Please Subscribe to this Channel for more solutions and lectures
http://www.youtube.com/onlineteaching
Chapter 2: Exploring Data with Tables and Graphs
2.3: Graphs that Enlighten and Graphs that Deceive
Please Subscribe to this Channel for more solutions and lectures
http://www.youtube.com/onlineteaching
Chapter 2: Exploring Data with Tables and Graphs
2.2: Histograms
Please Subscribe to this Channel for more solutions and lectures
http://www.youtube.com/onlineteaching
Chapter 2: Exploring Data with Tables and Graphs
2.1: Frequency Distributions for Organizing and Summarizing Data
Please Subscribe to this Channel for more solutions and lectures
http://www.youtube.com/onlineteaching
Chapter 2: Exploring Data with Tables and Graphs
2.4: Scatterplots, Correlation, and Regression
Please Subscribe to this Channel for more solutions and lectures
http://www.youtube.com/onlineteaching
Chapter 1: Introduction to Statistics
Section 1.3: Collecting Sample Data
Please Subscribe to this Channel for more solutions and lectures
http://www.youtube.com/onlineteaching
Elementary Statistics Practice Test 2
Chapter 4: Probability
Please Subscribe to this Channel for more solutions and lectures
http://www.youtube.com/onlineteaching
Chapter 1: Introduction to Statistics
Section 1.2: Types of Data, Key Concept
Please Subscribe to this Channel for more solutions and lectures
http://www.youtube.com/onlineteaching
Chapter 4: Probability
4.1: Basic Concepts of Probability
Please Subscribe to this Channel for more solutions and lectures
http://www.youtube.com/onlineteaching
Chapter 2: Exploring Data with Tables and Graphs
2.2: Histograms
Please Subscribe to this Channel for more solutions and lectures
http://www.youtube.com/onlineteaching
Chapter 2: Exploring Data with Tables and Graphs
2.1: Frequency Distributions for Organizing and Summarizing Data
Please Subscribe to this Channel for more solutions and lectures
http://www.youtube.com/onlineteaching
Chapter 2: Exploring Data with Tables and Graphs
2.4: Scatterplots, Correlation, and Regression
Please Subscribe to this Channel for more solutions and lectures
http://www.youtube.com/onlineteaching
Chapter 1: Introduction to Statistics
Section 1.3: Collecting Sample Data
Please Subscribe to this Channel for more solutions and lectures
http://www.youtube.com/onlineteaching
Elementary Statistics Practice Test 2
Chapter 4: Probability
Please Subscribe to this Channel for more solutions and lectures
http://www.youtube.com/onlineteaching
Chapter 1: Introduction to Statistics
Section 1.2: Types of Data, Key Concept
Please Subscribe to this Channel for more solutions and lectures
http://www.youtube.com/onlineteaching
Chapter 4: Probability
4.1: Basic Concepts of Probability
Please Subscribe to this Channel for more solutions and lectures
http://www.youtube.com/onlineteaching
Chapter 3: Describing, Exploring, and Comparing Data
3.2: Measures of Variation
Please Subscribe to this Channel for more solutions and lectures
http://www.youtube.com/onlineteaching
Chapter 3: Describing, Exploring, and Comparing Data
3.1: Measures of Center
Please Subscribe to this Channel for more solutions and lectures
http://www.youtube.com/onlineteaching
Elementary Statistics Practice Test 1
Module 1: Chapters 1-3
Chapter 1: Introduction to Statistics.
Chapter 2: Exploring Data with Tables and Graphs.
Chapter 3: Describing, Exploring, and Comparing Data.
