Stem-and-Leaf Plots

Abstract

This lesson is designed to introduce students to stem-and-leaf plots.

Objectives

Upon completion of this lesson, students will:

  • have been introduced to the notion of stem-and-leaf plots.
  • have learned the terminology used with stem-and-leaf plots.
  • have used stem-and-leaf plots to calculate the mean, median, and mode of a set of data.

Standards Addressed

Grade 3

  • Statistics and Probability

    • The student demonstrates an ability to classify and organize data.
    • The student demonstrates an ability to analyze data (comparing, explaining, interpreting, or justifying conclusions).

Grade 4

  • Statistics and Probability

    • The student demonstrates an ability to classify and organize data.
    • The student demonstrates an ability to analyze data (comparing, explaining, interpreting, evaluating; drawing or justifying conclusions).

Grade 5

  • Statistics and Probability

    • The student demonstrates an ability to classify and organize data.
    • The student demonstrates an ability to analyze data (comparing, explaining, interpreting, evaluating; drawing or justifying conclusions).

Grade 6

  • Statistics and Probability

    • The student demonstrates an ability to classify and organize data.
    • The student demonstrates an ability to analyze data (comparing, explaining, interpreting, evaluating; drawing or justifying conclusions).

Grade 7

  • Statistics and Probability

    • The student demonstrates an ability to classify and organize data.
    • The student demonstrates an ability to analyze data (comparing, explaining, interpreting, evaluating, making predictions; drawing or justifying conclusions).

Grade 8

  • Statistics and Probability

    • The student demonstrates an ability to classify and organize data.
    • The student demonstrates an ability to analyze data (comparing, explaining, interpreting, evaluating, making predictions, describing trends; drawing, formulating, or justifying conclusions).

Grade 9

  • Statistics and Probability

    • The student demonstrates an ability to classify and organize data.
    • The student demonstrates an ability to analyze data (comparing, explaining, interpreting, evaluating, making predictions, describing trends; drawing, formulating, or justifying conclusions).

Grade 10

  • Statistics and Probability

    • The student demonstrates an ability to classify and organize data.
    • The student demonstrates an ability to analyze data (comparing, explaining, interpreting, evaluating, making predictions, describing trends; drawing, formulating, or justifying conclusions).

Third Grade

  • Measurement and Data

    • Represent and interpret data.

Statistics and Probability

  • Interpreting Categorical and Quantitative Data

    • Summarize, represent, and interpret data on a single count or measurement variable

Grades 6-8

  • Data Analysis and Probability

    • Formulate questions that can be addressed with data and collect, organize, and display relevant data to answer them
    • Select and use appropriate statistical methods to analyze data

Grade 7

  • Number and Operations, Measurement, Geometry, Data Analysis and Probability, Algebra

    • COMPETENCY GOAL 4: The learner will understand and use graphs and data analysis.

Grade 8

  • Number and Operations, Measurement, Geometry, Data Analysis and Probability, Algebra

    • COMPETENCY GOAL 4: The learner will understand and use graphs and data analysis.

Introductory Mathematics

  • Algebra

    • COMPETENCY GOAL 4: The learner will understand and use graphs and data analysis.

  • Data Analysis and Probability

    • COMPETENCY GOAL 3: The learner will understand and use graphs and data analysis.

6th Grade

  • Data Analysis and Probability

    • The student will demonstrate through the mathematical processes an understanding of the relationships within one population or sample.

4th Grade

  • Data Analysis and Probability

    • Standard 4-6: The student will demonstrate through the mathematical processes an understanding of the impact of data-collection methods, the appropriate graph for categorical or numerical data, and the analysis of possible outcomes for a simple event.

8th Grade

  • Data Analysis and Probability

    • The student will demonstrate through the mathematical processes an understanding of the relationships between two variables within one population or sample.

7th Grade

  • Probability and Statistics

    • 7.16 The student will create and solve problems involving the measures of central tendency (mean, median, mode) and the range of a set of data.
    • 7.17 The student, given a problem situation, will collect, analyze, display, and interpret data, using a variety of graphical methods, including frequency distributions; line plots; histograms; stem-and-leaf plots; box-and-whisker plots; and scattergrams.

5th Grade

  • Probability and Statistics

    • 5.17c The student will create a problem statement involving probability and based on information from a given problem situation. Students will not be required to solve the created problem statement.

Textbooks Aligned

Grade Six

  • Data About Us

    • Investigation Three: Using Graphs to Group Data

7th

  • Module 5 - Recreation

    • Section 1: Ratios and Data Displays
      • Reason for Alignment: Stem and Leaf Plot is the introductory lesson and activity, and includes a discussion of mean, median, mode and range. This could be used, but only if additional practice is needed. Several sets of data are included for practice.

8th

  • Module 1 - Amazing Feats and Facts and Fiction

    • Section 2: Displaying Data
      • Reason for Alignment: Stem and Leaf Plot Lesson: This contains good discussion questions and a sample worksheet to be used by students. For Books 1, 2 and 3, this lesson could be a good additional help for students as they encounter this graph in the textbook.

Student Prerequisites

  • Arithmetic: Students must be able to:
    • perform integer and rational arithmetic
  • 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

Key Terms

Lesson Outline

  1. Focus and Review

    Remind students of what they 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:

  2. Objectives

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

    • Today, class, we will be talking about stem-and-leaf plots, which are used to help us statistically analyze sets of data.
    • We are going to use the computers to learn about stem-and-leaf plots, but please do not turn your computers on or go to this page until I ask you to. I want to show you a little about the program first.

  3. Teacher Input

    • When the students understand mean, median, and mode, lead the class in a discussion of stem-and-leaf plots.
    • Open your browser to Stem-and-Leaf Plotter in order to demonstrate this activity to the students.
    • You may choose to model the entering of a set of data into the Stem-and-Leaf Plotter. Ask the class to suggest scores that might have been made on the last math test in the class.
    • After entering the data into the applet, you may choose to have a student explain to the class what the stem-and-leaf plot means. Have the student use the correct terminology when explaining the plot.
    • Ask the class for questions and be sure that everyone understands how to use the applet.

  4. Guided Practice

    • Once you have verified that there are no questions regarding the use of the applet, pass out the Worksheet to accompany "Stem-and-Leaf Plots".
    • Walk the students through entering the data and finding the mean, median and mode for problem number 1.

  5. Independent Practice

    • Have the students finish the worksheet. Allow the students to work independently or in small groups as you monitor the room for progress.

  6. Closure

    • It is important that every student know the correct answers to the worksheet in order to fully understand stem-and-leaf plots. In particular, ask them to think about what it means for the mean to be bigger than or smaller than the median. Have them look at their plots and see that if the data are symmetric, the mean and median are close together, but if there are extreme low values, the mean is pulled down, and if there are extreme high values the mean is pulled up.

Alternate Outline

This lesson can be rearranged in several ways.

  • The students may create their own sets of data to enter into the Stem-and-Leaf Plotter.
  • Students may challenge a friend to find the mean, median, and/or mode of a set of data that they find or create.
  • You may rearrange this lesson to meet the needs and ability levels of students in your classroom.