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The Pizza Palace

Food Court
Data Analysis and Probability
Grace M. Burton
Location: unknown

Students will construct box plots independently. Students identify the mean, median, mode, and range of a set of data.

To assess prior knowledge:

  • Ask the students to take out the box plots they made yesterday.
  • Lead them in a discussion of how they were made. You may wish to review the meanings of "mean," "median," and "mode." The mode 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.

Assign the class to groups of two or three. Distribute index cards, calculators, and one copy of The Pizza Palace Activity Sheet to each group.

pdficon The Pizza Palace Activity Sheet 

Tell them to design a pizza for the three of them, then to use a calculator to find its cost.

When all are ready, 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 pizzas, to identify a mode if there is one, and to generate a box plot using the data.

After they have had time to complete the task, ask each group to report the mean, median, and mode that they found. Record these calculations where all the students can see them. Then ask volunteers to identify the high and low scores and to demonstrate their positions on the box plot they constructed.

As a final activity, go to the Box Plotter Tool.

appicon Box Plotter Tool 

Students should select "My Data" from the pull-down menu. Students enter their group's data in the place indicated.

Ask the students to compare the box plots they did by hand with the computer-generated box plot. Students can print out their box plots, and you may collect them as needed.

Assessment Options 

  1. At this stage of the unit, students should be able to:
    • construct and read a box plot
    • identify the mean, median, mode and range in a set of data
  2. The key questions suggest ways to help the students focus on the measures of center and the range of a set of data. 
  3. You may wish to add comments about students' understanding of these concepts to the Class Notes. The entries will be useful when you hold conferences with the students and/or with other adults who are interested in their progress.
  4. Put the students into pairs and ask each pair to plan a party for eight people. If they wish to order something that is not on the menu, they may wish to use the prices from a different menu or estimate the prices for the items.
    When they are ready, ask them to write the price of the party on the board. Then have the pairs construct a box plot from the data, and to find the mean, median, and mode of the price of the party. When all have had time to complete the task, identify one pair and call on a volunteer from that pair to describe the menu and to exhibit their box plot. Repeat with each pair.

Questions for Students 

1. What graph did we make today?

[The box plot.]

2. What was the least expensive pizza in the class? The most expensive? How did we show these values on the box plot? What was the difference between these numbers? What do we call that difference?

[Answers will depend upon student data; The difference is called the range.]

3. What were the mean and median of the data set? What does each term mean? How did we find the mean? The median?

[Answers will depend upon the student data; Mean is the average of the data set; Median is the middle number; To find the mean, take the sum of all of the data and divide by the number of data values; To find the median, order the data from least to greatest and find the middle number.]

4. How many students in the class had pizzas priced above the 75th percentile? How many students had pizzas priced below the 25th percentile?

[Answers will depend upon student data.]

5. How were these percentiles shown on the plot?

[They form the ends of the box.]

6. If you have three sizes of pizza and seven toppings, how many different one-topping pizzas can you make? What would the tree diagram look like? Is there another way you could find out? What equation would give you the answer?

[3 × 7 = 21.]

Teacher Reflection 

  • Which students easily found the range and mode? The median? The mean?
  • Which students could compare the measures of central tendency with understanding?
  • Were there students not yet able to draw a box plot? What did they have trouble with? What were they able to do without prompting?
  • How can I extend this instructional experience?
  • What will I do differently the next time I teach this lesson?
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Learning Objectives

Students will:

  • Compute prices from a menu.
  • Construct and read box plots.
  • Identify the mean, median, mode, and range of a set of data.

NCTM Standards and Expectations

  • Collect data using observations, surveys, and experiments.
  • Represent data using tables and graphs such as line plots, bar graphs, and line graphs.
  • Describe the shape and important features of a set of data and compare related data sets, with an emphasis on how the data are distributed.
  • Use measures of center, focusing on the median, and understand what each does and does not indicate about the data set.