Please Subscribe to this Channel for more solutions and lectures
http://www.youtube.com/onlineteaching
Chapter 6: Normal Probability Distribution
6.3: Sampling Distributions and Estimators
Solution to the practice test ch 10 correlation reg ch 11 gof ch12 anovaLong Beach City College
Please Subscribe to this Channel for more solutions and lectures
http://www.youtube.com/onlineteaching
Elementary Statistics Practice Test 5
Module 5
Chapter 10: Correlation and Regression
Chapter 11: Goodness of Fit and Contingency Tables
Chapter 12: Analysis of Variance
Please Subscribe to this Channel for more solutions and lectures
http://www.youtube.com/onlineteaching
Chapter 6: Normal Probability Distribution
6.5: Assessing Normality
Please Subscribe to this Channel for more solutions and lectures
http://www.youtube.com/onlineteaching
Chapter 10: Correlation and Regression
10.1: Correlation
Please Subscribe to this Channel for more solutions and lectures
http://www.youtube.com/onlineteaching
Elementary Statistics Practice Test 1
Module 1: Chapters 1-3
Chapter 1: Introduction to Statistics.
Chapter 2: Exploring Data with Tables and Graphs.
Chapter 3: Describing, Exploring, and Comparing Data.
Please Subscribe to this Channel for more solutions and lectures
http://www.youtube.com/onlineteaching
Elementary Statistics Practice Test 3
Practice Test Chapter 6 (Normal Probability Distributions)
Chapter 6: Normal Probability Distributions
Please Subscribe to this Channel for more solutions and lectures
http://www.youtube.com/onlineteaching
Chapter 3: Describing, Exploring, and Comparing Data
3.3: Measures of Relative Standing and Boxplots
Please Subscribe to this Channel for more solutions and lectures
http://www.youtube.com/onlineteaching
Elementary Statistics Practice Test 3
Module 2: Chapter 6 - Normal Probability Distribution
Please Subscribe to this Channel for more solutions and lectures
http://www.youtube.com/onlineteaching
Elementary Statistics Practice Test 3
Module 2: Chapter 6 - Normal Probability Distribution
Please Subscribe to this Channel for more solutions and lectures
http://www.youtube.com/onlineteaching
Chapter 4: Probability
4.3: Complements and Conditional Probability, and Bayes' Theorem
Please Subscribe to this Channel for more solutions and lectures
http://www.youtube.com/onlineteaching
Elementary Statistics Practice Test 2 Solutions
Chapter 4: Probability
Please Subscribe to this Channel for more solutions and lectures
http://www.youtube.com/onlineteaching
Chapter 4: Probability
4.2: Addition Rule and Multiplication Rule
Please Subscribe to this Channel for more solutions and lectures
http://www.youtube.com/onlineteaching
Elementary Statistics Practice Test 4
Module 4:
Chapter 8, Hypothesis Testing
Chapter 9: Two Populations
Please Subscribe to this Channel for more solutions and lectures
http://www.youtube.com/onlineteaching
Chapter 8: Hypothesis Testing
8.1: Basics of Hypothesis Testing
📺Please Subscribe to this Channel for more solutions and lectures
http://www.youtube.com/onlineteaching
Chapter 7: Estimating Parameters and Determining Sample Sizes
7.1: Estimating a Population Proportion
Please Subscribe to this Channel for more solutions and lectures
http://www.youtube.com/onlineteaching
Chapter 10: Correlation and Regression
10.2: Regression
Please Subscribe to this Channel for more solutions and lectures
http://www.youtube.com/onlineteaching
Chapter 3: Describing, Exploring, and Comparing Data
3.2: Measures of Variation
Please Subscribe to this Channel for more solutions and lectures
http://www.youtube.com/onlineteaching
Chapter 3: Describing, Exploring, and Comparing Data
3.1: Measures of Center
Please Subscribe to this Channel for more solutions and lectures
http://www.youtube.com/onlineteaching
Elementary Statistics Practice Test 1
Module 1: Chapters 1-3
Chapter 1: Introduction to Statistics.
Chapter 2: Exploring Data with Tables and Graphs.
Chapter 3: Describing, Exploring, and Comparing Data.
