitative
data showing the percentage of data values that are less than or
equal to the
upper class limit of each class.
Ogive A graph of a cumulative distribution.
Scatter diagram A graphical presentation of the relationship
3. between two quan-
titative variables. One variable is shown on the horizontal axis
and the other
variable is shown on the vertical axis.
Trendline A line that provides an approximation of the
relationship between two
variables.
Aleksandra Pawłowska Tabular and Graphical Presentations
Useful tips (part 1)
1 Often the number of classes in a frequency distribution is the
same as the
number of categories found in the data. Most statisticians
recommend
that classes with smaller frequencies be grouped into an
aggregate class
called „other”. Classes with frequencies of 5% or less would
most often be
treated in this fashion.
2 The sum of the frequencies in any frequency distribution
always equals
the number of observations. The sum of the relative frequencies
in any
relative frequency distribution always equals 1.00, and the sum
of the
percentages in a percent frequency distribution always equals
100.
Aleksandra Pawłowska Tabular and Graphical Presentations
4. Useful tips (part 2)
1 A bar chart and a histogram are essentially the same thing;
both are
graphical presentations of the data in a frequency distribution.
A
histogram is just a bar chart with no separation between bars.
For some
discrete quantitative data, a separation between bars is also
appropriate.
2 The last entry in a cumulative frequency distribution always
equals the
total number of observations. The last entry in a cumulative
relative
frequency distribution always equals 1.00 and the last entry in a
cumulative percent frequency distribution always equals 100.
Aleksandra Pawłowska Tabular and Graphical Presentations
Exercises
Task 1
The response to a question has three alternatives: A, B, and C.
A
sample of 120 responses provides 60 A, 24 B, and 36 C. Show
the
frequency and relative frequency distributions.
Aleksandra Pawłowska Tabular and Graphical Presentations
5. Task 1 – solution
frequency distribution relative frequency distribution
A 60 0.5
B 24 0.2
C 36 0.3
Total 120 1.00
Aleksandra Pawłowska Tabular and Graphical Presentations
Task 2
A questionnaire provides 58 Yes, 42 No, and 20 no-opinion
answers.
1 In the construction of a pie chart, how many degrees would be
in the section of the pie showing the Yes answers?
2 How many degrees would be in the section of the pie showing
the No answers?
3 Construct a pie chart.
4 Construct a bar chart.
Aleksandra Pawłowska Tabular and Graphical Presentations
Task 2 – solution
1 In the construction of a pie chart, how many degrees would be
in the
6. section of the pie showing the Yes answers? 174
2 How many degrees would be in the section of the pie showing
the No
answers? 126
3 Construct a pie chart.
4 Construct a bar chart.
Aleksandra Pawłowska Tabular and Graphical Presentations
Task 3
Consider the following frequency distribution.
Construct a cumulative frequency distribution and a cumulative
relative frequency distribution.
Aleksandra Pawłowska Tabular and Graphical Presentations
Task 3 – solution
Aleksandra Pawłowska Tabular and Graphical Presentations
Task 4
A doctor’s office staff studied the waiting times for patients
who ar-
rive at the office with a request for emergency service. The
7. following
data with waiting times in minutes were collected over a one-
month
period.
Use classes of 0–4, 5–9, and so on in the following:
1 Show the frequency distribution.
2 Show the relative frequency distribution.
3 Show the cumulative frequency distribution.
4 Show the cumulative relative frequency distribution.
5 What proportion of patients needing emergency service wait 9
minutes or less?
Aleksandra Pawłowska Tabular and Graphical Presentations
Task 4 – solution
1 Show the frequency distribution. Show the relative frequency
distribution.
Aleksandra Pawłowska Tabular and Graphical Presentations
Task 4 – solution
1 Show the cumulative frequency distribution. Show the
cumulative relative frequency distribution.
2 What proportion of patients needing emergency service wait 9
minutes or less? 0.6
8. Aleksandra Pawłowska Tabular and Graphical Presentations
Task 5
The following 20 observations are for two quantitative
variables, x
and y .
1 Develop a scatter diagram for the relationship between x and
y .
2 What is the relationship, if any, between x and y?
Aleksandra Pawłowska Tabular and Graphical Presentations
Task 5 – solution
A negative relationship between x and y ; y decreases as x
increases.
Aleksandra Pawłowska Tabular and Graphical Presentations
Task 6
A partial relative frequency distribution is given.
1 What is the relative frequency of class D?
2 The total sample size is 200. What is the frequency of class
D?
9. 3 Show the frequency distribution.
4 Show the percent frequency distribution.
Aleksandra Pawłowska Tabular and Graphical Presentations
Task 6 – solution
1 What is the relative frequency of class D? 0.20
2 The total sample size is 200. What is the frequency of class
D? 40
3 Show the frequency distribution. Show the percent frequency
distribution.
Aleksandra Pawłowska Tabular and Graphical Presentations
Task 7
Data for a sample of 55 members of the Baseball Hall of Fame
in
Cooperstown, New York, are shown on next slide. Each
observation
indicates the primary position played by the Hall of Famers:
pitcher
(P), catcher (H), 1st base (1), 2nd base (2), 3rd base (3),
shortstop
(S), left field (L), center field (C), and right field (R).
1 Use frequency and relative frequency distributions to
summarize the data.
10. 2 What position provides the most Hall of Famers?
3 What position provides the fewest Hall of Famers?
4 What outfield position (L, C, or R) provides the most Hall of
Famers?
5 Compare infielders (1, 2, 3, and S) to outfielders (L, C, and
R).
Aleksandra Pawłowska Tabular and Graphical Presentations
Aleksandra Pawłowska Tabular and Graphical Presentations
Task 7 – solution
1 Use frequency and relative frequency distributions to
summarize the data.
2 What position provides the most Hall of Famers? Pitcher
Aleksandra Pawłowska Tabular and Graphical Presentations
Task 7 – solution
1 What position provides the fewest Hall of Famers? 3rd base
2 What outfield position (L, C, or R) provides the most Hall of
Famers? Right field
3 Compare infielders (1, 2, 3, and S) to outfielders (L, C, and
11. R). Infielders 16 to outfielders 18
Aleksandra Pawłowska Tabular and Graphical Presentations
Measures of Variability
Statistics (exercises)
Aleksandra Pawłowska
May 12, 2020
Glossary
Range A measure of variability, defined to be the largest value
minus
the smallest value.
