Park City Mathematics Institute
Data, Statistics, and Probability

Our Backpack Data: Making Conclusions from Graphs
by William Thill


Teacher Notes:
MS Word || PDF format

Student Activity:
MS Word || PDF format

Student File: Fathom™ file

Group activity: students match different statistical questions from backpack data to an appropriate visual display. They choose graphs to answer the questions and make well-justified conclusions about each question. As an extension, students may create a new question, choose (or create) two graphs to answer the question, and make conclusions based on the graphs.

9 - 12


40-50 minutes for activity

Part I is designed to be done in groups of two or three. Part II can be done as a whole-class discussion. Part III is an extension activity that can be assigned individually.

    A set of Student Pages for each student
    A set of Graphs A-H for each group
    A Response Sheet (made using the Response Template) for each question for each group
    (Optional) Computer with Fathom™ 2 software for Part III (Extensions)

  • To introduce a variety of one-variable and two-variable displays of data
  • To choose appropriate visual displays to answer questions from a study
  • To discover multiple ways of reading a visual display, and to answer multiple questions from a single display
  • To communicate clear, responsive conclusions to a statistical question
  • To use and communicate clear evidence for conclusions
  • To generate new questions, make appropriate visual displays, and use them to make well-justified and clearly communicated evidence
  • Familiarity with a variety of visual displays: dot plot, histogram, box plot, scatter plot, two-way tables and plots, percentiles
  • Familiarity with the idea of describing a distribution by its shape, center, and spread
  • Familiarity with comparing groups, making conclusions about groups with evidence
  • Understanding the meaning of a percentile, relative frequency
  • Analyzing the information in a visual display

Students do not need access to Fathom to complete Parts I and II of this activity. Part III, however, requires students to make graphs, create attributes, and use the formula editor. Access to Fathom is recommended for Part III.

If Fathom is used, students must be able to define attributes using conditional functions, and experiment with a variety of graphs to explore answer to questions they generate.

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This material is based upon work supported by the National Science Foundation under DMS-0940733 and DMS-1441467. 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.