Please Subscribe to this Channel for more solutions and lectures
http://www.youtube.com/onlineteaching
Chapter 6: Normal Probability Distribution
6.3: Sampling Distributions and Estimators
Solution to the practice test ch 10 correlation reg ch 11 gof ch12 anovaLong Beach City College
Please Subscribe to this Channel for more solutions and lectures
http://www.youtube.com/onlineteaching
Elementary Statistics Practice Test 5
Module 5
Chapter 10: Correlation and Regression
Chapter 11: Goodness of Fit and Contingency Tables
Chapter 12: Analysis of Variance
Please Subscribe to this Channel for more solutions and lectures
http://www.youtube.com/onlineteaching
Chapter 6: Normal Probability Distribution
6.5: Assessing Normality
Please Subscribe to this Channel for more solutions and lectures
http://www.youtube.com/onlineteaching
Chapter 10: Correlation and Regression
10.1: Correlation
Please Subscribe to this Channel for more solutions and lectures
http://www.youtube.com/onlineteaching
Elementary Statistics Practice Test 1
Module 1: Chapters 1-3
Chapter 1: Introduction to Statistics.
Chapter 2: Exploring Data with Tables and Graphs.
Chapter 3: Describing, Exploring, and Comparing Data.
Please Subscribe to this Channel for more solutions and lectures
http://www.youtube.com/onlineteaching
Elementary Statistics Practice Test 3
Practice Test Chapter 6 (Normal Probability Distributions)
Chapter 6: Normal Probability Distributions
Please Subscribe to this Channel for more solutions and lectures
http://www.youtube.com/onlineteaching
Chapter 3: Describing, Exploring, and Comparing Data
3.3: Measures of Relative Standing and Boxplots
Please Subscribe to this Channel for more solutions and lectures
http://www.youtube.com/onlineteaching
Elementary Statistics Practice Test 3
Module 2: Chapter 6 - Normal Probability Distribution
Please Subscribe to this Channel for more solutions and lectures
http://www.youtube.com/onlineteaching
Elementary Statistics Practice Test 3
Module 2: Chapter 6 - Normal Probability Distribution
Please Subscribe to this Channel for more solutions and lectures
http://www.youtube.com/onlineteaching
Chapter 4: Probability
4.3: Complements and Conditional Probability, and Bayes' Theorem
Please Subscribe to this Channel for more solutions and lectures
http://www.youtube.com/onlineteaching
Elementary Statistics Practice Test 2 Solutions
Chapter 4: Probability
Please Subscribe to this Channel for more solutions and lectures
http://www.youtube.com/onlineteaching
Chapter 4: Probability
4.2: Addition Rule and Multiplication Rule
Please Subscribe to this Channel for more solutions and lectures
http://www.youtube.com/onlineteaching
Elementary Statistics Practice Test 4
Module 4:
Chapter 8, Hypothesis Testing
Chapter 9: Two Populations
Please Subscribe to this Channel for more solutions and lectures
http://www.youtube.com/onlineteaching
Chapter 8: Hypothesis Testing
8.1: Basics of Hypothesis Testing
📺Please Subscribe to this Channel for more solutions and lectures
http://www.youtube.com/onlineteaching
Chapter 7: Estimating Parameters and Determining Sample Sizes
7.1: Estimating a Population Proportion
Please Subscribe to this Channel for more solutions and lectures
http://www.youtube.com/onlineteaching
Chapter 10: Correlation and Regression
10.2: Regression
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.