Interquartile range (IQR) A measure of variability, defined to
be the
difference between the third and first quartiles.
Variance A measure of variability based on the squared
deviations
of the data values about the mean.
Standard deviation A measure of variability computed by taking
the
positive square root of the variance.
Coefficient of variation A measure of relative variability
computed
by dividing the standard deviation by the mean and multiplying
by
100.
12. Aleksandra Pawłowska Measures of Variability
Task 1
Consider a sample with data values of 10, 20, 12, 17, and 16.
Com-
pute the range and interquartile range.
Aleksandra Pawłowska Measures of Variability
Task 1 – solution
Consider a sample with data values of 10, 20, 12, 17, and 16.
Com-
pute the range and interquartile range. range = 10, IQR = 5
Aleksandra Pawłowska Measures of Variability
Task 2
Consider a sample with data values of 10, 20, 12, 17, and 16.
Com-
pute the variance and standard deviation.
Aleksandra Pawłowska Measures of Variability
Task 2 – solution
13. Consider a sample with data values of 10, 20, 12, 17, and 16.
Com-
pute the variance and standard deviation. s2 = 16, s = 4
Aleksandra Pawłowska Measures of Variability
Task 3
Consider a sample with data values of 27, 25, 20, 15, 30, 34, 28,
and
25. Compute the range, interquartile range, variance, and
standard
deviation.
Aleksandra Pawłowska Measures of Variability
Task 3 – solution
Consider a sample with data values of 27, 25, 20, 15, 30, 34, 28,
and
25. Compute the range, interquartile range, variance, and
standard
deviation.
range = 19, IQR = 6.5, s2 = 34.57, s = 5.88.
Aleksandra Pawłowska Measures of Variability
Task 4
A bowler’s scores for six games were 182, 168, 184, 190, 170,
14. and
174. Using these data as a sample, compute the following
descriptive
statistics:
1 Range
2 Variance
3 Standard deviation
4 Coefficient of variation
Aleksandra Pawłowska Measures of Variability
Task 4 – solution
1 Range 22
2 Variance 75.2
3 Standard deviation 8.67
4 Coefficient of variation 4.87%
Aleksandra Pawłowska Measures of Variability
Task 5
A home theater in a box is the easiest and cheapest way to
provide surround sound
for a home entertainment center. A sample of prices is shown
here (Consumer
Reports Buying Guide, 2004). The prices are for models with a
DVD player and
for models without a DVD player.
1 Compute the mean price for models with a DVD player and
the mean
15. price for models without a DVD player. What is the additional
price paid
to have a DVD player included in a home theater unit?
2 Compute the range, variance, and standard deviation for the
two samples.
What does this information tell you about the prices for models
with and
without a DVD player?
Aleksandra Pawłowska Measures of Variability
Task 5 – solution
1 Compute the mean price for models with a DVD player and
the mean price for models without a DVD player. What is the
additional price paid to have a DVD player included in a home
theater unit? For models with DVD player x̄ = 410 and for
models without DVD player x̄ = 310.
2 Compute the range, variance, and standard deviation for the
two samples. What does this information tell you about the
prices for models with and without a DVD player? For models
with DVD player range = 200, s2 = 5500, s = 74.16 and for
models without DVD player range = 70, s2 = 800, s = 28.28.
Aleksandra Pawłowska Measures of Variability
Task 6
Car rental rates per day for a sample of seven Eastern U.S.
cities are as follows
(The Wall Street Journal, January 16, 2004).
16. 1 Compute the mean, variance, and standard deviation for the
car rental
rates.
2 A similar sample of seven Western U.S. cities showed a
sample mean car
rental rate of $38 per day. The variance and standard deviation
were 12.3
and 3.5, respectively. Discuss any difference between the car
rental rates
in Eastern and Western U.S. cities.
Aleksandra Pawłowska Measures of Variability
Task 6 – solution
1 Compute the mean, variance, and standard deviation for the
car rental rates. x̄ = 38, s2 = 97, s = 9.85.
2 A similar sample of seven Western U.S. cities showed a
sample
mean car rental rate of $38 per day. The variance and
standard deviation were 12.3 and 3.5, respectively. Discuss
any difference between the car rental rates in Eastern and
Western U.S. cities. Eastern shows more variation.
Aleksandra Pawłowska Measures of Variability
Task 7
The Los Angeles Times regularly reports the air quality index
17. for
various areas of Southern California. A sample of air quality
index
values for Pomona provided the following data: 28, 42, 58, 48,
45,
55, 60, 49, and 50.
1 Compute the range and interquartile range.
2 Compute the sample variance and sample standard deviation.
3 A sample of air quality index readings for Anaheim provided
a
sample mean of 48.5, a sample variance of 136, and a sample
standard deviation of 11.66. What comparisons can you make
between the air quality in Pomona and that in Anaheim on
the basis of these descriptive statistics?
Aleksandra Pawłowska Measures of Variability
Task 7 – solution
1 Compute the range and interquartile range. range = 32, IQR
= 10.
2 Compute the sample variance and sample standard deviation.
s2 = 92.75, s = 9.63.
3 A sample of air quality index readings for Anaheim provided
a
sample mean of 48.5, a sample variance of 136, and a sample
standard deviation of 11.66. What comparisons can you make
between the air quality in Pomona and that in Anaheim on
the basis of these descriptive statistics? Air quality in
Anaheim is, on average, better than in Pomona, but also
18. shows more variation.
Aleksandra Pawłowska Measures of Variability
Task 8
How do grocery costs compare across the country? Using a
market basket
of 10 items including meat, milk, bread, eggs, coffee, potatoes,
cereal, and
orange juice, Where to Retire magazine calculated the cost of
the market basket
in six cities and in six retirement areas across the country
(Where to Retire,
November/December 2003). The data with market basket cost to
the nearest
dollar are as follows:
1 Compute the mean, variance, and standard deviation for the
sample of
cities and the sample of retirement areas.
