Box Plots

Abstract

The goal of this lesson is to introduce box plots and quartiles. An activity and discussion with supplemental exercises help students learn how data can be graphically represented.

Objectives

Upon completion of this lesson, students will:

  • have reviewed the concept of median
  • have learned how to calculate quartiles for any size data set
  • have learned how to build a box plot

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;
Use mathematical models to represent and understand quantitative relationships.
  • model and solve contextualized problems using various representations, such as graphs, tables, and equations.

Data Analysis and Probability

Formulate questions that can be addressed with data and collect, organize, and display relevent 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.

Student Prerequisites

  • Arithmetic: Students must be able to:
    • put numbers in order from smallest to largest
    • calculate the average of two numbers
  • 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
  • The worksheet for the box plot activity's built in data sets
  • The worksheet for working with the data collected from the class (see below)

Key Terms

This lesson introduces students to the following terms through the included discussions:

Lesson Outline

  1. Focus and Review

    Remind students what has been 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 examples of different ways that we have found to portray data?

  2. Objectives

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

    • Today, class, we are going to learn about box plots.
    • We are going to use the computers to learn about box plots, 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

    • Remind students of the ideas behind means and medians, as covered in the Mean, Median and Mode discussion.
    • Walk students through the construction of quartiles, the five-number summary and box plot construction as in the Box Plot discussion.
  4. Guided Practice

    • Have students experiment with the built-in data sets available in the Box Plot activity to be sure that they understand how to read the the box plots. Questions for the data sets can be found in the worksheet.

  5. Independent Practice

    • Have the students collect the following data from each other:
      • Gender
      • Height
      • Length of ride/walk to school in minutes
      • Estimate number of hours of TV watched in a week

      Have the students explore the questions on box plots by building the appropriate box plots either by hand or using the Box Plot activity. With less mature students, it would be best to help them decide which box plot to graph for each question.

  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.

  • Students can be asked to work with the notion of outliers, as can be done with the Box Plot activity.

Suggested Follow-Up

If the students have not yet seen histograms, the lesson on Histograms and Bar Graphs makes a good follow-up. For more advanced students, The Bell Curve, covers the normal distribution and the bell curve controversy.