Please Subscribe to this Channel for more solutions and lectures
http://www.youtube.com/onlineteaching
Elementary Statistics Practice Test 4
Chapter 9: Inferences about Two Samples
Please Subscribe to this Channel for more solutions and lectures
http://www.youtube.com/onlineteaching
Elementary Statistics Practice Test 4
Chapter 8: Hypothesis Testing
Please Subscribe to this Channel for more solutions and lectures
http://www.youtube.com/onlineteaching
Elementary Statistics Practice Test 5
Module 5
Chapter 10: Correlation and Regression
Chapter 11: Goodness of Fit and Contingency Tables
Chapter 12: Analysis of Variance
Solution to the practice test ch 8 hypothesis testing ch 9 two populationsLong Beach City College
Please Subscribe to this Channel for more solutions and lectures
http://www.youtube.com/onlineteaching
Elementary Statistics Practice Test 4
Module 4:
Chapter 8, Hypothesis Testing
Chapter 9: Two Populations
Solution to the Practice Test 3A, Chapter 6 Normal Probability DistributionLong Beach City College
Please Subscribe to this Channel for more solutions and lectures
http://www.youtube.com/onlineteaching
Elementary Statistics Practice Test 3
Practice Test Chapter 6 (Normal Probability Distributions)
Chapter 6: Normal Probability Distributions
Please Subscribe to this Channel for more solutions and lectures
http://www.youtube.com/onlineteaching
Chapter 12: Analysis of Variance
12.2: Two-Way ANOVA
Please Subscribe to this Channel for more solutions and lectures
http://www.youtube.com/onlineteaching
Chapter 12: Analysis of Variance
12.1: One-Way ANOVA
Please Subscribe to this Channel for more solutions and lectures
http://www.youtube.com/onlineteaching
Chapter 11: Goodness-of-Fit and Contingency Tables
11.2: Contingency Tables
Please Subscribe to this Channel for more solutions and lectures
http://www.youtube.com/onlineteaching
Chapter 11: Goodness-of-Fit and Contingency Tables
11.1: Goodness of Fit Notation
Please Subscribe to this Channel for more solutions and lectures
http://www.youtube.com/onlineteaching
Chapter 9: Inferences from Two Samples
9.4: Two Variances or Standard Deviations
Please Subscribe to this Channel for more solutions and lectures
http://www.youtube.com/onlineteaching
Chapter 9: Inferences from Two Samples
9.3 Two Means, Two Dependent Samples, Matched Pairs
Please Subscribe to this Channel for more solutions and lectures
http://www.youtube.com/onlineteaching
Chapter 9: Inferences from Two Samples
9.2: Two Means, Independent Samples
Please Subscribe to this Channel for more solutions and lectures
http://www.youtube.com/onlineteaching
Chapter 9: Inferences from Two Samples
9.1: Inferences about Two Proportions
Please Subscribe to this Channel for more solutions and lectures
http://www.youtube.com/onlineteaching
Chapter 8: Hypothesis Testing
8.4: Testing a Claim About a Standard Deviation or Variance
Please Subscribe to this Channel for more solutions and lectures
http://www.youtube.com/onlineteaching
Chapter 8: Hypothesis Testing
8.3: Testing a Claim About a Mean
Please Subscribe to this Channel for more solutions and lectures
http://www.youtube.com/onlineteaching
Chapter 8: Hypothesis Testing
8.2: Testing a Claim About a Proportion
Welcome to TechSoup New Member Orientation and Q&A (May 2024).pdfTechSoup
In this webinar you will learn how your organization can access TechSoup's wide variety of product discount and donation programs. From hardware to software, we'll give you a tour of the tools available to help your nonprofit with productivity, collaboration, financial management, donor tracking, security, and more.
Francesca Gottschalk - How can education support child empowerment.pptxEduSkills OECD
Francesca Gottschalk from the OECD’s Centre for Educational Research and Innovation presents at the Ask an Expert Webinar: How can education support child empowerment?
Acetabularia Information For Class 9 .docxvaibhavrinwa19
Acetabularia acetabulum is a single-celled green alga that in its vegetative state is morphologically differentiated into a basal rhizoid and an axially elongated stalk, which bears whorls of branching hairs. The single diploid nucleus resides in the rhizoid.
