Abstract

The goal of this lesson is to introduce histograms, bar graphs and the concept of class interval. An activity and three discussions with supplemental exercises help students learn how data can be graphically represented (and mis-represented). Students will learn to distinguish between bar graphs and histograms and to use each in the appropriate situations.

Objectives

Upon completion of this lesson, students will:

• have been introduced to histograms and bar graphs
• have understood the difference between bar graphs and histograms
• have seen examples of how data can be represented in a variety of graphical forms

Activities

• Histogram

Standards

The activities and discussions in this lesson address the following Standards:

• Probability and Data Analysis
• Geometry

Key Terms

• class interval
• bar graph
• histogram
• end point convention

Student Prerequisites

• Geometric: Students must be able to:
  • recognize how data can be plotted and interpreted from shapes such as bar graphs
• Technological: Students must be able to:
  • perform basic mouse manipulations such as point, click and drag
  • use a browser such as Netscape for experimenting with the activities

Teacher Preparation

Students will need:

• access to a browser
• pencil and Paper
• copies of supplemental materials for the activities:
  • Histogram Worksheet
  • Scales and Impressions Worksheet
  • Sample problems for bar graph scales
  • Sample problems for bar graph and class intervals
  • Sample problems for comparing histograms and bar graphs

Lesson Outline

1. Use the Histogram activity to demonstrate the importance of class interval size and vertical scale in histograms.

   Students can use the activity to easily see how class intervals and vertical scales influence the appearance of histograms. Students can try to obtain certain effects (e.g., to make the data look more stable or more unstable) and to compare different graphs of the same data. See also the recommendations from What? section of the activity.

2. Practice histograms further with the Scales and Impressions Worksheet.

3. Lead a class discussion about class intervals to deepen and formalize students' intuitive understanding of histograms, bar graphs, and class intervals. Use Sample Problems on Bar Graphs Scales to provide examples for the discussion.

   Students can read the sample problems and try to solve them individually or in groups, or use them as examples and create their own statistics problems for themselves and/or for other students.

4. Next, initiate a discussion based on vertical scale to enhance the students' understanding of how data can be represented graphically.

5. The Sample Problems on Bar Graph Class Intervals worksheet will help reinforce students' understanding of class intervals and data representation.

6. To bring together ideas introduced in the lesson so far, the Histograms vs. Bar Graphs Discussion will help students to compare the properties of histograms and bar graphs.

   The Sample Problems on Comparing Histograms and Bar Graphs will provide further practice.

Alternate Outlines

This lesson can be rearranged in several ways.

• Instead of initiating class discussions, have the students read the discussions independently, and then see how well they understood by having them complete the sample problems worksheets that accompany each discussion.
• For further investigation into the representation of data, and to practice working with fractions and decimals, students can work with Sample Problems on Data Abuse.

Suggested Follow-Up

After these discussions and activities, the students will have seen examples of bar graphs and histograms, and be able to tell them apart and know the circumstances when each should be used. The next lesson, The Bell Curve, covers the normal distribution and the bell curve controversy.