Abstract

The goal of this lesson is to introduce the concepts of mean, median and mode and to develop understanding and familiarity with these ideas. The Mean and Median Activity lets students explore mean and median in an efficient way; the Mean, Median and Mode Discussion helps them to formalize their knowledge.

Objectives

Upon completion of this lesson, students will:

• understand three different measures of "center"
• have been exposed to multiple ways of expressing a set of numbers
• have practiced their arithmetic skills

Standards

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

Algebra

Understand patterns, relations, and functions

• represent, analyze, and generalize a variety of patterns with tables, graphs, words, and, when possible, symbolic rules

Select and use appropriate statistical methods to analyze data

• find, use, and interpret measures of center and spread, including mean and interquartile range

Links to other standards.

Student Prerequisites

• Arithmetic prerequisites: Students should understand sums, differences, and quotients for all activities.
• Technological prerequisites: Each student or group of students working together will need a computer with a Java-capable browser. Students should be comfortable using the computer and browser. Calculators may be helpful for solving problems that arise in discussions.

Teacher Preparation

• Students will need access to a Java-capable browser
• Students will need pencil and paper.
• Students will need copies of the following worksheet:
  • The Measures activity

Key Terms

arithmetic mean average histogram mean median

mode multimodal range total

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:

   • Does anyone know what "average" means?

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 mean, median, and mode.
   • We are going to use the computers to learn about mean,median, and mode, but please do not turn your computers on until I ask you to. I want to show you a little about this activity first.

3. Teacher Input

   • Lead a discussion, or the instructor can prepare a "live" discussion, to deepen and formalize the students' intuitive understanding of mean, median, and mode. (10-20 min)
4. Guided Practice

   • Introduce and develop the concepts of mean and median with the Measures activity. Students will change parameters and discover patterns related to mean and median. Students can choose their own focus of measure, their own quantity, and their own units. (20 min)

5. Independent Practice
   • Have the students either individually or in groups read and try to solve sample problems on mean, median, and mode. (30 min)
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

• Combine this lesson with the Bell Curve Lesson for a look at how means are tied to distributions

Suggested Follow-Up

This lesson introduced the students to some basic ways of describing sets of data. The next lesson, Histograms and Bar Graphs, introduces histograms, bar graphs and the concept of class interval. Students will learn to distinguish between bar graphs and histograms and to use each in the appropriate situations.