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
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
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.