Lesson 6: Face Off

Lesson 6: Face Off

Objective:

Students will informally compare two or more distributions using their knowledge of shape, center, and spread to answer statistical questions. They will learn how to find the difference between two means and two medians using a histogram or dotplot.

Materials:

  1. Comparing Commute Times with Dotplots handout (LMR_2.8_Commute Times – Dotplots)

  2. Comparing Exam Scores with Histograms handout (LMR_2.9_Exam Scores – Histograms)

  3. Timer

  4. Comparing Fuel Efficiency with Boxplots handout (LMR_2.10_Fuel Efficiency – Boxplots)

Vocabulary:

rebuttal

Essential Concepts:

Essential Concepts:

Writing (and saying) precise comparisons between groups in which variability is present based on the (a) center, (b) spread, (c) shape, and (d) unusual outcomes help to make statements in context of the data. Actual comparison statements should use terms such as "less than," "about the same as," etc.

Lesson:

  1. Poll students about the method of transportation they use for their daily school commute. How many of them walk, ride in a car, take the bus, ride a bike, etc.? Record their responses on the board. Ask them to estimate the typical amount of time it takes for them to get to school, in minutes.

  2. Inform students that they have learned important features of distributions that will allow them to make decisions when working with data. More specifically, they will be able to use their knowledge of measures of center and measures of spread to compare 2 distributions in order to make a decision.

  3. In teams, have students complete the Comparing Commute Times with Dotplots handout (LMR_2.8). Allow students time to read the “Background” portion of the handout, and then discuss what statistical question(s) the student in the scenario is trying to answer.

  4. Once teams decide on their recommendation, engage half of the class in an Active Debate. Half of the students will stand in a debate line and the other half will “fishbowl” the debate. Roles will reverse later in the lesson (see Step14).

  5. Of those students standing on the debate line, half will argue the reasons why they recommend street travel and the other half will argue the reasons why they recommend freeway travel.

  6. On the debate line, each student will stand face to face with a student who has the opposite recommendation. In other words, a student who recommends street travel will stand facing a student who recommends freeway travel.

  7. Using a timer, allow one minute for students who recommend freeway travel to argue their point to the person they are facing. Then, repeat for students who recommend street travel. Students should not interrupt or respond; they should only listen to the other side.

  8. Next, give debaters two minutes to prepare a rebuttal of the other person’s argument. For example, if one student claimed that freeway travel is better, the other student may ask where the evidence is in the data or show that the data does not support the claim.

  9. Allow each debater two minutes to present his/her rebuttal.

  10. Finally, ask debaters if any of them changed their recommendations after engaging in the debate.

  11. In teams, have students complete the Comparing Exam Scores with Histograms handout (LMR_2.9). Allow students time to read the “Background” portion of the handout, and then discuss what statistical question(s) the student in the scenario is trying to answer.

  12. Repeat debate process (Steps 4 - 10) with the other half of the class.

  13. Summarize the lesson by conducting a class discussion about what to look for when comparing distributions. Students should be precise when estimating values of means, medians, MAD, and IQR. They should also be able to comment on when it is most appropriate to use each measure of center and spread. If a distribution is symmetric, it is best to use the mean as a measure of center and the MAD as a measure of spread. If a distribution is skewed, or has outliers, it is best to use the median as a measure of center and the IQR as a measure of spread.

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

Similar to the activities they did during class today, for homework, students should complete the Comparing Fuel Efficiency with Boxplots handout (LMR_2.10).