Creating and Using a Gannt Chart A Gantt chart is a t.docx

Creating and Using a Gannt Chart
A Gantt chart is a type of bar chart that illustrates a project
schedule. Gantt charts illustrate the start and finish dates of the
terminal elements
and summary elements of a project and the dependency
relationships between activities. Gantt charts can be used to
show current schedule
status using percent-complete shadings and a vertical "TODAY"
line.
The first known Gantt chart was developed in 1896 by Karol
Adamiecki, who called it a harmonogram. Adamiecki did not
publish his chart until
1931, however, and then only in Polish. The chart is commonly
known after Henry Gantt (1861–1919), who designed his chart
sometime
between 1910 and 1915.
Although now regarded as a common charting technique, Gantt
charts were considered revolutionary when they were
introduced. In
recognition of Henry Gantt’s contributions, the Henry Laurence
Gantt prize is awarded for distinguished achievement in
management and in

community service. This chart is used also in Information
Technology to represent data that has been collected. (first three
paragraphs appear in
Wikipedia Gantt chart entry, citing these three sources:
H.L. Gantt, Work, Wages and Profit, published by The
Engineering Magazine, New York, 1910; republished as Work,
Wages and
Profits, Easton, Pennsylvania, Hive Publishing Company, 1974,
ISBN 0879600489.
Blokdijk, Gerard (2007). Project Management 100 Success
Secrets. Lulu.com. p. 76. ISBN HYPERLINK
"http://en.wikipedia.org/wiki/Special:BookSources/0980459907
" 0980459907.
http://books.google.com/books?id=dgB-
QWHlnrUC&pg=PA76&dq=Adamiecki+Gantt&as_brr=3&sig=J
p- mgVODNRJpxqBRM1PYJbs7mOU.
Peter W. G. Morris, The Management of Projects, Thomas
Telford, 1994, ISBN 0727725939, Google Print, p.18)
There are two easy ways to create a Gantt chart to incorporate
in the status report for a project in this class: (1) use free
software, or (2) create a
table in MS Word or Corel WordPerfect.
http://en.wikipedia.org/wiki/Special:BookSources/0879600489
http://en.wikipedia.org/wiki/International_Standard_Book_Num
ber

p-mgVODNRJpxqBRM1PYJbs7mOU
http://en.wikipedia.org/wiki/Special:BookSources/0727725939
http://books.google.com/books?id=5ekyoWaeZ1UC&pg=PA18-
IA7&dq=Adamiecki+Gantt&as_brr=3&sig=xe_RAipoqlvhnu0xL
kIsxx-8OAQ
CREATING A GANTT CHART USING FREE SOFTWARE:
One free Gantt chart creator can be found on
http://www.ganttproject.biz/ and an example of its output
appears below:
This chart depicts milestones in completing “The Johnson
Genealogy Project.” The goal of the project is “to provide a

written history and genealogy
of the Johnson family from 1730 to the present for sale and
distribution to family and historical organizations.”
official sources or verified by at least one other source to be
considered
“firm” rather than “tentative.”
WHO said WHAT about an ancestor, WHEN it was said, and
HOW it was
known. “Traditional” stories may be used if labeled as such, but
every effort must be made to identify the SOURCE of the story.
generation should be developed for the book. For example, the
flu epidemic of
1917 impacted most Americans—did any Johnson contractor die
from the flu?
jects of photographs, portraits, and
related graphic items must be documented. The time period and
circumstances surrounding the picture should be described
wherever possible.
Note that the entire project is addressed in this depiction – not
merely the collection, processing, and verification of the
information involved. Note

also that the actual Gantt chart for a complex project would
have many more elements and the resulting interdependences
would also be included.
This depiction of a project leads to a NETWORK DIAGRAM,
also called a PERT CHART (Program Evaluation Review
Technique) or CRITICAL PATH
chart. All of these techniques are used in Project Management,
together with Lean Manufacturing concepts, including Six
Sigma. If you are writing
for managers using any of these applications, you should
become thoroughly familiar with them.
To insert a Gantt chart from this program into your text file,
export the completed chart as a JPG file and paste it in as a
picture.
http://www.ganttproject.biz/
CREATING A GANTT CHART USING TABLE TOOLS:
You can create a simple Gantt chart by creating a table in MS
Word or Corel WordPerfect. Because this involves creating a
cell for each unit of
time, we will reduce the detail to weeks and create a 13 by 9
cell table (which is NOT as precise as the Gantt Project
software, but will do for your
proposal to produce a researched proposal for a company or
community).

