Writing Intensive Statistics Course

Dr. Renan Sezer

LaGuardia Community College

Why Write?

Write to learn

Improve communication skills

Develop analytical reading ability

Develop ability to interpret result

Frequent feedback

Writing Exercises

Low stake writing assignments

Lead Up or Follow Up

“Staged” high stake writing assignments

Outcomes

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? 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)

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. Find the mode, median, mean income in this company.

2. The union representative wants to negotiate new wages. In this negotiation would he emphasize mode, median or mean? Explain why in a paragraph.

3. Which of the three measures would the president of the company stress in the negotiations? Explain why in a paragraph.

4. Which do you think best represents this sample? Explain why in a paragraph.

5. 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.

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)

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)

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.

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.

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)

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) 

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.

 

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?

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?

  Find Diane’s percentile and Tom’s percentile.

Writing Assignment VI (Week 8)  Often in real life it is almost impossible to find the

mean of a large population.

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?

B)   Does the method that you describe in part A take into consideration the possible occurrence of great numbers of outliers?

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)

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) 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)

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.

  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.

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.

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 ?

Workload? Time? Class size? Other?

YOU CAN FIND THIS INFORMATION IN OUR COURSE WEB SITE:

http://faculty.lagcc.cuny.edu/rsezer/