Overview

Students learn about box-and-whisker plots through a class activity that compares their heights. As an extension of this activity, they learn how to use two different forms of technology to check their answers.

Objective

Students will be able to design and construct a box-and-whisker plot.

Standards Address

Mathematics — Data Analysis

Grade 5

Statistical Methods, Benchmark F

06. Determine and use the range, mean, median and mode, and explain what each does and does not indicate about the set of data.

 

Grade 6

Data Collection, Benchmark E

02. Select, create and use graphical representations that are appropriate for the type of data collected.

Statistical Methods, Benchmark F

04. Understand the different information provided by measures of center (mean, mode and median) and measures of spread (range).

 

Grade 7

Data Collection, Benchmark A

01. Read, create and interpret box-and-whisker plots, stem-and-leaf plots, and other types of graphs, when appropriate.

Statistical Methods, Benchmark F

03. Analyze a set of data by using and comparing combinations of measures of center (mean, mode, median) and measures of spread (range, quartile, interquartile range), and describe how the inclusion of exclusion of outliers affects those measures.

 

Materials

• Index cards

• Meter sticks

• Construction paper

• Cash register tape or string

• Long strip of bulletin board paper

• Three flags -— two red and one blue (can be handmade out of rulers or straws and construction paper)

Procedure

1. Make three flags — one blue and two red — with “median” written on them.

2. Explain that the class is going to learn how to make an interesting graph with an interesting name — a box-and-whisker plot. The students are going to do this based on their heights.

3. Group students in pairs and pass out one meter stick to each pair. Give instructions to have each person measure the other in centimeters and write the height on an index card.

4. Instruct students to order themselves from shortest to tallest (shoulder to shoulder) across the front of the room.

5. Explain that the class needs to find the median student (the student in the middle). To find the median, or middle number, have students at each end of the line say “1” at the same time and sit on the floor. Ask students next to them to say “2.” Have students count off in this fashion until only one or two students are standing. If there is an odd number of students, there will be one student; if there is an even number, there will be two students.

6. Give the remaining student the blue flag with “median” written on it. If by chance you have an even number of students in your class, then have the class find the mean of these two heights. These two students must hold the flag between them.

7. At this point, explain to the students that we have divided the class into two groups or halves — the short half and the tall half.

8. Explain that the class is now going to find the quartiles of our data set. Ask the class what quartile means, for example: What does it sound like? A quarter? What is a quarter — 25 cents? One fourth? What is the relationship between one fourth and one half?

9. The quartiles of a data set are the middle (half) of each half. Who is in the middle of the short half? This person is the lower quartile. Give him or her a red flag. Who is in the middle of the tall half? This person is the upper quartile and gets a red flag as well. Once again, if there are two students in the middle, the mean of the two would be used.

10. At this point, students of the same height need to stand behind one another.

11. Explain that there are two other important data points/people in the making of our graph — the endpoints or the maximum and the minimum — in this case the shortest person and the tallest person in our class. These people are the lower and upper endpoints, respectively.

12. Use a piece of yarn or register tape to make a box around the students in the lower to upper quartile. Have students locate the median student in relationship to the box. Discuss that the median student should be in the box but not necessarily in the middle of the box.

13. Now for the whiskers. Explain that the whiskers run from quartile to endpoint. Unroll each roll of register tape or string so that it goes from lower quartile to lower endpoint and upper quartile to upper endpoint. Students should assist in holding paper.

14. Review the process with students, answering any questions they have. Record the steps on the board/overhead for reference.

15. Technology Extension: Students can check their box-and-whisker plot in two different ways. First, they can go to the following Web site and follow the directions for putting in their own data and drawing the box plotter. This site also lets you print out the box plot.

    http://illuminations.nctm.org/ActivityDetail.aspx?ID=77

    Second, if computers are not readily available, students can use a graphing calculator to check their work. If the classroom is equipped with a white board use the graphing calculator software installed and show the students exactly how to make the box plot on the white board.

16. Extensions:

To develop their understanding further, ask students how the box-and-whisker plot would change if the teacher’s height was included in the data set.

Suppose a new student came into the class. How would that change the plot we made?

Suppose (student name) moved away. How would that change the plot? (Repeat with other names.)

 

Evaluation

In order to assess students’ comprehension of the activity, give them a similar data set (you might want to use another class’s heights) and have them go through the process on paper. They should identify the median, upper and lower quartiles and upper and lower endpoints, then draw the graph on a number line.