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

Standards

The activities and discussions in this lesson address the following NCTM standards:

Data Analysis and Probability

Formulate questions that can be addressed with data and collect, organize, and display relevant data to answer them

• select, create, and use appropriate graphical representations of data, including histograms, box plots, and scatterplots

Select and use appropriate statistical methods to analyze data

• discuss and understand the correspondence between data sets and their graphical representations, especially histograms, stem-and-leaf plots, box plots, and scatterplots

Links to other standards.

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

Key Terms

• bar graph
• class interval
• histogram

Lesson Outline

1. Focus and Review

   Remind students of what they have learned in previous lessons that will be pertinent to this lesson and/or have them begin to think about the words and ideas of this lesson:

   • What are some different ways to represent data?
   • Is there one way that is superior to all the others?

2. Objectives

   Let the students know what they will be doing and learning today. Say something like this:

   • Today, class, we are going to learn about the differences between bar graphs and histograms.
   • We are going to use the computers to learn about the differences between bar graphs and histograms, but please do not turn your computers on until I ask you to. I want to show you a little about these activities first.

3. Teacher Input

   • Use the Bar Graph activity to familiarize students with visually representing data. Be sure to demonstarte the importance of vertical scale in bar graphs.
   • Use the Histogram activity to demonstrate the importance of class interval size and vertical scale in histograms.
   • 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. Guided Practice

   • 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.
   • Next, initiate a discussion based on Vertical Scale to enhance the students' understanding of how data can be represented graphically.
   • 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.

5. Independent Practice
   • Practice histogram further with the Scales and Impressions Worksheet.
   • The Sample Problems on Comparing Histograms and Bar Graphs will provide further practice.
6. Closure

   • You may wish to bring the class back together for a discussion of the findings. Once the students have been allowed to share what they found, summarize the results of the lesson.

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 the 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.