2 What observations can be made based on the two samples?
Aleksandra Pawłowska Measures of Variability
Task 8 – solution
1 Compute the mean, variance, and standard deviation for the
sample of cities and the sample of retirement areas. For the
sample of cities: x̄ = 33, s2 = 14.4, s = 3.79 and the sample
of retirement areas: x̄ = 32, s2 = 3.6, s = 1.90.
19. 2 What observations can be made based on the two samples?
Aleksandra Pawłowska Measures of Variability
Task 9
Scores turned in by an amateur golfer at the Bonita Fairways
Golf
Course in Bonita Springs, Florida, during 2005 and 2006 are as
follows:
1 Use the mean and standard deviation to evaluate the golfer’s
performance over the two-year period.
2 What is the primary difference in performance between 2005
and 2006? What improvement, if any, can be seen in the 2006
scores?
Aleksandra Pawłowska Measures of Variability
Task 9 – solution
1 Use the mean and standard deviation to evaluate the golfer’s
performance over the two-year period. In 2005:
x̄ = 76, s = 2.07 and in 2006: x̄ = 76, s = 5.26.
2 What is the primary difference in performance between 2005
and 2006? What improvement, if any, can be seen in the 2006
scores? There was, on average, no improvement in the scores
in season 2006 comparing to the season 2005, but the scores
in 2006 show more variation.
20. Aleksandra Pawłowska Measures of Variability
Data and Statistics
Statistics (exercises)
Aleksandra Pawłowska
March 31, 2020
Glossary (part 1)
Statistics The art and science of collecting, analyzing,
presenting, and interpret-
ing data.
Data The facts and figures collected, analyzed, and summarized
for presentation
and interpretation.
Data set All the data collected in a particular study.
Elements The entities on which data are collected.
Variable A characteristic of interest for the elements.
Observation The set of measurements obtained for a particular
element.
Nominal scale The scale of measurement for a variable when the
data are labels
or names used to identify an attribute of an element. Nominal
data may be
nonnumeric or numeric.
Ordinal scale The scale of measurement for a variable if the
data exhibit the
properties of nominal data and the order or rank of the data is
meaningful.
21. Ordinal data may be nonnumeric or numeric.
Interval scale The scale of measurement for a variable if the
data demonstrate
the properties of ordinal data and the interval between values is
expressed in
terms of a fixed unit of measure. Interval data are always
numeric.
Aleksandra Pawłowska Data and Statistics
Glossary (part 2)
Ratio scale The scale of measurement for a variable if the data
demonstrate all
the properties of interval data and the ratio of two values is
meaningful. Ratio
data are always numeric.
Categorical data Labels or names used to identify an attribute of
each element.
Categorical data use either the nominal or ordinal scale of
measurement and may
be nonnumeric or numeric.
Quantitative data Numeric values that indicate how much or
how many of
something. Quantitative data are obtained using either the
interval or ratio scale
of measurement.
Categorical variable A variable with categorical data.
Quantitative variable A variable with quantitative data.
Cross-sectional data Data collected at the same or
approximately the same
point in time.
Time series data Data collected over several time periods.
Descriptive statistics Tabular, graphical, and numerical
summaries of data.
22. Population The set of all elements of interest in a particular
study.
Sample A subset of the population.
Census A survey to collect data on the entire population.
Sample survey A survey to collect data on a sample.
Statistical inference The process of using data obtained from a
sample to make
estimates or test hypotheses about the characteristics of a
population.
Aleksandra Pawłowska Data and Statistics
Useful tips
1 An observation is the set of measurements obtained for each
element in a data set. Hence, the number of observations is
always the same as the number of elements. The number of
measurements obtained for each element equals the number
of variables. Hence, the total number of data items can be
determined by multiplying the number of observations by the
number of variables.
2 Quantitative data may be discrete or continuous. Quantitative
data that measure how many (e.g. number of calls received in
5 minutes) are discrete. Quantitative data that measure how
much (e.g. weight or time) are continuous because no
separation occurs between the possible data values.
Aleksandra Pawłowska Data and Statistics
Exercises
23. Aleksandra Pawłowska Data and Statistics
Task 1
The U.S. Department of Energy provides fuel economy
information
for a variety of motor vehicles. A sample of 10 automobiles is
shown
in Table 1.6 (Fuel Economy website, February 22, 2008). Data
show
the size of the automobile (compact, midsize, or large), the
number
of cylinders in the engine, the city driving miles per gallon, the
highway driving miles per gallon, and the recommended fuel
(diesel,
premium, or regular).
1 How many elements are in this data set?
2 How many variables are in this data set?
3 Which variables are categorical and which variables are
quantitative?
4 What type of measurement scale is used for each of the
variables?
Aleksandra Pawłowska Data and Statistics
Task 2
24. Refer to Table 1.6.
1 What is the average miles per gallon for city driving?
2 On average, how much higher is the miles per gallon for
highway driving as compared to city driving?
3 What percentage of the cars have four-cylinder engines?
4 What percentage of the cars use regular fuel?
Aleksandra Pawłowska Data and Statistics
Aleksandra Pawłowska Data and Statistics
Task 3
Table 1.7 shows data for seven colleges and universities. The
en-
dowment (in billions of dollars) and the percentage of
applicants
admitted are shown (USA Today, February 3, 2008). The state
each school is located in, the campus setting, and the NCAA Di-
vision for varsity teams were obtained from the National Center
of
Education Statistics website, February 22, 2008.
1 How many elements are in the data set?
2 How many variables are in the data set?
3 Which of the variables are categorical and which are
quantitative?
Aleksandra Pawłowska Data and Statistics
25. Task 4
Consider the data set in Table 1.7
1 Compute the average endowment for the sample.
2 Compute the average percentage of applicants admitted.
3 What percentage of the schools have NCAA Division III
varsity teams?
4 What percentage of the schools have a City: Midsize campus
setting?
Aleksandra Pawłowska Data and Statistics
Task 5
The FinancialTimes/Harris Poll is a monthly online poll of
adults
from six countries in Europe and the United States. A January
poll
included 1015 adults in the United States. One of the questions
asked was, “How would you rate the Federal Bank in handling
the
credit problems in the financial markets?” Possible responses
were
Excellent, Good, Fair, Bad, and Terrible (Harris Interactive
website,
January 2008).
