Lesson 7: Plot Match

Lesson 7: Plot Match

Objective:

Students will learn how to create a boxplot from an already-established dotplot.

Materials:

  1. From Dotplots to Boxplots handout (LMR_2.11_Dotplots to Boxplots)

  2. Sets of plots from Plot Match file (LMR_2.12_Plot Match) – one for each team

    Advanced preparation required (see Step 7 below)

Vocabulary:

representation

Essential Concepts:

Essential Concepts:

Boxplots are an alternative visualization of histograms or dotplots. They capture most, but not all, of the features we can see in a dotplot or histogram.

Lesson:

  1. Ask students to complete an Entrance Slip by recalling the components of the five-number summary that make up a boxplot. Five-number summary: minimum, 1st quartile (Q1), median, 3rd quartile (Q3), maximum.

  2. Randomly select students to share the components and briefly discuss what each means in a boxplot. If students are missing a component, ask them to add the component to their list.

  3. Remind students that during Lesson 5, they created a boxplot from students’ heights.

  4. Explain that a boxplot is one representation of the distribution of a variable in a data set. They have worked with other representations of distributions. Ask students:

    1. What other representations of distributions have we seen? Answers may include: dotPlots, bar charts, scatterplots, histograms, and tables.
  5. Distribute the From Dotplots to Boxplots handout (LMR_2.11). In teams, students will sketch boxplots from dotplots. They will need to determine the five-number summaries of each plot, and should clearly label each value on their boxplots.

  6. Students should answer the 3 questions included in the handout. The can discuss their answers in pairs, and then have a class share out of the responses.

  7. Once the discussion wraps up, inform the students that they will now attempt to find plots that represent the same data but are plotted differently.

  8. Distribute one set of plots, from the Plot Match file (LMR_2.12), to each student team.

    Advanced preparation required: Each student team will receive a set of plots containing all 15 plots from the Plot Match file (LMR_2.12). Copies will need to be cut and sorted prior to class time. To keep the plots together, you can either paper clip them or place them in zippered bags.

    Note: Do not distribute the handout for students to cut out the plots!

  9. Inform students that they are now going to gather in their teams and practice matching different representations of distributions. Each group will receive 15 plots (5 dotPlots, 5 histograms, and 5 boxplots). Their task is to determine which dotplots, histograms, and boxplots represent the same data.

  10. Once each group has decided upon their 5 groupings, engage the students in a class share out until all students agree. Then, have the students record their responses to the following statements and/or questions in their DS journals:

    1. What types of data are best for using a histogram? Histograms are useful for almost any type of data. They can easily show the shape of a distribution (including skewness and multiple peaks). They are usually best with larger data sets.

    2. What types of data are best for using a dotplot? Dotplots can also easily show the shape of a distribution. They are preferred over histograms when there is a relatively small amount of data.

    3. What types of data are best for using a boxplot? Boxplots are useful when the distribution has one mode (one peak). They are also useful to describe data that are heavily skewed or that contain outliers.

    4. Describe some characteristics of data that become hidden when a boxplot is used instead of a dotplot or histogram. Dotplots and histograms can show the number of modes in a distribution, but a boxplot cannot. If a distribution is bimodal, we will not be able to tell in a boxplot. In general, we lose the ability to talk about the overall shape of the distribution.

  11. Display the uncut version of the Plot Match file (LMR_2.12) so that students see the letters that correspond to each set of representations.

    Solution key:

    Set 1: Plots (d), (a), (b)

    Set 2: Plots (m), (c), (h)

    Set 3: Plots (f), (j), (o)

    Set 4: Plots (e), (l), (i)

    Set 5: Plots (n, (k), (g)

  12. Have a few students share out their responses. For homework, students will record some pros and cons of using different types of graphical representations to display the same data.

Class Scribes:

One team of students will give a brief talk to discuss what they think the 3 most important topics of the day were.

Homework

Students should reflect on today’s class discussion and record their ideas of some pros and cons of using different types of graphical representations to display the same data.

LAB 2B: Oh the Summaries…

Complete Lab 2B prior to the Practicum.