Now we will adjust the cell width and fill in the X and Y axes
information:
Johnson Family Book Dec Jan Feb
Week 1 2 3 4 1 2 3 4 1 2
Research Family
Get Pictures
Anecdotes
Verify
Draft
Review
Publish

Finally, we can adjust lines, color cells to distinguish different
activities and their specific durations, and remove the lines
between the cells that are
colored to represent the activities (using the “merge cells”
command). Here is the finished product:
OHNSON AMILY OOK Dec
Jan
Feb
Week 1 2 3 4 1 2 3 4 1 2
Research Family
Get Pictures
Anecdotes
Verify

Draft
Review
Publish
Note that the activities that take less time than the time period
selected (in this example, one week) lose their accuracy in this
scale (note the Review
and Publish time lines); however, using a cell to represent a day
would create a 76-cell width which, if reduced, would result in
a Gantt chart that
would be too small to read.
The number of steps required to explain the sequence and
relationship of tasks you will need to complete to turn in your
researched proposal on
time are small and the time can be expressed accurately enough
in whole weeks, so the table version is adequate as a planning
effort for this
assignment.
The Gantt Chart is a very useful planning and status checking
tool that can keep a manager on track in completing a complex
project on time. A
good Gantt Chart (one that includes all of the key steps needed
to complete a project) can avert disaster as you complete a
complex project
bounded by non-negotiable time constraints (such as a paper

due on a specific day).
PERT CHARTS
A PERT chart is a project management tool used to schedule,
organize, and coordinate tasks within a project. PERT stands for
Program Evaluation
Review Technique, a methodology developed by the U.S. Navy
in the 1950s to manage the Polaris submarine missile program.
A similar
methodology, the Critical Path Method (CPM) was developed
for project management in the private sector at about the same
time.
A PERT chart presents a graphic illustration of a project as a
network diagram consisting of numbered nodes (either circles or
rectangles) representing
events, or milestones in the project linked by labeled vectors
(directional lines) representing tasks in the project. The
direction of the arrows on the lines
indicates the sequence of tasks. In the diagram, for example, the
tasks between nodes 1, 2, 4, 8, and 10 must be completed in
sequence. These are
called dependent or serial tasks. The tasks between nodes 1 and
2, and nodes 1 and 3 are not dependent on the completion of one
to start the other

and can be undertaken simultaneously. These tasks are called
parallel or concurrent tasks. Tasks that must be completed in
sequence but that don't
require resources or completion time are considered to have
event dependency. These are represented by dotted lines
with arrows and are called dummy activities. For example, the
dashed arrow linking nodes 6 and 9 indicates that the system
files must be
converted before the user test can take place, but that the
resources and time required to prepare for the user test (writing
the user manual and
user training) are on another path. Numbers on the opposite
sides of the vectors indicate the time allotted for the task.
The PERT chart is sometimes preferred over the Gantt Chart,
another popular project management charting method, because it
clearly illustrates
task dependencies. On the other hand, the PERT chart can be
much more difficult to interpret, especially on complex
projects. Frequently,
project managers use both techniques. (
http://searchsoftwarequality.techtarget.com/definition/PERT-
chart)
APPLICATION EXAMPLE:

At the CIA, Strategic Arms Limitation Treaty (SALT)
compliance verification required analysis of overhead
photography to discover any alteration
to Soviet missile silos (nuclear warheads were larger, requiring
visible construction modifications). Discrepancies spotted then
required a check of
millions of photographs by six analysts requiring at least 72
hours (432 analyst hours). I developed a PERT program that
allowed one analyst to
recover critical stage photos in less than two hours. This chart
depicted visible stages in the construction process, the time
required for each
stage, with other factors including weather and holiday stand-
downs. One analyst could search backwards from the date of the
photo depicting
the current stage of modifications to the silo by searching only
the dozen or so photos from the most likely date for the
preceding identifiable
stage. While it could be argued by the Soviets that a single
photo did not represent a violation; an aggregate of photos
showing the stages of
modifying the silo could not be contested.
http://searchsoftwarequality.techtarget.com/definition/PERT-
chart
Statistics
Using
Technology
By Kathryn Kozak

