Park City Mathematics Institute
Reasoning and Data and Chance
Project Abstracts

Drafts of Project Files (password required)

iSleuthing with iTunes Data
Faye Chiu, Richard Stewart*, and Judith Carlin

This group activity requires students to examine and analyze a collection of iTunes data. Students will make observations about the data and use statistics from each music library to identify library owners. Students will engage in small group discussions and justify their findings using evidence from statistical analysis and interpretation of visual displays in creative or unconventional ways.

Level A: collecting data, analyzing data, interpretation
Level B: analyzing data, interpretation
Level C: question formulation, analyzing data, interpretation
How Does the Sample Size Affect the Understanding of the Population?
Dave Goodwin

This is a summery activity to help students see how the size of a sample affects the relationship between the population mean and the sample mean. This activity is designed to use Fathom® (or TI-83/84 calculators) to quickly generate many samples from a population, of varying sizes, in order to compare the difference of the sample mean and the population mean. This activity is intended to reinforce student's understanding of the effect of sample size rather that to create an understanding, and should only be done after a more concrete exploration has been done with physical manipulatives.

Sneaker Survey
Ana Pamela Castro, Craig Morgan*

In this group activity the students will survey their peers to investigate the following items: gender, brand of sneakers and shoes size of 7th grade students. After the initial classroom activity, the students will receive a blank handout with a table containing the elements of the survey. They will then gather data from their peers. Using the data, groups of students will process the information, choose graphs that would be most appropriate, and make well-justified conclusions about the probing question. Students are expected to base their conclusions on specific evidence from the data they gathered and the graph(s) or tables they choose. Using this data, the students are expected to answer the probing question and will be able to compare the different conclusions and discuss the different solutions with their classmates. Teacher will use the Fathom® software program and show results to students. If Fathom® is available to students, they are to follow directions to complete Fathom® activity. To conclude, the students will be able to predict by using the graphs and the tables to answer the final question by group presentation.

Backpack Data Extended
William Thill

This activity is designed to be a first lesson in understanding the concept of a data distribution. Students in a single class will weigh their backpacks and record the information in a table. After learning key principles in constructing a simple data display (a dot plot), they will be asked questions that help them understand two fundamental characteristics of a distribution: How does "average" apply for a sample of data? How much variation exists from the average? No numerical summaries are assumed for this activity. In fact they are deliberately omitted from the discussion in order to help students develop an understanding of these ideas without a reliance on formulas.

Hotdog
Ekponwan Ebong, Richard Opaka Awichi

Teaching statistics meaningfully involves providing students with experiences that enable them to make sense of statistical ideas. Using Fathom® and hotdog related data, students can create various types of graphs including histograms, scatter plots, line plots, and box plots. Students can compare hotdog brands to determine which one is healthier.

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IAS/Park City Mathematics Institute is an outreach program of the School of Mathematics
at the Institute for Advanced Study, Einstein Drive, Princeton, NJ 08540

Send questions or comments to: Suzanne Alejandre and Jim King

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This material is based upon work supported by the National Science Foundation under Grant No. 0314808.
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.