June 3, 2024 Anti-Semitism Letter Sent to MIT President Kornbluth and MIT Cor...Levi Shapiro
Letter from the Congress of the United States regarding Anti-Semitism sent June 3rd to MIT President Sally Kornbluth, MIT Corp Chair, Mark Gorenberg
Dear Dr. Kornbluth and Mr. Gorenberg,
The US House of Representatives is deeply concerned by ongoing and pervasive acts of antisemitic
harassment and intimidation at the Massachusetts Institute of Technology (MIT). Failing to act decisively to ensure a safe learning environment for all students would be a grave dereliction of your responsibilities as President of MIT and Chair of the MIT Corporation.
This Congress will not stand idly by and allow an environment hostile to Jewish students to persist. The House believes that your institution is in violation of Title VI of the Civil Rights Act, and the inability or
unwillingness to rectify this violation through action requires accountability.
Postsecondary education is a unique opportunity for students to learn and have their ideas and beliefs challenged. However, universities receiving hundreds of millions of federal funds annually have denied
students that opportunity and have been hijacked to become venues for the promotion of terrorism, antisemitic harassment and intimidation, unlawful encampments, and in some cases, assaults and riots.
The House of Representatives will not countenance the use of federal funds to indoctrinate students into hateful, antisemitic, anti-American supporters of terrorism. Investigations into campus antisemitism by the Committee on Education and the Workforce and the Committee on Ways and Means have been expanded into a Congress-wide probe across all relevant jurisdictions to address this national crisis. The undersigned Committees will conduct oversight into the use of federal funds at MIT and its learning environment under authorities granted to each Committee.
• The Committee on Education and the Workforce has been investigating your institution since December 7, 2023. The Committee has broad jurisdiction over postsecondary education, including its compliance with Title VI of the Civil Rights Act, campus safety concerns over disruptions to the learning environment, and the awarding of federal student aid under the Higher Education Act.
• The Committee on Oversight and Accountability is investigating the sources of funding and other support flowing to groups espousing pro-Hamas propaganda and engaged in antisemitic harassment and intimidation of students. The Committee on Oversight and Accountability is the principal oversight committee of the US House of Representatives and has broad authority to investigate “any matter” at “any time” under House Rule X.
• The Committee on Ways and Means has been investigating several universities since November 15, 2023, when the Committee held a hearing entitled From Ivory Towers to Dark Corners: Investigating the Nexus Between Antisemitism, Tax-Exempt Universities, and Terror Financing. The Committee followed the hearing with letters to those institutions on January 10, 202
Honest Reviews of Tim Han LMA Course Program.pptxtimhan337
Personal development courses are widely available today, with each one promising life-changing outcomes. Tim Han’s Life Mastery Achievers (LMA) Course has drawn a lot of interest. In addition to offering my frank assessment of Success Insider’s LMA Course, this piece examines the course’s effects via a variety of Tim Han LMA course reviews and Success Insider comments.
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.
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.
Embracing GenAI - A Strategic ImperativePeter Windle
Artificial Intelligence (AI) technologies such as Generative AI, Image Generators and Large Language Models have had a dramatic impact on teaching, learning and assessment over the past 18 months. The most immediate threat AI posed was to Academic Integrity with Higher Education Institutes (HEIs) focusing their efforts on combating the use of GenAI in assessment. Guidelines were developed for staff and students, policies put in place too. Innovative educators have forged paths in the use of Generative AI for teaching, learning and assessments leading to pockets of transformation springing up across HEIs, often with little or no top-down guidance, support or direction.
This Gasta posits a strategic approach to integrating AI into HEIs to prepare staff, students and the curriculum for an evolving world and workplace. We will highlight the advantages of working with these technologies beyond the realm of teaching, learning and assessment by considering prompt engineering skills, industry impact, curriculum changes, and the need for staff upskilling. In contrast, not engaging strategically with Generative AI poses risks, including falling behind peers, missed opportunities and failing to ensure our graduates remain employable. The rapid evolution of AI technologies necessitates a proactive and strategic approach if we are to remain relevant.
