Abstract

The goal of this lesson is to introduce the concepts of the normal curve, skewness and the standard deviation. The controversy over the 1994 book is also examined.

Objectives

Upon completion of this lesson, students will:

• have been introduced to the normal distribution
• have an understanding of how the normal distribution has been used and misused to support conclusions

Standards

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

• Mathematics as Communication
• Mathematics as Reasoning
• Geometry

Key Terms

• bell curve
• normal distribution
• mean
• median
• standard deviation

Activities

• normal distribution activity.
• skewness activity.

Student Prerequisites

• Arithmetic prerequisites: Students should understand sums, differences, and quotients for all activities.
• Geometric prerequisites: Students will need to understand both the concept of area in general and, specifically, the area of a rectangle.
• 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 worksheets:
  • The Normal Distribution activity
  • The Skew Distribution activity
• Especially if doing the Bell Curve sections "live", the instructor should have some background on the bell curve.

Lesson Outline

1. Introduce the "Bell Curve" controversy with a discussion, and/or hold a live discussion based on newspaper articles from the time. (10-20 min)
2. Introduce the concept of standard deviation or spread with the normal distribution activity. Also explore the differences between individual data points, samples of various sizes, and expected theoretical distributions. (15-20 min)
3. Revisit "Bell Curve" with a discussion. (10 min)
4. Revisit the ideas of mean, median, mode, and standard deviation graphically with the skewness activity. (15 min)
5. Interconnect ideas of theoretical and experimental probability with discrete-valued histograms and continuous distributions. (10 min)

Alternate Outlines

• Look at the normal distribution without discussing the bell curve controversy. This saves time and avoids controversial material.
• Relate the histograms produced by the normal and skew distributions to the idea of finding area under a curve by counting the rectangles that fit under it (simple graphical numerical integration). Use the grid and the scale on the normal distribution to find the area under the normal curve. (It should be close to 1).

Suggested Follow-Up

This lesson introduced the notion of the normal curve and illustrated a real life (mis)use of the statistics drawn from a given situation. Revisiting the initial lessons on Statistics and Shopping and Probability and Sports and applying the new knowledge on statistics would make an excellent capstone activity.