# Histogram Sorting Using Cooperative Learning

### This activity has been undergone anonymous peer review.

This activity was anonymously reviewed by educators with appropriate statistics background according to the CAUSE review criteria for its pedagogic collection.

This page first made public: Nov 16, 2006

This material is replicated on a number of sites as part of the SERC Pedagogic Service Project

#### Summary

Using cooperative learning methods, this activity provides students with 24 histograms representing distributions with differing shapes and characteristics. By sorting the histograms into piles that seem to go together, and by describing those piles, students develop awareness of the different versions of particular shapes (e.g., different types of skewed distributions, or different types of normal distributions), and that not all histograms are easy to classify. Students also learn that there is a difference between models (normal, uniform) and characteristics (skewness, symmetry, etc.).

## Learning Goals

## Context for Use

## Description and Teaching Materials

The following website can be used for a follow-up debriefing activity: http://www.tc.umn.edu/~delma001/stat_tools/. Detailed lesson plan of how to use cooperative learning for this activity. (Acrobat (PDF) 32kB Jun30 06)

## Teaching Notes and Tips

See "Histogram Sorting Using CL Lesson" file for specific directions about teaching this lesson using Cooperative Learning strategies.

Time Involved:

- 5 minutes to introduce the activity

- 10-15 minutes for students to work in groups, sorting graphs

- 10 minutes for instructor-led discussion of graphs

- 5 minutes for follow up questions

Practical Tips:

- Each group of students will need one set of histograms. Make sure

you have enough sets of histograms for the number of groups in

your classroom.

- The activity works best BEFORE students have formally studied different shapes of graphs.

- Typically, students will sort their graphs into the following categories: uniform, normal, skewed, and bimodal. There may also be some smaller groupings such as right skewed and left skewed.

- Students often find the uniform and normal graphs easiest to sort. The also find unimodal graphs easier to classify than bimodal graphs. Students have more difficulty with the graphs that are skewed and bimodal.

- Throughout the lesson, instructors should encourage students to consider why it is important to describe a distribution.

- After students complete their sorting, the instructor can lead a class discussion using questions such as:

o What was the easiest group to sort? Which graphs are in that group?

o How many different groups did you find? Which graphs are in each? What did you call them? What features did they have in common? Etc.

o Which graphs were hardest to sort or classify? Why?

- As students suggest their categories, the instructor may also want to refer to graphs on the following website:

http://www.tc.umn.edu/~delma001/stat_tools/.

This applet includes most of the graphs in the activity. There are buttons along the bottom that represent five different categories of distributions. When you click one, it brings up the set of graphs with that type of characteristic. You use the PREV and NEXT buttons on the right to view the graphs in each set.

- The correct statistical terms for the graphs (uniform, normal, right and left skewed, bimodal) can be introduced if students have not yet learned these terms. Models (uniform, normal) can be described in terms of symmetry and shape (bell shape or rectangular). Other distributions that don't fit these models can be described in terms of their characteristics (skewness, bimodality or unimodality, etc). A discussion of which descriptors can and cannot go together may follow.

- These points may be included in the discussion of graphs following the activity:

o Ideal shapes: density curves vs. histograms

o Different versions of ideal shapes

o Idea of models, characteristics of distributions

o Statistical words vs. descriptors

o Normal, skewed, uniform, bimodal, symmetric: which can be used together?

## Assessment

A sample assessment is included with the original activity. This assessment can be used to assess students' ability to correctly describe graphs and understand the difference between graphs.

## References and Resources

The following website provides graphs and categories that students might use to create their categories for sorting histograms in part one: http://www.tc.umn.edu/~delma001/stat_tools/

CAUSEweb includes the original version of of this activity