# Interpreting Graphical Displays of Univariate Distributions

as part of its collaboration with the SERC Pedagogic Service.

#### Summary

## Learning Goals

- identify shape, center, and spread of histograms & stemplots
- interpret the "story" illustrated by the graphs (i.e. give the practical interpretation)
- critique others' interpretations of graphs

## Context for Use

This activity is appropriate for a college introductory statistics class of any size. The activity is based on a class size of 60 students and will take approximately 40 minutes. The size and number of groups can be modified to suit various needs.

Prior to this activity students should have been introduced to histograms & stemplots, including identifying shape, center, and spread.

## Teaching Materials

A Gallery Walk is a simple way to help students change their thoughts about what will happen in a class. Students often assume they should sit in their chairs and the professor will talk. A Gallery Walk gets students up and requires them to move about the classroom. During the activity they think about topics, express opinions, compose answers and critique the answers of other students. This particular example of a Gallery Walk has students providing practical interpretations and thinking critically about graphics (histograms and stem plots) of distributions. This activity is a good way to get students to begin thinking about the story behind the distribution.

In this activity, the instructor posts a series of graphics around the classroom with specific questions about those graphics. These graphics are arranged in clusters of 3 graphics at different parts of the room. Students form teams and rotate between stations. At each station, students answer open-ended questions about the graphics. Students post short bulleted answers to the questions. The groups then rotate to the next station. They add to the answers posted by the previous groups. As the students move to new stations, instructors may spur them to examine issues missed by previous items. This continues until students have seen all stations.

- Example Graphs for Gallery Walk (Microsoft Word 26kB Jun22 07)
- Solutions to Sample Graphs (Microsoft Word 35kB Sep10 07)
- Example of Student Responses to Sample Graphs (Acrobat (PDF) 77kB Sep13 07)
- In-class Student Handout (Microsoft Word 28kB Sep10 07)
- Take-home Student Assignment (Microsoft Word 31kB Jul18 06)

## Teaching Notes and Tips

Preparation:

- Gallery Walk instructions.
- Consider how the students will be grouped and clustered. It is helpful to prenumber the group handouts with the group number. In this example groups will rotate within a "cluster" of 3 groups.
- Plan the positioning of the graphs in the classroom (i.e. How many stations per cluster? How many clusters? etc.).
- Prepare copies of the graphs for each "cluster".
- Prepare copies of the group handout for each group.
- Prepare copies of the student take-home assignment for each student.
- Think about possible student responses and be prepared to prompt students for missing information. Sample student responses from a classroom trial are provided in the teaching materials section.

Progression:

- Break students into groups of no more than 5, then distribute the group handout.
- Form "clusters" of three groups and assign each cluster to a station. Every group will provide an interpretation for all three situations. At the beginning, interpretations should be left open ended to encourage thought and discussion. Allow approximately 10-15 minutes for groups to develop their interpretations.
- Assign each group to a graph for which they will post their interpretation. Allow approximately 3-5 minutes for posting.
- Students will now rotate graphs within their cluster, critiquing the interpretations posted by other groups. To help generate ideas for critiquing, instruct students on things to look for when critiquing. (i.e. Does the interpretation address shape, center, and spread including outliers?) Allow approximately 3-5 minutes per graph.
- After critiques are finished, pass out the student take-home assignment. Groups now rotate back to their posted interpretation and record their interpretation and peer critiques on their take-home assignment. Allow approximately 3-5 minutes to record this information. It might also be useful to allow students to take the postings back to their seat and copy the results.
- If time allows, bring the students back together as a class and discuss the general ideas of what to look for in graphics and ask for student comments on how to interpret the "story behind the data."