
Park City Mathematics Institute
Data, Statistics, and Probability

Our Backpack Data: Making Conclusions from Graphs
by William Thill
Download:
Teacher Notes:
MS Word  PDF format
Student Activity:
MS Word  PDF format
Student File: Fathom™ file

WHAT IS IT?
Group activity: students match different statistical questions from backpack data to an appropriate visual display. They choose graphs to answer the questions and make welljustified 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.
GRADE LEVEL
9  12
STRAND
Statistics
CLASS TIME
4050 minutes for activity
SETTING
Part I is designed to be done in groups of two or three. Part II can be done as a wholeclass discussion. Part III is an extension activity that can be assigned individually.
MATERIALS
A set of Student Pages for each student
A set of Graphs AH 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)

OBJECTIVES
 To introduce a variety of onevariable and twovariable 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 welljustified and clearly communicated evidence
PREREQUISITES
Statistics:
 Familiarity with a variety of visual displays: dot plot, histogram, box plot, scatter plot, twoway 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
Fathom:
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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IAS/Park City Mathematics Institute is an outreach program of the Institute for Advanced Study, 1 Einstein Drive, Princeton, NJ 08540
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With program support provided by Math for America
This material is based upon work supported by the National Science Foundation under DMS0940733 and DMS1441467. 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.
