Teacher Note: 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.
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 two lunches.
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 by 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 median.
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 percentile.
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.
Finally, 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 files.
To conclude the lesson, go to the NCTM Box Plotter Tool.
Students can choose from given sets of data to create box and whisker plots, or they can enter their own data.
