# Histograms and Bar Graphs

Shodor > Interactivate > Lessons > Histograms and Bar Graphs

### 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

### 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 for experimenting with the activities

### Teacher Preparation

• Pencil and Paper
• Copies of supplemental materials for the activities:

### Key Terms

 bar graph A diagram showing a system of connections or interrelations between two or more things by using bars class interval In plotting a histogram, one starts by dividing the range of all values into non-overlapping intervals, called class intervals, in such a way that every piece of data is contained in some class interval histogram A bar graph such that the area over each class interval is proportional to the relative frequency of data within this interval

### 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 demonstrate 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.

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 Graph 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 Histogram vs. Bar Graphs Discussion will help students to compare the properties of histograms and bar graphs.

5. Independent 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 Outline

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. 