Writing Intensive Statistics
Course
Dr. Renan Sezer
LaGuardia Community College
Why Write?
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Write to learn
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Improve communication skills
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Develop analytical reading ability
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Develop ability to interpret result
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Frequent feedback
Writing Exercises
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Low stake writing assignments
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Lead Up or Follow Up
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“Staged” high stake writing
assignments
Outcomes
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Better understanding of the concepts
Higher success rate on exams
Increased teacher-student interaction
Improved writing
Reduced fear of writing
What did the students say?
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77% - helpful in learning the subject better
85% - helped better prepare for the exam
69% - recommend such course for future
students
15% - not sure
15% - not recommend
Writing Assignment I (Week 1)
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A small company pays its president $200,000.
The vice-president gets $150,000. The foreman
earns $30,000. There are three workers in the
company, earning $25,000, $22,000, 22,000
respectively. The secretary earns $19,000.
1.
2.
3.
4.
5.
Find the mode, median, mean income in this
company.
The union representative wants to negotiate new
wages. In this negotiation would he emphasize
mode, median or mean? Explain why in a
paragraph.
Which of the three measures would the president
of the company stress in the negotiations? Explain
why in a paragraph.
Which do you think best represents this sample?
Explain why in a paragraph.
Can you say that the measure you chose in #4 is
always best to use? Explain why or why not in a
paragraph.
A Mediocre One:
1)
Mode = $22,000 (appears twice)
19,000, 22,000, 22,000, 25,000, 30,000,
150,000, 200,000
 Mean: 468,000 / 7 = $ 66,857
 Median: 19t, 22t, 22t, 25t, 30t, 150t, 200t
2)I think that the union representative would
want to base his petition on the mode salary.
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By doing this, using the mode, he can argue that
the three workers and the secretary are underpaid.
3) ? (I have no idea) but as a president of a company
I would be primarily concerned in the company’s
profits and not increasing my employees’ wages.
I would stress the mean since it a higher number
than the median or mode.
4) Median is best choice. I think that the mean
($66,857) wage is not a true representation of the
individual wages since there are such large
discrepancies among them, but then neither is the
mode or the median. There is no best
representation.
5) Since I feel that neither mean, mode or median
are of any use to best represent this sample: the
best choice would depend on job descriptions and
their respective hourly wages.
My answer probably makes no sense but neither
does this problem since union and management
are usually at odds when it comes
to coming to common ground when the
problem is about employee demands and
especially wages. The union wants better
wages and working conditions while
management is concerned about production
and profit margin. I do not feel that this
approach of using mean, mode and median
will help to solve the problem.
A Bad One:
1) a) Mode is $22,000
b) Mean is $3319714.2
The sam of all wages divited by 7
23238000 / 7 = 3319714.2
c) Median is $25000
2) The union representative who wants to
negotiate new wages has to emphazize
the median of that company. He has to
compare it with the standarts given by the
graph. By doing so, he can show that the
median of the company is far less than the
standarst.
3) The president of the company would stress
in the negotiations on the Mode because it
is close to the standarts given in the graph.
4) Median represents best this sample.
5) The measure that I chosed in this sample is
Median But, that doesn’t mean that it is
always the best to use because it is not
going to be fair in other circumstances.
Some times is better to use Mean.
Writing Assignment II (Week 2)
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Describe in your own words what mean and
standard deviation indicate. Give examples.
(Note: You are not asked to describe how mean
and standard deviation are calculated.)
Writing Assignment III (Week 3)
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Drug X has standard deviation of 3 days recovery time.
Drug Y has standard deviation of 7 days recovery time.
Based solely on this information which of the following
statements is true?
a) Drug X is a better drug than drug Y.
b) Drug Y is a better drug than drug X.
c) Drug X and drug Y are equally good.
d) No decision can be made.
Given the standard deviation above, suppose drug X has
mean recovery time of 30 days and drug Y has mean
recovery time of 15 days. Explain which drug is better.
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Given the standard deviation above, suppose drug
X has mean recovery time of 8 days and drug Y
has mean recovery time of 20 days. Explain
which drug is better.
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Looking back on your answers to previous
questions, write a paragraph about reaching a
decision based solely on standard deviation.
Writing Assignment IV (Week 4)
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Explain in your own words what it means for two events
to be independent. (You are not asked to give a formula.)