2. Chapter 2:
Exploring Data with Tables and Graphs
2.1 Frequency Distributions for Organizing and
Summarizing Data
2.2 Histograms
2.3 Graphs that Enlighten and Graphs that Deceive
2.4 Scatterplots, Correlation, and Regression
2
Objectives:
1. Organize data using a frequency distribution.
2. Represent data in frequency distributions graphically using histograms, frequency polygons, and ogives.
3. Represent data using bar graphs, Pareto charts, time series graphs, and pie graphs.
4. Draw and interpret a stem and leaf plot.
5. Draw and interpret a scatter plot for a set of paired data.
3. Key Concept:
Common graphs that foster understanding of data and some graphs that are
deceptive because they create impressions about data that are somehow misleading
or wrong.
2.3 Graphs that Enlighten and Graphs that Deceive
3
Dot plots & its Features:
A graph of quantitative data in which each data value is plotted as a point (or dot) above a horizontal
scale of values. Dots representing equal values are stacked.
Displays the shape of distribution of data.
It is usually possible to recreate the original list of data values.
Example 1: Construct a Dotplot and find an outlier if any.
Number 36 seems to be an outlier.
80 94 58 66 56 82 78 86 88 56 36 66 84 76 78 64 66 78 60 64
4. Stemplots (or stem-and-leaf plot)
Represents quantitative data by separating each value into two parts: the
stem (such as the leftmost digit) and the leaf (such as the rightmost digit).
Features of a Stemplot
Shows the shape of the distribution of the data.
Retains the original data values.
The sample data are sorted (arranged in order).
4
Graphs that Enlighten: Stemplots (or stem-and-leaf plot)
Example 2:
Construct a Stemplot.
80 94 58 66 56 82 78 86 88 56 36 66 84 76 78 64 66 78 60 64
5. Time-Series Graph
A graph of time-series data, which are quantitative data that have been collected at different
points in time, such as monthly or yearly
Feature of a Time-Series Graph: Reveals information about trends over time.
5
Graphs that Enlighten
From 1990 to 2010, there seems to be upward trend
that appears to be leveling off in recent years. It would
help close the gender gap in earning.
Example 3: Construct a Time-Series Graph.
Women’s median earning as a percentage of men’s median earning from 1990 to 2010
are listed as follows; Is there a trend? Any affect?
6. Example 4: Construct the Pareto Chart.
A study of retractions (admission of wrong claim) in biomedicine
showed, 472 were due to error, 225 were due to plagiarism, 881 were due
to fraud, 295 were due to duplications of publications, and 249 had other
causes. Construct a Pareto chart. Among such retractions, does
misconduct (fraud, duplication, plagiarism) appear to be a major factor?
Bar Graphs: A graph of bars of equal width to show frequencies of categories of categorical
(or qualitative) data. The bars may or may not be separated by small gaps.
Feature of a Bar Graph: Shows the relative distribution of categorical data so that it is easier
to compare the different categories.
6
Graphs that Enlighten
Pareto Charts: A Pareto chart is a bar graph for categorical data, with the
added condition that the bars are arranged in descending order according
to frequencies, so the bars decrease in height from left to right.
Features of a Pareto Chart: Shows the relative distribution of categorical data
so that it is easier to compare the different categories.
Draws attention to the more important categories.
Yes, it
does.
7. Pie Charts
A very common graph that depicts categorical data as slices of a
circle, in which the size of each slice is proportional to the
frequency count for the category
Feature of a Pie Chart: Each sector =→ 𝟑𝟔𝟎𝟎
× %
Shows the distribution of categorical data in a commonly used format.
7
Graphs that Enlighten
Example 5: Construct the Pie Chart.