1 What was the sample size for this survey?
2 Are the data categorical or quantitative?
3 Would it make more sense to use averages or percentages as a
26. summary of the data for this question?
4 Of the respondents in the United States, 10% said the Federal
Bank is doing a good job. How many individuals provided this
response?
Aleksandra Pawłowska Data and Statistics
Task 6
The Commerce Department reported receiving the following
appli-
cations for the Malcolm Baldrige National Quality Award: 23
from
large manufacturing firms, 18 from large service firms, and 30
from
small businesses.
1 Is type of business a categorical or quantitative variable?
2 What percentage of the applications came from small
businesses?
Aleksandra Pawłowska Data and Statistics
Task 7
State whether each of the following variables is categorical or
quan-
titative and indicate its measurement scale.
27. 1 Annual sales
2 Soft drink size (small, medium, large)
3 Employee classification (GS1 through GS18)
4 Earnings per share
5 Method of payment (cash, check, credit card)
Aleksandra Pawłowska Data and Statistics
Aleksandra Pawłowska Data and Statistics
Task 8
Figure 1.8 provides a bar chart showing the amount of federal
spend-
ing for the years 2002 to 2008 (USA Today, February 5, 2008).
1 What is the variable of interest?
2 Are the data categorical or quantitative?
3 Are the data time series or cross-sectional?
4 Comment on the trend in federal spending over time.
Aleksandra Pawłowska Data and Statistics
Aleksandra Pawłowska Data and Statistics
Task 9
The Food and Drug Administration (FDA) reported the number
28. of
new drugs approved over an eight-year period (The Wall Street
Jour-
nal, January 12, 2004). Figure 1.9 provides a bar chart
summarizing
the number of new drugs approved each year.
1 Are the data categorical or quantitative?
2 Are the data time series or cross-sectional?
3 How many new drugs were approved in 2003?
4 In what year were the fewest new drugs approved? How
many?
5 Comment on the trend in the number of new drugs approved
by the FDA over the eight-year period.
Aleksandra Pawłowska Data and Statistics
Task 10
Asample of midterm grades for five students showed the
following
results: 72, 65, 82, 90, 76. Which of the following statements
are
correct, and which should be challenged as being too
generalized?
1 The average midterm grade for the sample of five students is
77.
2 The average midterm grade for all students who took the
exam is 77.
29. 3 An estimate of the average midterm grade for all students
who took the exam is 77.
4 More than half of the students who take this exam will score
between 70 and 85.
5 If five other students are included in the sample, their grades
will be between 65 and 90.
Aleksandra Pawłowska Data and Statistics
Exploratory Data Analysis
Statistics (exercises)
Aleksandra Pawłowska
May 26, 2020
Glossary
Five-number summary An exploratory data analysis technique
that
uses five numbers to summarize the data: smallest value, first
quar-
tile, median, third quartile, and largest value.
Box plot A graphical summary of data based on a five-number
sum-
mary.
Aleksandra Pawłowska Exploratory Data Analysis
30. Task 1
Consider a sample with data values of 27, 25, 20, 15, 30, 34, 28,
and 25. Provide the five-number summary for the data.
Aleksandra Pawłowska Exploratory Data Analysis
Task 1 – solution
Consider a sample with data values of 27, 25, 20, 15, 30, 34, 28,
and 25. Provide the five-number summary for the data.
five-number summary: 15, 22.5, 26, 29, 34
Aleksandra Pawłowska Exploratory Data Analysis
Task 2
Show the box plot for the data in task 1 (use excel).
Aleksandra Pawłowska Exploratory Data Analysis
Task 2 – solution
Show the box plot for the data in task 1 (use excel).
Aleksandra Pawłowska Exploratory Data Analysis
31. Task 3
Show the five-number summary and the box plot for the
following
data: 5, 15, 18, 10, 8, 12, 16, 10, 6.
Aleksandra Pawłowska Exploratory Data Analysis
Task 3 – solution
Show the five-number summary and the box plot for the
following
data: 5, 15, 18, 10, 8, 12, 16, 10, 6.
five-number summary: 5, 8, 10, 15, 18
Aleksandra Pawłowska Exploratory Data Analysis
Task 3 – solution
Aleksandra Pawłowska Exploratory Data Analysis
Task 4
A data set has a first quartile of 42 and a third quartile of 50.
Compute the lower and upper limits for the corresponding box
plot.
Should a data value of 65 be considered an outlier?
Aleksandra Pawłowska Exploratory Data Analysis
32. Task 4 – solution
A data set has a first quartile of 42 and a third quartile of 50.
Compute the lower and upper limits for the corresponding box
plot.
Should a data value of 65 be considered an outlier?
lower limit = 30,
upper limit = 62,
65 is an outlier
Aleksandra Pawłowska Exploratory Data Analysis
Task 5
Annual sales, in millions of dollars, for 21 pharmaceutical
companies follow.
1 Provide a five-number summary.
2 Compute the lower and upper limits.
3 Do the data contain any outliers?
4 Johnson & Johnson’s sales are the largest on the list at
$14,138 million.
Suppose a data entry error (a transposition) had been made and
the sales
had been entered as $41,138 million. Would the method of
detecting
outliers in part (c) identify this problem and allow for
correction of the
data entry error?
33. 5 Show a box plot (use excel).
Aleksandra Pawłowska Exploratory Data Analysis
Task 5 – solution
1 Provide a five-number summary. 608, 1872, 4019, 8305,
14138
2 Compute the lower and upper limits. lower limit = -7777.5,
upper limit = 17954.5
3 Do the data contain any outliers? Data contain no outliers
4 Johnson & Johnson’s sales are the largest on the list at
$14,138 million. Suppose a data entry error (a transposition)
had been made and the sales had been entered as $41,138
million. Would the method of detecting outliers in part (c)
identify this problem and allow for correction of the data entry
error? Yes, 41138 would be an outlier, data value would be
reviewed and detected
5 Show a box plot. See next slide
Aleksandra Pawłowska Exploratory Data Analysis
Task 5 – solution
Aleksandra Pawłowska Exploratory Data Analysis
34. Measures of Association Between Two Variables
Statistics (exercises)
Aleksandra Pawłowska
Jun 2, 2020
Glossary
Covariance A measure of linear association between two
variables.