Photo taken by Richard Kozak at Dorrigo National Park in
NSW, Australia
Creative Commons Attribution Sharealike. This license is
considered to be some to be
the most open license. It allows reuse, remixing, and
distribution (including commercial),
but requires any remixes use the same license as the original.
This limits where the
content can be remixed into, but on the other hand ensures that
no-one can remix the
content then put the remix under a more restrictive license.
2014 Kathryn Kozak
ISBN: 978-1-312-18519-7
Statistics Using Technology
i
Table of Content:
Preface iii
Chapter 1: Statistical Basics 1
Section 1.1: What is Statistics? 1

Section 1.2: Sampling Methods 8
Section 1.3: Experimental Design 14
Section 1.4: How Not to Do Statistics 19
Chapter 2: Graphical Descriptions of Data 25
Section 2.1: Qualitative Data 25
Section 2.2: Quantitative Data 36
Section 2.3: Other Graphical Representations of Data 56
Chapter 3: Numerical Descriptions of Data 71
Section 3.1: Measures of Center 71
Section 3.2: Measures of Spread 83
Section 3.3: Ranking 99
Chapter 4: Probability 111
Section 4.1: Empirical Probability 111
Section 4.2: Theoretical Probability 114
Section 4.3: Conditional Probability 130
Section 4.4: Counting Techniques 142
Chapter 5: Discrete Probability Distributions 147
Section 5.1: Basics of Probability Distributions 147
Section 5.2: Binomial Probability Distribution 156
Section 5.3: Mean and Standard Deviation of Binomial
Distribution 169
Chapter 6: Continuous Probability Distributions 175
Section 6.1: Uniform Distribution 175
Section 6.2: Graphs of the Normal Distribution 178
Section 6.3: Finding Probabilities for the Normal Distribution
181

Section 6.4: Assessing Normality 190
Section 6.5: Sampling Distribution and the Central Limit
Theorem 202
ii
Chapter 7: One-Sample Inference 215
Section 7.1: Basics of Hypothesis Testing 215
Section 7.2: One-Sample Proportion Test 228
Section 7.3: One-Sample Test for the Mean 234
Chapter 8: Estimation 247
Section 8.1: Basics of Confidence Intervals 247
Section 8.2: One-Sample Interval for the Proportion 250
Section 8.3: One-Sample Interval for the Mean 255
Chapter 9: Two-Sample Inference 265
Section 9.1: Paired Samples for Two Means 265
Section 9.2: Independent Samples for Two Means 284
Section 9.3: Two Proportions 306
Chapter 10: Regression and Correlation 317
Section 10.1: Regression 317
Section 10.2: Correlation 336

Section 10.3: Inference for Regression and Correlation 344
Chapter 11: Chi-Square and ANOVA Tests 359
Section 11.1: Chi-Square Test for Independence 359
Section 11.2: Chi-Square Goodness of Fit 375
Section 11.3: Analysis of Variance (ANOVA) 382
Appendix: Critical Value Tables 395
Table A.1: Normal Critical Values for Confidence Levels 396
Table A.2: Critical Values for t-Interval 397
Index 398
iii
Preface:
I hope you find this book useful in teaching statistics. When
writing this book, I tried to
follow the GAISE Standards (GAISE recommendations. (2014,
January 05). Retrieved
from
http://www.amstat.org/education/gaise/GAISECollege_Recomm
endations.pdf
), which are
1.) Emphasis statistical literacy and develop statistical
understanding.

