University of Arizona
Institute for Mathematics and Education

April 6, 2010

The Data Says What?! Applying Data Analysis to a Complicated World presented by Sarah Hoffman

Sarah Hoffman provided data from the 2010 winter olympics for four countries: Canada, Germany, Norway, and the United States. Participants were separated into four groups. Each group was assigned one of the four countries and challenged to use the data provided to present a case for why their country "won" the olympics. The groups took turns presenting their arguments. This was an excellent example of how different conclusions can be drawn from the same data set.

After dinner, participants examined six different histogram distributions of results from 10-point quizzes. Using each graph, we were challenged to determine what the average score was.

Sarah presented numerous examples from media sources with questionable use of averages to draw conclusions. We discussed what the data really meant, as far as we could tell.

During the last election, some political analysts used a Starbucks to Walmart ratio to predict how Democratic or Republican a state is. We discussed why this information might be used and what assumptions might be the impetus for using them.
Finally, we plotted data and used trendlines. Sarah presented several examples of practical data sets that have very strong correlations, yet no causality between them. Hidden variables were at work in each case.
Click here for a copy of Sarah Hoffman's Handout.

The evening's activities and discussions directly related to statistics and data analysis. Some of the AIMS Standards addressed include:
MS2C1-01 Solve problems by selecting, constructing and interpreting displays of data.
MS2C1-01 Interpret trends in a data set, estimate values for missing data, and predict values for points beyond the range of the data set.
MS2C1-02 Formulate and answer questions by interpreting, analyzing, and drawing inferences from displays of data.
MS5C2-03 Analyze and compare mathematical strategies for efficient problem solving.
MS5C2-04 Apply a previously used problem-solving strategy in a new context.
MS5C2-05 Represent a problem situation using multiple representations, describe the process used to solve the problem, and verify the reasonableness of the solution.
MS5C2-06 Communicate the answer to a question in a problem using appropriate representations.
MS5C2-07 Isolate and organize mathematical information taken from graphs to make inferences and draw conclusions; and justify reasoning.
MS5C2-08 Make and test conjectures based on information collected from explorations and experiments.

Sarahintro wholegrp Carolyn&Eric
Sarah Hoffman introduces the winter olympics data.Participants worked in groups to analyze data.Carolyn Hollis and Eric Welch search
the web for more details.

Michael&Chris SarahGroupCarrie&Jen
Michael Warrick and Chris Loria explain why the U.S. "won" the olympics.Sarah listens as a group
explains their arguments.
Carrie Wright and Jen Eli work
together on the data.