Math 114Q - Quantitative Reasoning

Fall 2008, Sections 9 and 11

Term Paper

Note: what follows is a working draft, not yet final. The ideas won't change much. The details might.

In this assignment, you will choose a topic, find some data and quantitative information about it, perhaps form a hypothesis, explore some "what-if" questions, make some estimates, do some data analysis, and make some conclusions. In other words, you will use many of the techniques and ideas of this course to make a quantitative analysis of a topic that is interesting to you. The goal is to write this up as paper, including any graphs and calculations that support your work.

This is a serious assignment, and we expect you to take the time and effort to do it well. We have outlined a series of due dates to help you stay on track with the assignment. As we see many times in class, a good approach to a challenging assignment is to break it down into small and manageable pieces. We have done some of this work for you by setting these due dates. We expect you to take the same approach with the work involved in organizing your information, analyzing it, and writing up the results. Please feel free to talk with us if you are struggling with this. We are happy to read drafts and point you to information or topics.

Due dates

• Thursday, October 9: Turn in a typewritten description of your choice of topic. This should include preliminary questions you will try to answer and ideas about where you will find the data you need. You should list at least three different sources, and at least one of these sources must be a print source.
• Thursday, November 6: By this date, you must turn in a typed outline of your paper (or a rough draft, if you have made it this far). This should include a tentative organization of the paper, a list of carefully formulated questions about your topic, some data that you have collected and analyzed, and some possible answers to questions. All sources need to be clearly specified. This should be typed.
  
• Thursday, November 20: Turn in a rough draft of your paper. This draft should include the analysis of data or information, the answers to your questions, and an overview of your conclusions. It should be typed, with all necessary graphs and data included. References should be clearly listed.
• Thursday, December 4. Final submission. The final version of the paper is due today. E-mail submissions will not be accepted. It is your responsibility to proofread and spellcheck your paper.

How will we grade this paper?

Here is what we will look for when we grade your paper:

• Did you follow the basic instructions and meet the deadlines?
• Does your paper have a solid introduction and does it state your hypothesis or theme? Does it have a good conclusion that summarizes what you did?
• Does your paper include an exploration of the data? Did you look at some "what-if" questions and try to answer them, either using Excel or by looking for other information? Do you describe this carefully and clearly in your paper?
• Are your statements supported by the data and by the analysis you did?
• Is the mathematics correct? Did you include units, when necessary, and make correct and complete statements?
• Are the graphics visually appealing, easy to read, and properly labeled?
• Did you interpret the graphics for the reader, and highlight important details from the graphs and charts?
• Did you cite your references using one of the standard styles? See for a guide to properly citing sources in papers.
• Is your paper typed, properly formatted, spell-checked?

How long should the paper be?

The correct answer is simply "as long as it needs to be to make your argument, not longer." So the actual length depends on the complexity of the questions you are asking.

We expect about 5 pages, double spaced (but not big type and large margins and almost all graphs). Of course your paper will include some graphs, but most of it will consiste of the words you choose to explain your questions and conclusions.

We are not assigning topics, since the most important part of the paper is that it be about something that you really care about.

What should I write about?

Here are some ideas suggested by classmates from previous semesters. (This is not a list for you to choose from, it's a guide as to the kinds of topics that might work.)

We've suggested a range of questions in each case. You need not address them all - they are meant to be places to begin.

• Should I trade in my gas guzzling car for a fuel-efficient hybrid?

  Even if you don't have a gas guzzler, pick a model and look up information about gas mileage. Use the price of gas to estimate weekly or monthly gas expenses for such a car. What other assumptions should you make?

  How much would it cost to buy a (new) hybrid car? Would you pay all of the cost at once or take a loan? At what interest rate? What kind of trade-in could you get for the used car?

  How would the mileage on the new car compare to the old car? With the savings from gas, how long would it take before the new car pays for itself? Would insurance and repair rates be the same for the new car? Investigate!

• Can I buy a house?

  Pick a community, find out what the range of real estate prices is there. Maybe track how it has changed over time.

  Find out how much a mortgage costs. There's a chance to use Excel here to draw a graph showing how the monthly payment depends on the interest rate and the length of time your mortgage is for. Or you can look for a web site that will do the computations for you. Maybe even one that will draw the graph. The important thing is to find the information and display and interpret it correctly. If Excel helps that's fine, but it's not required.

  How much will you need to borrow? What kind of a down payment can you make? Imagine some predictions about the amount of money you will earn, per year, as time goes on. (You probably won't be working at McDonald's any longer once you get your degree, so you can safely predict an increase in income.) What fraction of your income will/can you spend on housing? Speculate (quantitatively, of course) on the possible benefits of cutting back on some expenses for a while in order to borrow less or buy a better house.

