A Program of The Actuarial Foundation. Aligned with Common Core State and NCTM Standards.

What is an actuary? An actuary is an expert in statistics who works with businesses, governments, and organizations to help them plan for the future. Actuarial science is the discipline that applies math and statistical methods to assess risk.

6-8

DURATION
60

COLLECTION
Cultivating Data

# Lesson 1: Representation of Statistical Information

In this "Cultivating Data" lesson, students will learn to construct and interpret line plots, stem-and-leaf plots, and box-and-whisker plots, as well as use these graphic representations of data to find measures of central tendency and answer critical-thinking questions.

STANDARDS

• Grades 6-8: NCTM Data Analysis and Probability

OBJECTIVE

Students will be able to use statistical information to construct:

• line plots;
• stem-and-leaf plots; and
• box-and-whisker plots.

TIME REQUIRED: 60 minutes, plus additional time for worksheets (may be split over two or more days)

MATERIALS

NOTE: The lesson is based on the assumption that students have a working knowledge of mean, median, mode, and range. If needed, a lesson and worksheets on these topics are available here.

DIRECTIONS

1. Ask the class how many phones they have in their homes. Have students respond one at a time and record each answer on the board. (Note that any similar question that works for your particular class will serve the purpose.) Ask if there is a way to organize the data on the board.

2. If it isn't mentioned, suggest a line plot. Demonstrate how to construct a line plot. First, find the smallest and largest answers, and then construct a number line with the smallest value at one end and the largest at the other. Draw an "X" on the number line for each answer, with duplicate responses placed above previously recorded responses.

3. Point out how to use the plot to find the range, mode, and median. Review the meaning of these terms as necessary.

4. Indicate that a line plot can be useful when range of the data isn't very wide. To provide an example of data with a wider range, write the points scored by the San Antonio Spurs in games they played in April 2013* on the board: 90, 98, 88, 99, 86, 108, 86, 106, 95, 91, 102, 120, 103. (Feel free to select statistics for a team you and/or your class support!)

5. Demonstrate how to construct a stem-and-leaf plot from the data on the board:

6.
Point out how to find the range, mode, and median using the plot and remind the class how to find the mean.

7. Indicate to the class that a box-and-whisker plot is another way to display and analyze data. Write test scores for two classes on the board:

Class 1: 30, 75, 75, 80, 80, 85, 85, 85, 90, 95, 95
Class 2: 50, 60, 65, 70, 75, 75, 80, 85, 85, 90, 100

8. Ask how the performance of the two classes can be compared.

9. Demonstrate how to construct a box-and-whisker plot for each class, showing how the five points of minimum, first quartile, median, third quartile, and maximum are determined and displayed as follows:

10.  Discuss how class 1, even though their highest and lowest scores were below class 2, can be considered to have performed better because the middle two quartiles are higher on the number line.

*Source: nba.com/gameline/spurs

EMAIL THIS