Give an example.
Explain in your own words what it means for two events
to be dependent. (You are not asked to give a formula.)
Give an example.
Explain in your own words what it means for two events
to be mutually exclusive. Be sure to use the concepts of
dependence and independence, which you have used in
part A, and B, in explaining mutually exclusive events.
Give an example.
Writing Assignment V (Week 7)
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It is impossible to set up a table giving areas of
regions lying beneath normal curves for each
different pair of means, , and standard
deviations, . Clearly one way to get around this
problem is to standardize the distribution so that
we can work with a normal curve having mean 0,
and standard deviation 1. Then, a single table will
be sufficient to estimate areas.
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Suppose that Tom and Diane are enrolled in two
different sections of a statistics class. Assume a
sufficiently large class size, so that the scores on
the first exam follow a normal distribution. In
Tom’s section, the average is 60 and his score is
72. In Diane’s section, the average is 71 and her
score is 83. Both are happy because their scores
are 12 points above the average of each respective
section. Who did better and why?
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Suppose that the standard deviations in
Diane’s section was =6.4 and in Tom’s
section was =6.5. Now who did better and
why?
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Find Diane’s percentile and Tom’s percentile.
Writing Assignment VI
(Week 8)
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Often in real life it is almost impossible to find
the mean of a large population.
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A) If you were a statistician and needed to find
the mean of a large population, what could you do
to estimate the population mean?
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B) Does the method that you describe in part A
take into consideration the possible occurrence of
great numbers of outliers?
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C) How might you modify or extend the method
you describe in part A to reduce the influence of
outliers on your estimate of the mean.
Writing Assignment VII (Week 9)
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Describe in your own words the (celebrated)
Central Limit Theorem. What assumptions must
be met in order to use its conclusions? Give an
example of a situation where the Central Limit
theorem may fail because of unmet assumptions
Writing Assignment VIII
(Week 10)
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Compare the graph of the normal distribution of x
(whole population) to the graph of the normal
distribution of (means of the samples that are
taken, that is, sample means). In your discussion
be sure to include comparison of the means,
standard deviations.
Could the two curves coincide exactly?
Writing Assignment IX (Week 11)
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Cancer patients using a certain treatment have an
average survival time of 2 years with a standard
deviation of 4 months. A physician claims that
his new method of treatment increases the
average survival time of patients, while keeping
the standard deviation the same.
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100 randomly chosen patients who received this
new treatment had an average survival time of 26
months.
1) What is the probability that 100 randomly chosen
patients had an average survival of 26 months or
more?
2)Interpret the result of problem 1 in a paragraph,
defending your reasoning whether the claim that
the new treatment is more effective or is bogus
(not more effective).
Steps For Completing The Final Project:
(1) Use the Internet to obtain sample data. There are many,
many possibilities here, depending mainly on you own
interests. The only restriction is that the data that you
choose must be part of a larger whole. For example, data
collected over the 50 states on teenage pregnancy would
be a natural sample of “national” teenage pregnancy.
Data collected over various countries could be a
reasonable sample of “global” data, but you would have
to be careful about country selection.
 Task assigned: week 1. Due date: Beginning of week 3.
Feedback: week 4.
(2) Compute the descriptive statistics for your
data (mean, mode, median, standard
deviation, minimum, maximum, quartiles),
and prepare a histogram and box plot.
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Task assigned: beginning of week 4. Due
date: beginning of week 5. Feedback: end of
week 5.
(3) Describe in your own words the data you have
chosen for your project, and why you have
selected it. What goals do you hope to achieve in
carrying out your project? Please include in this
writing a discussion of any formulas you will use
in the computation section to follow. Define the
variables used in the formulas.
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Task assigned: beginning of week 4. Due date:
beginning of week 7. Feedback: beginning of
week 9.
(4) Carry out the computation at a confidence level
of 95%.
 Task assigned: end of week 9. Due date: end of
week 11. Feedback: week 12.
(5) Write a cogent conclusion for your project and
submit the completed work to your teacher.
 Task assigned: end of week 9. Due date: end of
week 11. Feedback: week 12.
Questions ?
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Workload?
Time?
Class size?
Other?
YOU CAN FIND THIS INFORMATION
IN OUR COURSE WEB SITE:
http://faculty.lagcc.cuny.edu/rsezer/