  How might the other costs/benefits of home ownership influence a decision? (For example: cost of repairs and insurance, commuting costs from a house farther away, tax benefits of home ownership, likely increase in the value of your house.)

• Boston Celtics statistics.

  How does the Celtics' payroll relate to whether the team loses or wins? To salaries in the rest of the NBA? To changes in the value of the dollar over time? To star salaries in other sports? Does the range of salaries change over time?

  The data you collect for this project will suggest other questions along the way. The hard part might be limiting the discussion to a few questions you can find good answers to.

• The cost of owning a car.

  You can start with depreciation: find out (or estimate) what you could sell your car for at any age. (That's a little tricky.)

  What does it cost to own your car? Some annual costs are fixed, or nearly so, like insurance. Some depend on how far you drive (gas, tires, and, to a lesser extent, general wear and tear). If you've borrowed to buy the car, you have car payments. If you paid cash, then you're not collecting interest on that money, which you might have put into a certificate of deposit.

  Could you save money by taking public transportation when it was available, taking taxis and renting a car on other occasions? How do zip cars work, and would they suit you?

• Environmental impact of driving.
• Criminal Justice

  Several CJ majors thought about writing in that area. There are probably good topics available. You might talk with one of your CJ professors. Here are few ideas that occur to me.

  • What is the cost of incarceration? What are the main contributors to that cost? How much of what might be considered the CJ budget for the state or the country go toward supporting prisons? How have these numbers changed over time? How do they compare to what is spent elsewhere in the country or the world?
  • Discuss historical or regional or national trends in some statistics of interest.
• The obesity problem.

  What are the effects of obesity on life expectancy, cost of medical care (for individuals, and relative to total medical care spending), job productivity? How have these changed over time? Can you make any predictions?

• The prevelance of video games.

  How many people (and which people) own video game consoles? What kinds? How often do they replace them? How many hours do they spend? What's the economics? How do console costs and game costs compare? How do these statistics vary over time?

• Oil and gasoline prices

  Change over time (in constant dollars). Per capita consumption. Average automobile gas mileage. Number of miles driven per year (per person, per car).

  How does the price of oil relate to the price of gas? As the price of oil changes, how does this effect our economy (airline prices, price of food, etc.)?

  What other issues are important here? If people start conserving gas, will the price drop? What could happen then? What about alternate fuels -- what impact do they have on this problem?

• Cancer statistics.

  Incidence, mortality, testing and diagnosis. Smoking rates (hard to measure impact because of time delay).

• Credit card costs.

  Personal and societal. How much credit card debt is there? Does it vary by region, or by income level? How much interest is paid? How many bills are settled in full at the due date so no interest paid? How do any of these statistics change over time. Reading the fine print on your bill, or when you're offered a new card.

• Global warming (a hot topic these days).
• The gambling industry. Who wins? Who loses? How much? What are the odds for slot machines, blackjack, poker? Is there any skill involved?
• The statistics and economics of post Katrina homelessness in New Orleans.
• The value of a college degree.

What should the paper look like?

Here are some suggestions for structure (not topics)

• Did something you discovered surprise you? Did you start out thinking one thing and have to change your mind because the data told you otherwise? If so, that's a story.
• Did you find people arguing from the same (or similar) data to reach opposite (or different) conclusions? Or lying with statistics in ways we've seen? If so, you might speculate on their motives. Remember that noting that two things happened does not necessarily mean that one caused the other.
• Writing in the first person ("I thought", "I discovered") is OK. You don't need the anonymity of "they say" or "it is known that". (Of course just "I think" unsupported by quantitative reasoning isn't OK.)
• If you can frame your paper so that you actually enjoy writing it then it is much more likely to be a good paper.

Don't just go out and grab some numbers from the internet and paste them into a document. Your paper should tell a story - one you care about. It doesn't need to be long, but it does need to be interesting - we hope compelling. We would like to find out things we didn't know before - things that aren't generally accepted as common knowledge. So if you write a paper that says there are more poor people than rich people or that smoking causes cancer we won't be very impressed.

Be sure to acknowledge your sources. We will NOT be happy if pretty much everything comes from wikipedia, or from the first hit in your google search. Data you find on the web that comes from a real publication (rather than existing just on the internet) is generally more reliable. So you shpould acknowledge your sources' sources too: instead of "I found this at such-and-such-a-website" you should be able to say "The data at such-and-such-a-website comes from such-and-such a government publication(or scholarly study, or industry propaganda organization)" Use a standard style for citing references and see the suggested link in the section about grading for more information.

How can I get help?