Positive values indicate a positive relationship; negative values
indi-
cate a negative relationship.
Correlation coefficient A measure of linear association between
two
variables that takes on values between -1 and +1. Values near
+1
indicate a strong positive linear relationship; values near -1
indicate
a strong negative linear relationship; and values near zero
indicate
the lack of a linear relationship.
Aleksandra Pawłowska Measures of Association Between Two
Variables
Task 1
Five observations taken for two variables follow.
35. 1 Develop a scatter diagram with x on the horizontal axis (use
excel).
2 What does the scatter diagram developed in part (a) indicate
about the relationship between the two variables?
3 Compute and interpret the sample covariance.
4 Compute and interpret the sample correlation coefficient.
Aleksandra Pawłowska Measures of Association Between Two
Variables
Task 1 – solution
Aleksandra Pawłowska Measures of Association Between Two
Variables
Task 1 – solution
1 What does the scatter diagram developed in part (a) indicate
about the relationship between the two variables? negative
relationship
2 Compute and interpret the sample covariance. -60
3 Compute and interpret the sample correlation coefficient.
-0.97, there is strong negative correlation between x and y
Aleksandra Pawłowska Measures of Association Between Two
Variables
36. Task 2
Five observations taken for two variables follow.
1 Develop a scatter diagram for these data (use excel).
2 What does the scatter diagram indicate about a relationship
between x and y?
3 Compute and interpret the sample covariance.
4 Compute and interpret the sample correlation coefficient.
Aleksandra Pawłowska Measures of Association Between Two
Variables
Task 2 – solution
Aleksandra Pawłowska Measures of Association Between Two
Variables
Task 2 – solution
1 What does the scatter diagram indicate about a relationship
between x and y? positive relationship
2 Compute and interpret the sample covariance. 26.5, it
suggests positive relationship between x and y
3 Compute and interpret the sample correlation coefficient.
0.69, there is positive (but not strong) linear relationship
between x and y
37. Aleksandra Pawłowska Measures of Association Between Two
Variables
Task 3
Nielsen Media Research provides two measures of the television
viewing audience:
a television program rating, which is the percentage of
households with televisions
watching a program, and a television program share, which is
the percentage
of households watching a program among those with televisions
in use. The
following data show the Nielsen television ratings and share
data for the Major
League Baseball World Series over a nine-year period
(Associated Press, October
27, 2003).
1 Develop a scatter diagram with rating on the horizontal axis
(use excel).
2 What is the relationship between rating and share? Explain.
3 Compute and interpret the sample covariance.
4 Compute the sample correlation coefficient. What does this
value tell us
about the relationship between rating and share?
Aleksandra Pawłowska Measures of Association Between Two
Variables
Task 3 – solution
38. Aleksandra Pawłowska Measures of Association Between Two
Variables
Task 3 – solution
1 What is the relationship between rating and share? Explain.
positive relationship
2 Compute and interpret the sample covariance. 10, it suggests
positive relationship
3 Compute the sample correlation coefficient. What does this
value tell us about the relationship between rating and share?
0.99, so that means that there is strong linear positive
relationship between rating and share
Aleksandra Pawłowska Measures of Association Between Two
Variables
Task 4
A department of transportation’s study on driving speed and
miles
per gallon for midsize automobiles resulted in the following
data:
Compute and interpret the sample correlation coefficient.
Aleksandra Pawłowska Measures of Association Between Two
Variables
39. Task 4 – solution
Compute and interpret the sample correlation coefficient. -0.91,
so
there is strong linear negative relationship between speed and
miles
per gallon
Aleksandra Pawłowska Measures of Association Between Two
Variables
Task 5
The Dow Jones Industrial Average (DJIA) and the Standard &
Poor’s 500 Index
(S&P 500) are both used to measure the performance of the
stock market. The
DJIA is based on the price of stocks for 30 large companies; the
S&P 500 is
based on the price of stocks for 500 companies. If both the
DJIA and S&P 500
measure the performance of the stock market, how are they
correlated? The
following data show the daily percent increase or daily percent
decrease in the
DJIA and S&P 500 for a sample of nine days over a three-month
period (The
Wall Street Journal, January 15 to March 10, 2006).
1 Show a scatter diagram (use excel).
2 Compute the sample correlation coefficient for these data.
3 Discuss the association between the DJIA and S&P 500. Do
40. you need to
check both before having a general idea about the daily stock
market
performance?
Aleksandra Pawłowska Measures of Association Between Two
Variables
Task 5 – solution
Aleksandra Pawłowska Measures of Association Between Two
Variables
Task 5 – solution
1 Compute the sample correlation coefficient for these data.
0.91
2 Discuss the association between the DJIA and S&P 500. Do
you need to check both before having a general idea about
the daily stock market performance? there is strong positive
linear relationship
Aleksandra Pawłowska Measures of Association Between Two
Variables
The Weighted Mean and Working with Grouped
Data
41. Statistics (exercises)
Aleksandra Pawłowska
Jun 9, 2020
Glossary
Weighted mean The mean obtained by assigning each
observation
a weight that reflects its importance.
Grouped data Data available in class intervals as summarized by
a
frequency distribution. Individual values of the original data are
not
available.
Aleksandra Pawłowska The Weighted Mean and Working with
Grouped Data
Task 1
Consider the following data and corresponding weights.
1 Compute the weighted mean.
2 Compute the sample mean of the four data values without
weighting. Note the difference in the results provided by the
two computations.
Aleksandra Pawłowska The Weighted Mean and Working with
42. Grouped Data
Task 1 – solution
1 Compute the weighted mean. 3.69
2 Compute the sample mean of the four data values without
weighting. Note the difference in the results provided by the
two computations. 3.175
Aleksandra Pawłowska The Weighted Mean and Working with
Grouped Data
Task 2
Consider the sample data in the following frequency
distribution.
