To assess prior knowledge, provide a small data set and ask them to find these statistics. You may wish to use the number of vowels in their last names.
Give each student an index card. Ask them to write their first and last names on their cards and then record the number of letters in each name and the total letters. Tell them that they are going to make a human box plot, and that this special graph shows the range and median for a set of data.
Ask students to hold their index cards in front of them. Help students order themselves, starting with the student whose name has the fewest letters. Students who have the same name length should stand side by side.
| Sample Ordered List of Student Names |
| Diana Rigg | 9 |
Susan Sarandon | 12 |
Anthony Hopkins | 14 |
| Paul Newman | 10 |
Nicholas Cage | 12 |
Katharine Hepburn | 16 |
| Meryl Streep | 11 |
Michael Caine | 12 |
Christopher Reeve | 16 |
| Ben Kingsley | 11 |
Jack Nicholson | 13 |
Valerie Bertinelli | 17 |
| |
| Maximum: | 17 |
Range: | 9 |
Mode: | 12 |
| Minimum: | 9 |
Median: | 12 |
Mean: | 12.9 |
Give the student with the smallest number (for example, 9) a card on which you have written "Minimum." Give the student with the longest name (for example, 17) a card on which you have written "Maximum." Ask students to find the range of the data. To find the range, subtract the minimum from the maximum. Record the range on the board.
Finding the Mode
The mode, which cannot be determined from a box plot, is the data point that occurs most often. The mean is the arithmetic average. The median is the halfway point or 50th percentile in the ordered data—one half the observations are above it and one half are below it.
To find the mode, have students determine which value occurs more times than all the others. Identify that value as the mode and record it on the board.
Finding the Median
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 are an odd number of students, there will be one student; if there is an even number, there will be two students. If there is one student, identify this number as the median. If there are two students, the arithmetic average of their numbers is the median.
Ask a student to write the median on the board under the mode and label both measures of center. Give student(s) who represent the median a card on which you have written "median" and invite them to stand again. Tell students that another name for median is "50th percentile," because 50% of the students have shorter names, and 50% have longer names.
Creating Box and Whisker Plots
Tell students that they will next find the median, or middle number, on each of the two sides. Have the student with the shortest name and the person in the median position count off as before. Ask the group on the other side of the median to find the middle point of the upper half of the set. Provide a card that says "75th percentile" to the center student on the upper end and a card that says "25th percentile" to the center student on the lower end.
As this terminology may be new to students, you may wish to explain that the 25th percentile is that point greater than 25 percent of the score. To use a money analogy, it is like a quarter. Similarly, the 75th percentile is the point greater than 75 percent of the scores. In the money analogy, it is like 75 cents.
You may wish to line the index cards up on the blackboard tray so the data is visible to all the students. If you have done so, you could indicate with sticky notes the low and high values, the median, the mean, and the mode with labeled index cards used in the human box and whiskers plot.
Tell students that they will become part of a graph called a box plot. Have students holding the 25th percentile and 75th percentile cards to stretch their arms out to make the ends of the box. Put one end of a long piece of yarn in the right hand of the student holding the 75th percentile card. Then, holding the yarn, walk back to the student who holds the 25th percentile card and place yarn in his or her right hand. As you pass in front of that student, ask the student to grab the yarn with the left hand, so that a line of yarn is stretched across the front of his or her body.
Complete the fourth side of the box by carrying the yarn back to the student holding the 75th percentile card. Ask the student to grab the yarn in his or her left hand. To make the "whiskers," stretch a piece of yarn between the student holding the "minimum" card and the student at the 25th percentile. This creates the lower "whisker." Similarly, stretch a piece of yarn between the student holding the "maximum" card and the student at the 75th percentile. This creates the upper "whisker."
Invite students, a few at a time, to step out of the line to see that a yarn "box" with “whiskers” is formed. Explain that they have made a human box and whiskers plot. The maximum and minimum points are the endpoints of the "whiskers" and the 25th and 75th percentile parts are called the lower and upper hinges, respectively, of the box. Copy the plot on the board, then collect the yarn and the cards and ask the students to take their seats.
Call on a volunteer to label the 25th, 50th, and 75th points. Call on another volunteer to draw a line from the left-hand side of the box and label the end of the line with the lowest value in the data set.
Have another student draw a line from the right-hand side of the box and label the end of the line with the highest value in the data set. Ask students to copy the figure from the board, naming the highest and lowest values, the 25th and 75th percentiles, and the median.
Invite students to find the mean by computing with paper and pencil or using their calculators to add all the values and dividing by the number of students in the class. If any value occurs more than once, it should be entered into the sum as many times as it appears.
Tell students that they will next construct a box plot on the computer. Go to the Illuminations Box Plotter Tool, where students should follow the directions for entering their own data and drawing the box plotter.
This site allows you to print out the box plot, so you may wish to complete several box plots while you are here.
