Give each student a small handful of pasta letters of the type used in alphabet soup. Ask the students to sort the letters, write their first and last names using the letters, and then glue the alphabet letters found in their name onto an index card. (Optional opening: Ask the students to write their first and last names on an index card, then count the number of letters altogether.) Have the students write the total on the other side of the card. (In this lesson, the students will learn about a different way to graph data, the box-and-whisker plot (or box plot). This graph clearly displays the endpoints, range, and median
of quantitative data. Its construction begins with ordering the data.]
Now help the students form a line in which they order themselves from greatest to least according to the number on their index card. [If more than one student has the same number, the students should stand side by side.] Ask them
to face front. Now give the student with the smallest number a card on which you have written "Minimum." Now give the student with the highest
number a card on which you have written "Maximum." Ask the students to find the range of the data. [To find the range, subtract the minimum from the maximum.] Record the range on the board.
Next, have the students determine whether any value occurs more times than all others. Identify that value as the mode, and record it on the board. Next, ask the students at the two ends of the line to say "one" at the same time, then the students next to them to say "two." Continue counting off in this fashion until the middle of the line is reached. [If there is an odd number of students, one student will be at the middle; if there is an even number, two students will be there. If there is one student, the number he or she holds is the median. If
there are two students, the arithmetic average of their numbers is the median. If this happens, you may need to work out the problem on the board.] Ask the students what this "middle" number is called. Write the median on the board under the mean, and label it. Provide the student(s) who represent the median with a card on which you have written "Median." Tell the students that the halfway mark is called the 50th percentile, just as a half-dollar represents 50 cents.
Now have the students on either side of the median find the median of just their side. Provide a card that says "75th Percentile" to the center student on the higher 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. In the money analogy, it is like a quarter. Similarly, the 75th percentile is the point greater than 75 percent of the scores, and, in the money analogy, is like 75 cents.]
Give the student at the 75th percentile place one end of a long piece of yarn to hold in his or her right hand. Then, holding the yarn, walk to the student who holds the 25th percentile card and place yarn in his or her right hand. Walk in front of that student and place the yarn in his or her left hand as well. Then, carrying the yarn, walk back to the student holding the 75th percentile card and put the other end of the yarn in his or her left hand to complete the loop. Now have those students hold out their arms, so that a yarn "box" is formed. Explain that they have made a human box-and-whisker plot.
Allow students, a few at a time, to leave the line and stand where they can see the box. Call on a volunteer to draw the figure on the board. Then collect the yarn and the cards and ask the students to take their seats and copy the plot, naming the high and low scores and the median. Encourage them to use color to show the various parts of the plot.
Now tell the students to use their calculators to find the mean. When they have found it, enter the mean under the median on the board. Now ask them how they could find the mode. When they have suggested a way and found the mode,
have them add it to the list of measures of center. Identify these statistics as measures of center or central tendency. [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 in the ordered data, one-half the observations are above it and one-half are below it. These three statistics are called measures of central tendency or averages.] Ask the
students what they notice about the averages and which one best describes the "average" length of names in the class. [The averages are probably not the same. The median is the best average in this case.]
Go to the National Library of Virtual Manipulative's Box Plot.
Call on one or more students to collect the index cards and enter the data on the Web site. When it is entered, generate the box plot. You may wish to line the index cards up on the board tray so the data is visible to all the students. If you do so, you could indicate the low and high values, the median, the mean, and the mode with the labeled index cards used in
the human box-and-whisker plot.
If time allows, ask the students how the box-and-whisker plot would change if the length of the teacher's name were included in the data set. Finally, ask the students to add the measures of central tendency to their copy of the box plot so they can have a record for their files.