1 Compute the sample mean.
2 Compute the sample variance and sample standard deviation.
Aleksandra Pawłowska The Weighted Mean and Working with
Grouped Data
Task 2 – solution
1 Compute the sample mean. 13
2 Compute the sample variance and sample standard deviation.
s2 = 25, s = 5
43. Aleksandra Pawłowska The Weighted Mean and Working with
Grouped Data
Task 3
The grade point average for college students is based on a
weighted
mean computation. For most colleges, the grades are given the
following data values: A (4), B (3), C (2), D (1), and F (0).
After
60 credit hours of course work, a student at State University
earned
9 credit hours of A, 15 credit hours of B, 33 credit hours of C,
and
3 credit hours of D.
1 Compute the student’s grade point average.
2 Students at State University must maintain a 2.5 grade point
average for their first 60 credit hours of course work in order
to be admitted to the business college. Will this student be
admitted?
Aleksandra Pawłowska The Weighted Mean and Working with
Grouped Data
Task 3 – solution
1 Compute the student’s grade point average. 2.5
2 Students at State University must maintain a 2.5 grade point
44. average for their first 60 credit hours of course work in order
to be admitted to the business college. Will this student be
admitted? Yes, they will
Aleksandra Pawłowska The Weighted Mean and Working with
Grouped Data
Task 4
Morningstar tracks the total return for a large number of mutual
funds. The
following table shows the total return and the number of funds
for four categories
of mutual funds (Morningstar Funds500, 2008).
1 Using the number of funds as weights, compute the weighted
average
total return for the mutual funds covered by Morningstar.
2 Suppose you had invested $10,000 in mutual funds at the
beginning of
2007 and diversified the investment by placing $2000 in
Domestic Equity
funds, $4000 in International Equity funds, $3000 in Specialty
Stock
funds, and $1000 in Hybrid funds. What is the expected return
on the
portfolio?
Aleksandra Pawłowska The Weighted Mean and Working with
Grouped Data
45. Task 4 – solution
1 Using the number of funds as weights, compute the weighted
average total return for the mutual funds covered by
Morningstar. 7.83
2 Suppose you had invested $10,000 in mutual funds at the
beginning of 2007 and diversified the investment by placing
$2000 in Domestic Equity funds, $4000 in International Equity
funds, $3000 in Specialty Stock funds, and $1000 in Hybrid
funds. What is the expected return on the portfolio? 12.27
Aleksandra Pawłowska The Weighted Mean and Working with
Grouped Data
Task 5
Based on a survey of 425 master’s programs in business
administration, the U.
S. News & World Report ranked the Indiana University Kelley
Business School
as the 20th best business program in the country (America’s
Best Graduate
Schools, 2009). The ranking was based in part on surveys of
business school
deans and corporate recruiters. Each survey respondent was
asked to rate the
overall academic quality of the master’s program on a scale
from 1 „marginal”
to 5 „outstanding”. Use the sample of responses shown below to
compute the
weighted mean score for the business school deans and the
corporate recruiters.
Discuss.
46. Aleksandra Pawłowska The Weighted Mean and Working with
Grouped Data
Task 5 – solution
x̄ deans = 3.8, x̄ recruiters = 3.7.
Aleksandra Pawłowska The Weighted Mean and Working with
Grouped Data
Index Numbers
Statistics (exercises)
Aleksandra Pawłowska
Jun 16, 2020
Task 1
The median sales prices for new single-family houses for the
years
2004–2007 are as follows (Census Bureau website, March 19,
2009).
1 Use 2004 as the base year and develop a price index for new
single-family homes over this four-year period.
2 Use 2005 as the base year and develop a price index for new
47. single-family homes over this four-year period.
Aleksandra Pawłowska Index Numbers
Task 1 – solution
1 Use 2004 as the base year and develop a price index for new
single-family homes over this four-year period. 100, 109,
111.5, 112.2
2 Use 2005 as the base year and develop a price index for new
single-family homes over this four-year period. 91.7, 100,
102.3, 102.9
Aleksandra Pawłowska Index Numbers
Task 2
Nickerson Manufacturing Company has the following data on
quan-
tities shipped and unit costs for each of its four products:
1 Compute the price relative for each product.
2 Compute a weighted aggregate price index that reflects the
shipping cost change over the four-year period.
Aleksandra Pawłowska Index Numbers
Task 2 – solution
48. 1 Compute the price relative for each product. 151.4, 196.9,
142.6, 177.5
2 Compute a weighted aggregate price index that reflects the
shipping cost change over the four-year period. 170
Aleksandra Pawłowska Index Numbers
Task 3
Use the price data in task 2 to compute a Paasche index for the
shipping cost if 2009 quantities are 4000, 3000, 7500, and 3000
for
each of the four products.
Aleksandra Pawłowska Index Numbers
Task 3 – solution
Use the price data in task 2 to compute a Paasche index for the
shipping cost if 2009 quantities are 4000, 3000, 7500, and 3000
for
each of the four products. 163.7
Aleksandra Pawłowska Index Numbers
Task 4
Consider the following price relatives and quantity information
49. for
grain production in Iowa (Census Bureau website, March 19,
2009).
What is the 2007 weighted aggregate price index for the Iowa
grains?
Aleksandra Pawłowska Index Numbers
Task 4 – solution
What is the 2007 weighted aggregate price index for the Iowa
grains?
182.8
Aleksandra Pawłowska Index Numbers
Measures of Location
Statistics (exercises)
Aleksandra Pawłowska
April 28, 2020
Glossary (part 1)
Sample statistic A numerical value used as a summary measure
for
a sample (e.g. the sample mean, x̄ , the sample variance, s2, and
50. the sample standard deviation, s).
Population parameter A numerical value used as a summary
measure
for a population (e.g. the population mean, µ).
Point estimator The sample statistic, when used to estimate the
corresponding population parameter.
Mean A measure of central location computed by summing the
data
values and dividing by the number of observations.
Aleksandra Pawłowska Measures of Location
Glossary (part 2)
Median A measure of central location provided by the value in
the
middle when the data are arranged in ascending order.
Mode A measure of location, defined as the value that occurs
with
greatest frequency.
