In this lesson, students will learn a different way to graph data, the
box plot. This graph displays clearly the endpoints and range of
quantitative data, and the median. Its construction begins with
ordering the data.
Call the class together and assign them to pairs. Distribute file cards, calculators, and one copy of The Clucking Chicken Activity Sheet to each pair.
The Clucking Chicken Activity Sheet
Tell them to choose a lunch for the two of
them from the menu, based upon their personal preferences. If necessary
or appropriate, students can use a calculator to find the cost of the
When they have computed the price, ask them to write it on an
index card. When they have done so, call on a volunteer to write the
prices on the board as one student from each group calls them out. Have
the students use their calculators to find the mean cost of the two
lunches and write the amount on the board, labeled "Mean."
Ask the students from the pairs to come to the front of the
room and order themselves according to the number on their file card.
(If more than one student has the same number, they should stand side
Give the student with the smallest number (for example, $4.75)
a card on which you have written "Minimum." Now give the student with
the highest total 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 if any amount occurs more times than all
others. Identify that value as the mode, and record it on the board
under the mean.
Next, to find the median, ask the students at the two ends of
the line to say "1" at the same time, then the students next to then to
say "2." Continue counting off in this fashion until the middle of the
line is reached. If there is an odd number of students, this will be
one student; if there is an even number, it will be two students. 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
Write the median on the board under the mean and mode, and
label it. Provide the student(s) who represent the median with a card
on which you have written "median." Inform the students that the
halfway mark is called the 50th percentile.
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.
Give the student with the smallest amount a piece of yarn and
give the other end of it to the student at the 25th percentile.
Similarly, give the student with the largest amount a second piece of
yarn and give the other end of it to the student at the 25th
Present the student in the 75th percentile with one end of a
long piece of yarn to hold in his or her right hand. Holding the yarn,
walk to the student who holds the 25th percentile card and place yarn
in that student's 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 plot.
Call on a volunteer to draw the figure on the board.
collect the yarn and the cards and ask all the students to take their
seats and copy the plot, labeling and naming the high and low scores
and the median. Now give the rest of the class a chance to construct a
human box plot.
Call students' attention to the mean, median, and mode, and tell
them that these are called averages, or measures of center. (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.)
Ask the students what they notice about the three numbers and
which one they
think best describes the "average" cost of two meals. [The averages are
probably not the same. The median is the best average in this case.]
Finally, ask the students to write the measures of central tendency
under their copy of the box plot so they can have a record for their
To conclude the lesson, go to the Box Plotter Tool.
Students can choose from given sets of data to create box and whisker plots, or they can enter their own data.