Data Analysis, Statistics and Probability Summary

Monday - Friday, July 4 - 8, 2005

On Tuesday, a full group discussion was held in order to identify a narrower list of topics from the brainstorming session held on Friday.

Oscar, Meiling and Judi decided to create a Fathom™ document relating to the Dietary Change in Cholesterol activity that is found in the NCTM Navigation series on Data and Probability. Oscar also mentioned an article on math and medicine found at the following web address. http://chance.dartmouth.edu/chancewiki/index.php/Mix_math_and_medicine_and_create_confusion

Matt C developed a simulation using "Let em Roll" from the Price is Right.

Damein and Youngson are looking into game simulation.

Seth, Matt B, Arnell and Jerry are looking at using census data in a variety of ways. Jerry also mentioned trying to use Fathom™ to explore Fibonacci.

The remainder of the time was spent working in small groups on the topics identified earlier in the session.

On Wednesday, the group reported on their progress to date. Meiling, Oscar and Judi are working on a simulation. They are using Fifty Fathoms as a resource. (Fifty Fathoms is resource book for AP Stat level.) There is a section in back on with step by step instructions on how to program in Fathom™. Carol reminded the group there is a Fathom™ user group where they can ask questions, if the help menu was not helpful!

[Note from Suzanne: Because the Fathom Discussion is hosted by the Math Forum you use the same login information as you use for the PCMI Discussion. The difference is that it is not a "private" discussion and so you can view it also as a "guest." If you login you can Watch a User (for example if Tim Erickson or Bill Finzer post you can set it to notify you) and other customizable features.

Carol and Beverly had sent an email requesting information on restricting the domain and range of a function. Within about 30 minutes Tim Erickson had sent a response with two possible solutions. Here is his response:

>Is it possible to restrict the domain of a function when using
>the function plot? If it can be done, how does one go about doing it?
>Thanks for your help

You bet!

In your definition for the function, use an IF statement.

For example, suppose you wanted y = x^2 for x > 0 and nonexistent otherwise.
You might use (allowing for not sending a graphic....)

y = IF(x > 0) { (top) x^2 : (bottom) "" }

NOTE that I use the double-quote (as for a string) but leave it empty (the empty string, Fathom™'s "null" object), for the region where the function is undefined.

TIP: You can also use the built-in function InRange(), as in

IF (InRange(x, 0, 1) , 2, "") for a function that is 2 in [0, 1) and nonexistent elsewhere.

Another note: you can, of course, use this "if" technology to define piecewise functions as well as those with limited domains.

Whee!
Tim

------------------------------------
Tim Erickson * Epistemological Engineering
5269 Miles Avenue, Oakland CA 94618 * 510.653.3377
http://www.eeps.com

Carol has tried the first method but has had difficulty with the InRange command. If you can't find in the help menu email them from the following address: http://www.keypress.com/fathom/pages/community_exchange/email_discussion_list.php This is a good discussion group, you won't get tons of emails.

Another group is using the census in a variety of ways. Arnell was interested in what attributes could be imported and would like to work on correlation similar to prior year's projects. Jerry is looking into the relationship between level of education and income. He has restricted the sample to 16 - 65, working years, using a filter. The graphs and charts seem to be a trend but would like to stratify more.

Matt B is looking at immigrant population vs. natural population. He will begin with informal polls with student and give them time to play with it. He also mentioned an article that Oscar found on the topic http://chance.dartmouth.edu/chancewiki/index.php/Misperception_of_minorities_and_immigrants

Carol told us about an experience she had at her school when going through accreditation. Her students did an analysis of the school population and processed in Fathom™. It was almost a census as 1500 out of 1650 students responded. One issue they looked at was in response to a concern that students of color lack access to computers. It turned out that access to computers and the Internet was not true at her school. Students were surprised at the results but when asked to look at the composition of the community, they realized why the results were the way they were. The group was reminded that polls are done in areas that have a variety of people in order to be accurate.

Seth is looking into racial identity. There was a change in requesting this from the 1990 and 2000 census. He wondered if there was a difference in the concept of identity because of how the question is asked on the census. He then wants to extend this to an in school survey to see how the class fills out the census forms. How does the census try to incorporate this?

Matt C is looking into a game from The Price is Right. It involves rolling 5 dice to see what the probability a contestant will win a car provided all 5 dice show a car on the face. He has emailed them to see about getting a video clip.

Demain and Youngson are incorporating sliders as a way to create an image and restricted domain to control the shape. They had experienced some difficulty in restricting the domain but later figured it out on their own.

Thursday and Friday were spent working on the ideas talked about on Wednesday.

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This material is based upon work supported by the National Science Foundation under Grant No. 0314808 and Grant No. ESI-0554309. Any opinions, findings, and conclusions or recommendations expressed in this material are those of the author(s) and do not necessarily reflect the views of the National Science Foundation.