Percentile A value such that at least p percent of the
observations
are less than or equal to this value and at least (100− p) percent
of
the observations are greater than or equal to this value. The
50th
percentile is the median.
Quartiles The 25th, 50th, and 75th percentiles, referred to as the
first quartile, the second quartile (median), and third quartile,
re-
spectively. The quartiles can be used to divide a data set into
four
parts, with each part containing approximately 25% of the data.
51. Aleksandra Pawłowska Measures of Location
Task 1
Consider a sample with data values of 10, 20, 12, 17 and 16.
Com-
pute the mean and median.
Aleksandra Pawłowska Measures of Location
Task 1 – solution
Consider a sample with data values of 10, 20, 12, 17 and 16.
Com-
pute the mean and median. mean = x̄ = 15, median = 16
Aleksandra Pawłowska Measures of Location
Task 2
Consider a sample with data values of 10, 20, 21, 17, 16, and
12.
Compute the mean and median.
Aleksandra Pawłowska Measures of Location
Task 2 – solution
52. Consider a sample with data values of 10, 20, 21, 17, 16, and
12.
Compute the mean and median. mean = x̄ = 16, median = 16.5
Aleksandra Pawłowska Measures of Location
Task 3
Consider a sample with data values of 27, 25, 20, 15, 30, 34, 28,
and 25. Compute the 20th, 25th, 65th, and 75th percentiles.
Aleksandra Pawłowska Measures of Location
Task 3 – solution
Consider a sample with data values of 27, 25, 20, 15, 30, 34, 28,
and 25. Compute the 20th, 25th, 65th, and 75th percentiles.
20th percentile = 20,
25th percentile = 22.5,
65th percentile = 28,
75th percentile = 29.
Aleksandra Pawłowska Measures of Location
Task 4
Consider a sample with data values of 53, 55, 70, 58, 64, 57, 53,
69, 57, 68, and 53. Compute the mean, median, and mode.
53. Aleksandra Pawłowska Measures of Location
Task 4 – solution
Consider a sample with data values of 53, 55, 70, 58, 64, 57, 53,
69, 57, 68, and 53. Compute the mean, median, and mode.
mean = x̄ = 59.73, median = 57, mode = 53
Aleksandra Pawłowska Measures of Location
Task 5
The Dow Jones Travel Index reported what business travelers
pay for
hotel rooms per night in major U.S. cities (The Wall Street
Journal,
January 16, 2004). The average hotel room rates for 20 cities
are
presented on the next slide.
1 What is the mean hotel room rate?
2 What is the median hotel room rate?
3 What is the mode?
4 What is the first quartile?
5 What is the third quartile?
Aleksandra Pawłowska Measures of Location
Aleksandra Pawłowska Measures of Location
54. Task 5 – solution
1 What is the mean hotel room rate? 159.05
2 What is the median hotel room rate? 161
3 What is the mode? 167
4 What is the first quartile? 136.5
5 What is the third quartile? 170
Aleksandra Pawłowska Measures of Location
Task 6
During the 2007–2008 NCAA college basketball season, men’s
basketball teams
attempted an all-time high number of 3-point shots, averaging
19.07 shots per
game (Associated Press Sports, January 24, 2009). In an attempt
to discourage
so many 3-point shots and encourage more inside play, the
NCAA rules commit-
tee moved the 3-point line back from 19 feet, 9 inches to 20
feet, 9 inches at the
beginning of the 2008–2009 basketball season. Shown in the
following table are
the 3-point shots taken and the 3-point shots made for a sample
of 19 NCAA
basketball games during the 2008–2009 season (see next slide).
1 What is the mean number of 3-point shots taken per game?
2 What is the mean number of 3-point shots made per game?
3 Using the closer 3-point line, players were making 35.2% of
their shots.
55. What percentage of shots were players making from the new 3-
point line?
4 What was the impact of the NCAA rules change that moved
the 3-point
line back to 20 feet, 9 inches for the 2008–2009 season? Would
you agree
with the Associated Press Sports article that stated, „Moving
back the
3-point line hasn’t changed the game dramatically”? Explain.
Aleksandra Pawłowska Measures of Location
Aleksandra Pawłowska Measures of Location
Task 6 – solution
1 What is the mean number of 3-point shots taken per game?
18.42
2 What is the mean number of 3-point shots made per game?
6.32
3 Using the closer 3-point line, players were making 35.2% of
their shots. What percentage of shots were players making
from the new 3-point line? 34.3%
4 What was the impact of the NCAA rules change that moved
the 3-point line back to 20 feet, 9 inches for the 2008–2009
season? Would you agree with the Associated Press Sports
article that stated, „Moving back the 3-point line hasn’t
56. changed the game dramatically”? Explain. Yes, agree but not
dramatically. Reductions of only 0.65 shots and 0.9
percentage points for made shots per game
Aleksandra Pawłowska Measures of Location
Task 7
The cost of consumer purchases such as single-family housing,
gasoline, Internet
services, tax preparation, and hospitalization were provided in
The Wall-Street
Journal (January 2, 2007). Sample data typical of the cost of
tax-return prepa-
ration by services such as H&R Block are:
1 Compute the mean, median, and mode.
2 Compute the first and third quartiles.
3 Compute and interpret the 90th percentile.
Aleksandra Pawłowska Measures of Location
Task 7 – solution
1 Compute the mean, median, and mode. mean = 160, median
= 135, mode = 120
2 Compute the first and third quartiles. Q1 = 115, Q3 = 187.5
3 Compute and interpret the 90th percentile. 90th percentile =
245. 90% of the tax returns cost $245 or less.
57. Aleksandra Pawłowska Measures of Location
Measures of Distribution Shape and Detecting
Outliers
Statistics (exercises)
Aleksandra Pawłowska
May 19, 2020
Glossary
Skewness A measure of the shape of a data distribution. Data
skewed to the
left result in negative skewness; a symmetric data distribution
results in zero
skewness; and data skewed to the right result in positive
skewness.
z-score A value computed by dividing the deviation about the
mean (xi − x̄ ) by
the standard deviation s. A z-score is referred to as a
standardized value and
denotes the number of standard deviations xi is from the mean.