2.) Use real data.
3.) Stress conceptual understanding, rather than mere
knowledge of procedure.
4.) Foster active learning in the classroom.
5.) Use technology for developing concepts and analyzing data.
To this end, I ask students to interpret the results of their
calculations. I incorporated the
use of technology for most calculations. Because of that you
will not find me using any
of the computational formulas for standard deviations or
correlation and regression since
I prefer students understand the concept of these quantities.
Also, because I utilize
technology you will not find the standard normal table,
Student’s t-table, binomial table,
chi-square distribution table, and F-distribution table in the
book. The only tables I
provided were for critical values for confidence intervals since
they are more difficult to
find using technology. Another difference between this book
and other statistics books is
the order of hypothesis testing and confidence intervals. Most
books present confidence
intervals first and then hypothesis tests. I find that presenting
hypothesis testing first and
then confidence intervals is more understandable for students.
Lastly, I have de-
emphasized the use of the z-test. In fact, I only use it to
introduce hypothesis testing, and
never utilize it again. You may also notice that when I
introduced hypothesis testing and
confidence intervals, proportions were introduced before means.
However, when two
sample tests and confidence intervals are introduced I switched

this order. This is
because usually many instructors do not discuss the proportions
for two samples.
However, you might try assigning problems for proportions
without discussing it in class.
After doing two samples for means, the proportions are similar.
Lastly, to aid student
understanding and interest, most of the homework and examples
utilize real data. Again,
I hope you find this book useful for your introductory statistics
class.
I want to make a comment about the mathematical knowledge
that I assumed the students
possess. The course for which I wrote this book has a higher
prerequisite than most
introductory statistics books. However, I do feel that students
can read and understand
this book as long as they have had basic algebra and can
substitute numbers into formulas.
I do not show how to create most of the graphs, but most
students should have been
exposed to them in high school. So I hope the mathematical
level is appropriate for your
course.
The technology that I utilized for creating the graphs was
Microsoft Excel, and I utilized
the TI-83/84 graphing calculator for most calculations,
including hypothesis testing,
confidence intervals, and probability distributions. This is
because these tools are readily
available to my students. Please feel free to use any other
technology that is more
appropriate for your students. Do make sure that you use some
technology.

iv
Acknowledgments:
I would like to thank the following people for taking their
valuable time to review the
book. Their comments and insights improved this book
immensely.
Jane Tanner, Onondaga Community College
Rob Farinelli, College of Southern Maryland
Carrie Kinnison, retired engineer
Sean Simpson, Westchester Community College
Kim Sonier, Coconino Community College
Jim Ham, Delta College
I also want to thank Coconino Community College for granting
me a sabbatical so that I
would have the time to write the book. Lastly, I want to thank
my husband Rich and my
son Dylan for supporting me in this project. Without their love
and support, I would not
have been able to complete the book.
Chapter 1: Statistical Basics
1

Section 1.1: What is Statistics?
You are exposed to statistics regularly. If you are a sports fan,
then you have the
statistics for your favorite player. If you are interested in
politics, then you look at the
polls to see how people feel about certain issues or candidates.
If you are an
environmentalist, then you research arsenic levels in the water
of a town or analyze the
global temperatures. If you are in the business profession, then
you may track the
monthly sales of a store or use quality control processes to
monitor the number of
defective parts manufactured. If you are in the health
profession, then you may look at
how successful a procedure is or the percentage of people
infected with a disease. There
are many other examples from other areas. To understand how
to collect data and
analyze it, you need to understand what the field of statistics is
and the basic definitions.
Statistics is the study of how to collect, organize, analyze, and
interpret data collected
from a group.
There are two branches of statistics. One is called descriptive
statistics, which is where
you collect and organize data. The other is called inferential
statistics, which is where
you analyze and interpret data. First you need to look at
descriptive statistics since you
will use the descriptive statistics when making inferences.

To understand how to create descriptive statistics and then
conduct inferences, there are a
few definitions that you need to look at. Note, many of the
words that are defined have
common definitions that are used in non-statistical terminology.
In statistics, some have
slightly different definitions. It is important that you notice the
difference and utilize the
statistical definitions.
The first thing to decide in a statistical study is whom you want
to measure and what you
want to measure. You always want to make sure that you can
answer the question of
whom you measured and what you measured. The who is known
as the individual and
the what is the variable.
Individual – a person or object that you are interested in finding
out information about.
Variable (also known as a random variable) – the measurement
or observation of the
individual.
If you put the individual and the variable into one statement,
then you obtain a population.
Population – set of all values of the variable for the entire group
of individuals.
Notice, the population answers who you want to measure and
what you want to measure.
Make sure that your population always answers both of these
questions. If it doesn’t,
then you haven’t given someone who is reading your study the