A study of retractions (admission of wrong claim) in biomedicine
showed, 472 were due to error, 225 were due to plagiarism, 881 were due
to fraud, 295 were due to duplications of publications, and 249 had other
causes. Construct a Pareto chart. Among such retractions, does
misconduct (fraud, duplication, plagiarism) appear to be a major factor?
8. Frequency Polygon
A graph using line segments connected to points located directly above class midpoint values
A frequency polygon is very similar to a histogram, but a frequency polygon uses line segments instead of bars.
Relative Frequency Polygon
A variation of the basic frequency polygon is the relative frequency polygon, which uses relative frequencies (proportions
or percentages) for the vertical scale.
8
Graphs that Enlighten
9. Relative F
f/n
9
Graphs that Enlighten
Example 6
Construct a histogram, frequency polygon, and ogive using relative
frequencies for the distribution (shown here) of the miles that 20
randomly selected runners ran during a given week.
Class
Boundaries
F
5.5 - 10.5
10.5 - 15.5
15.5 - 20.5
20.5 - 25.5
25.5 - 30.5
30.5 - 35.5
35.5 - 40.5
1
2
3
5
4
3
2
1/20 =
2/20 =
3/20 =
5/20 =
4/20 =
3/20 =
2/20 =
f = 20 rf = 1.00
0.05
0.10
0.15
0.25
0.20
0.15
0.10
Midpoints
8
13
18
23
28
33
38
10. Relative F
f/n
10
Graphs that Enlighten
Example 6 Continued
Construct a histogram, frequency polygon, and ogive using
relative frequencies for the distribution (shown here) of the miles
that 20 randomly selected runners ran during a given week.
Class
Boundaries
F
5.5 - 10.5
10.5 - 15.5
15.5 - 20.5
20.5 - 25.5
25.5 - 30.5
30.5 - 35.5
35.5 - 40.5
1
2
3
5
4
3
2
1/20 =
2/20 =
3/20 =
5/20 =
4/20 =
3/20 =
2/20 =
f = 20 rf = 1.00
0.05
0.10
0.15
0.25
0.20
0.15
0.10
Midpoints
8
13
18
23
28
33
38
12. 12
Graphs that Enlighten
Example 6
Construct an ogive:
It’s a line graph that depicts cumulative frequencies
Ogives use upper class boundaries and cumulative frequencies or
cumulative relative frequencies of the classes.
Class
Boundaries
Cumulative F
5.5 - 10.5
5.5 - 15.5
5.5 - 20.5
5.5 - 25.5
5.5 - 30.5
5.5 - 35.5
5.5 - 40.5
1
3
6
11
15
18
20
Cum. Rel.
Frequency
1/20 =
3/20 =
6/20 =
11/20 =
15/20 =
18/20 =
20/20 =
0.05
0.15
0.30
0.55
0.75
0.90
1.00 What percent of runners
ran 22 miles or less? About 41%
13. Nonzero Vertical Axis
A common deceptive graph involves using a vertical scale that starts at some value
greater than zero to exaggerate differences between groups.
13
Graphs that Deceive
Always examine a graph carefully to see whether a vertical axis begins at
some point other than zero so that differences are exaggerated.
14. Drawings of objects, called pictographs, are often misleading. Data that are one-dimensional in
nature (such as budget amounts) are often depicted with two-dimensional objects (such as
dollar bills) or three-dimensional objects (such as stacks of coins, homes, or barrels).
By using pictographs, artists can create false impressions that grossly distort differences by
using these simple principles of basic geometry:
When you double each side of a square, its area doesn’t merely double; it increases by a factor of four.
When you double each side of a cube, its volume doesn’t merely double; it increases by a factor of eight.
14
Graphs that Deceive: Pictographs
Misleading. Depicts one-dimensional
data with three-dimensional boxes. Last
box is 64 times as large as first box, but
income is only 4 times as large. Fair, objective,
clear from any
distracting features.