# Human box and whisker plot

Students will learn how to construct box and whisker plots as they actively participate in being a part of one based upon their heights. As an extension of the lesson, students will learn how to interpret a graph of this type.

**A lesson plan for grades 6–8 Mathematics**

## Learning outcomes

Students will:

- construct and interpret box and whisker plots.
- interpret and analyze box and whisker plots.

## Teacher planning

### Time required for lesson

90 Minutes

### Materials/resources

- heights of students in class in centimeters
- index cards (write each student’s height on a card)
- construction paper
- 2 rolls of cash register tape
- strip of bulletin board paper about one foot wide and 20 feet long
- flags (2 of one color and 1 of another)
- large open area (large classroom, gym, etc.)

## Pre-activities

Students must understand how to find the median of a data set.

Teacher needs to construct flags (for example 2 red and 1 blue). I use rulers or drinking straws and construction paper.

## Activities

- Explain that we are going to learn how to make an interesting graph with an interesting name - a box and whisker plot. We are going to do this based on our heights.
- Distribute index cards with student’s height to each student.
- Instruct students to order themselves from shortest to tallest (shoulder to shoulder) across the front of the room with students of the same height standing beside each other.
- Explain that we (the class) need to find the median student (the student in the middle). Give this student the flag that is a different color from the other two. If by chance you have an even number of students in your class, then review how to find the median in this situation. These two students must hold the flag between them.
- 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.
- Explain that we are now going to find the quartiles of our data set. Discuss the word quartile (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?) The quartiles of a data set are middle (half) of each half. Who is in the middle of the short half? This person is the lower quartile. Give them a flag. Who is in the middle of the tall half? This person is the upper quartile. Give them a flag as well.
- At this point, students of the same height need to stack themselves (stand behind one another). All students but one may return to their seats.
- Place pieces of construction paper on the floor for heights that are not represented by individual students (for example: if you have a student who is 138 cm tall and the next is student in 140 cm, then you need to place a piece of construction paper on the floor to represent the height of 139 cm).
- Explain that there are two other important data points/people in the making of our graph - the endpoints - in this case the shortest person and the tallest person in our class. These people are the lower and upper endpoints (respectively).
- Explain that in a box and whisker plot the box runs from quartile to quartile. Again, go over and ask - who are our quartiles? Unroll your strip of bulletin board paper, beginning at the lower quartile and ending at the upper quartile. Students should assist in holding the paper.
- 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.
- Now for the whiskers. Explain that the whiskers run from quartile to endpoint. Unroll each roll of register tape so that it goes from lower quartile to lower endpoint and upper quartile to upper endpoint. Students should assist in holding paper.
- Have all students except the endpoints, quartiles, and median return to their seats so that they can see the box and whisker plot.
- Review the process with students, answering any questions they have. Record the steps on the board/overhead for reference.
- Collect all materials and have all students return to their seats.
- Explain how to make box and whisker plots on paper. Make a number line that begins a bit before and extends a bit after your endpoints. For example, if your endpoints are 131 and 182, I would have my number line range from 130 to 185 and use increments of five. The next step is to plot the five points (median, quartiles, and endpoints) on the number line, approximating when needed. Then, draw the box (quartile to quartile) and draw a line through the median. Last, draw in the whiskers (quartile to endpoint).

Assessment (see below)

In an effort to teach students how to analyze and interpret box and whisker plots, display one on the overhead. Explain to students that 25% of data is held between the lower endpoint and the lower quartile and 25% between the upper endpoint and upper quartile. This leaves 50% of the data to be held within the box. Ask students if they can determine what percent of the data would be held from the lower quartile to the upper endpoint? (75%) The other type of question students should be able to answer from a graph of this type requires them to know how many items there are in the data set. For example, you give students a box and whisker plot and tell them that it represents the prices of twenty pair of running shoes. If the median price was $70, then you ask the students what percent of the running shoes cost $70 or more? (one half of twenty is 10) If the lower quartile is $55, what percent of the shoes cost $55 or more? (three fourths of twenty is 15)

## Assessment

In order to assess student’s comprehension of the activity, give them a similar data set (I use my other 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.

## Supplemental information

### Comments

I have a large classroom, so this activity works fine for me. If you have a large class but a not so large classroom you might think about doing this activity in a larger space, such as the gym or outside.

I have found that students have some difficulty actually making the box and whisker plot on the number line.

- Common Core State Standards
- Mathematics (2010)
#### Grade 6

- Statistics & Probability
- 6.SP.4Display numerical data in plots on a number line, including dot plots, histograms, and box plots.
- 6.SP.5Summarize numerical data sets in relation to their context, such as by: Reporting the number of observations. Describing the nature of the attribute under investigation, including how it was measured and its units of measurement. Giving quantitative...

- Statistics & Probability

## North Carolina curriculum alignment

### Mathematics (2004)

#### Grade 7

**Goal 4**: Data Analysis and Probability - The learner will understand and use graphs and data analysis.**Objective 4.01**: Collect, organize, analyze, and display data (including box plots and histograms) to solve problems.**Objective 4.02**: Calculate, use, and interpret the mean, median, mode, range, frequency distribution, and inter-quartile range for a set of data.

#### Grade 8

**Goal 4**: Data Analysis and Probability - The learner will understand and use graphs and data analysis.**Objective 4.01**: Collect, organize, analyze, and display data (including scatterplots) to solve problems.