Chebyshev’s theorem A theorem that can be used to make
statements about the
proportion of data values that must be within a specified
number of standard
deviations of the mean.
Empirical rule A rule that can be used to compute the
percentage of data values
58. that must be within one, two, and three standard deviations of
the mean for
data that exhibit a bell-shaped distribution.
Outlier An unusually small or unusually large data value.
Aleksandra Pawłowska Measures of Distribution Shape and
Detecting Outliers
Task 1
Consider a sample with data values of 10, 20, 12, 17, and 16.
Com-
pute the z-score for each of the five observations.
Aleksandra Pawłowska Measures of Distribution Shape and
Detecting Outliers
Task 1 – solution
Consider a sample with data values of 10, 20, 12, 17, and 16.
Com-
pute the z-score for each of the five observations. z1 = −1.25,
z2 = 1.25, z3 = −0.75, z4 = 0.5, z5 = 0.25
Aleksandra Pawłowska Measures of Distribution Shape and
Detecting Outliers
Task 2
Consider a sample with a mean of 500 and a standard deviation
59. of
100. What are the z-scores for the following data values: 520,
650,
500, 450, and 280?
Aleksandra Pawłowska Measures of Distribution Shape and
Detecting Outliers
Task 2 – solution
Consider a sample with a mean of 500 and a standard deviation
of 100. What are the z-scores for the following data values: 520,
650, 500, 450, and 280? z1 = 0.2, z2 = 1.5, z3 = 0, z4 = −0.5,
z5 = −2.2
Aleksandra Pawłowska Measures of Distribution Shape and
Detecting Outliers
Task 3
Consider a sample with a mean of 30 and a standard deviation
of 5.
Use Chebyshev’s theorem to determine the percentage of the
data
within each of the following ranges:
1 20 to 40
2 15 to 45
3 22 to 38
4 18 to 42
5 12 to 48
60. Aleksandra Pawłowska Measures of Distribution Shape and
Detecting Outliers
Task 3 – solution
1 20 to 40 75%
2 15 to 45 89%
3 22 to 38 61%
4 18 to 42 83%
5 12 to 48 92%
Aleksandra Pawłowska Measures of Distribution Shape and
Detecting Outliers
Task 4
Suppose the data have a bell-shaped distribution with a mean of
30
and a standard deviation of 5. Use the empirical rule to
determine
the percentage of data within each of the following ranges:
1 20 to 40
2 15 to 45
3 25 to 35
Aleksandra Pawłowska Measures of Distribution Shape and
Detecting Outliers
Task 4 – solution
61. 1 20 to 40 95%
2 15 to 45 almost 100%
3 25 to 35 68%
Aleksandra Pawłowska Measures of Distribution Shape and
Detecting Outliers
Task 5
The results of a national survey showed that on average, adults
sleep 6.9 hours per night. Suppose that the standard deviation is
1.2 hours.
1 Use Chebyshev’s theorem to calculate the percentage of
individuals who sleep between 4.5 and 9.3 hours.
2 Use Chebyshev’s theorem to calculate the percentage of
individuals who sleep between 3.9 and 9.9 hours.
3 Assume that the number of hours of sleep follows a
bell-shaped distribution. Use the empirical rule to calculate
the percentage of individuals who sleep between 4.5 and 9.3
hours per day. How does this result compare to the value that
you obtained using Chebyshev’s theorem in part (a)?
Aleksandra Pawłowska Measures of Distribution Shape and
Detecting Outliers
Task 5 – solution
1 Use Chebyshev’s theorem to calculate the percentage of
62. individuals who sleep between 4.5 and 9.3 hours. 75%
2 Use Chebyshev’s theorem to calculate the percentage of
individuals who sleep between 3.9 and 9.9 hours. 84%
3 Assume that the number of hours of sleep follows a
bell-shaped distribution. Use the empirical rule to calculate
the percentage of individuals who sleep between 4.5 and 9.3
hours per day. How does this result compare to the value that
you obtained using Chebyshev’s theorem in part (1)? 95%; if
we assume, that data are distributed symetrically, then more
observations are closer to the mean
Aleksandra Pawłowska Measures of Distribution Shape and
Detecting Outliers
Task 6
The Energy Information Administration reported that the mean
re-
tail price per gallon of regular grade gasoline was $2.05
(Energy
Information Administration, May 2009). Suppose that the
standard
deviation was $0.10 and that the retail price per gallon has a
bell-
shaped distribution.
1 What percentage of regular grade gasoline sold between $1.95
and $2.15 per gallon?
2 What percentage of regular grade gasoline sold between $1.95
and $2.25 per gallon?
63. 3 What percentage of regular grade gasoline sold for more than
$2.25 per gallon?
Aleksandra Pawłowska Measures of Distribution Shape and
Detecting Outliers
Task 6 – solution
1 What percentage of regular grade gasoline sold between $1.95
and $2.15 per gallon? 68%
2 What percentage of regular grade gasoline sold between $1.95
and $2.25 per gallon? 81.5%
3 What percentage of regular grade gasoline sold for more than
$2.25 per gallon? 2.5%
Aleksandra Pawłowska Measures of Distribution Shape and
Detecting Outliers
Task 7
The national average for the math portion of the College
Board’s
Scholastic Aptitude Test (SAT) is 515 (The World Almanac,
2009).
The College Board periodically rescales the test scores such that
the standard deviation is approximately 100. Answer the
following
questions using a bell-shaped distribution and the empirical rule
for
the verbal test scores.
64. 1 What percentage of students have an SAT verbal score
greater than 615?
2 What percentage of students have an SAT verbal score
greater than 715?
3 What percentage of students have an SAT verbal score
between 415 and 515?
4 What percentage of students have an SAT verbal score
between 315 and 615?
Aleksandra Pawłowska Measures of Distribution Shape and
Detecting Outliers
Task 7 – solution
1 What percentage of students have an SAT verbal score
greater than 615? 16%
2 What percentage of students have an SAT verbal score
greater than 715? 2.5%
3 What percentage of students have an SAT verbal score
between 415 and 515? 34%
4 What percentage of students have an SAT verbal score
between 315 and 615? 81.5%
Aleksandra Pawłowska Measures of Distribution Shape and
Detecting Outliers