entire picture. As an
example, if you just say that you are going to collect data from
the senators in the U.S.
2
Congress, you haven’t told your reader want you are going to
collect. Do you want to
know their income, their highest degree earned, their voting
record, their age, their
political party, their gender, their marital status, or how they
feel about a particular issue?
Without telling what you want to measure, your reader has no
idea what your study is
actually about.
Sometimes the population is very easy to collect. Such as if
you are interested in finding
the average age of all of the current senators in the U.S.
Congress, there are only 100
senators. This wouldn’t be hard to find. However, if instead
you were interested in
knowing the average age that a senator in the U.S. Congress
first took office for all
senators that ever served in the U.S. Congress, then this would
be a bit more work. It is
still doable, but it would take a bit of time to collect. But what
if you are interested in
finding the average diameter of breast height of all of the
Ponderosa Pine trees in the
Coconino National Forest? This would be impossible to

actually collect. What do you
do in these cases? Instead of collecting the entire population,
you take a smaller group of
the population, kind of a snap shot of the population. This
smaller group is called a
sample.
Sample – a subset from the population. It looks just like the
population, but contains less
data.
How you collect your sample can determine how accurate the
results of your study are.
There are many ways to collect samples. Some of them create
better samples than others.
No sampling method is perfect, but some are better than others.
Sampling techniques
will be discussed later. For now, realize that every time you
take a sample you will find
different data values. The sample is a snapshot of the
population, and there is more
information than is in the picture. The idea is to try to collect a
sample that gives you an
accurate picture, but you will never know for sure if your
picture is the correct picture.
Unlike previous mathematics classes where there was always
one right answer, in
statistics there can be many answers, and you don’t know which
are right.
Once you have your data, either from a population or a sample,
you need to know how
you want to summarize the data. As an example, suppose you
are interested in finding
the proportion of people who like a candidate, the average
height a plant grows to using a

new fertilizer, or the variability of the test scores.
Understanding how you want to
summarize the data helps to determine the type of data you want
to collect. Since the
population is what we are interested in, then you want to
calculate a number from the
population. This is known as a parameter. As mentioned
already, you can’t really collect
the entire population. Even though this is the number you are
interested in, you can’t
really calculate it. Instead you use the number calculated from
the sample, called a
statistic, to estimate the parameter. Since no sample is exactly
the same, the statistic
values are going to be different from sample to sample. They
estimate the value of the
parameter, but again, you do not know for sure if your answer is
correct.
3
Parameter – a number calculated from the population. Usually
denoted with a Greek
letter. This number is a fixed, unknown number that you want to
find.
Statistic – a number calculated from the sample. Usually
denoted with letters from the
Latin alphabet, though sometimes there is a Greek letter with a
^ (called a hat) above it.
Since you can find samples, it is readily known, though it
changes depending on the

sample taken. It is used to estimate the parameter value.
One last concept to mention is that there are two different types
of variables – qualitative
and quantitative. Each type of variable has different parameters
and statistics that you
find. It is important to know the difference between them.
Qualitative or categorical variable – answer is a word or name
that describes a quality
of the individual.
Quantitative or numerical variable – answer is a number,
something that can be
counted or measured from the individual.
Example #1.1.1: Stating Definitions for Qualitative Variable
In 2010, the Pew Research Center questioned 1500 adults in the
U.S. to estimate
the proportion of the population favoring marijuana use for
medical purposes. It
was found that 73% are in favor of using marijuana for medical
purposes. State
the individual, variable, population, and sample.
Solution
:
Individual – a U.S. adult
Variable – the response to the question “should marijuana be
used for medical

purposes?” This is qualitative data since you are recording a
person’s response –
yes or no.
Population – set of all responses of adults in the U.S.
Sample – set of 1500 responses of U.S. adults who are
questioned.
Parameter – percentage who favor marijuana for medical
purposes calculated
from population
Statistic– percentage who favor marijuana for medical purposes
calculated from
sample
Example #1.1.2: Stating Definitions for Qualitative Variable
A parking control officer records the manufacturer of every 5th
car in the college
parking lot in order to guess the most common manufacturer.

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