Lesson 6: Face Off

Objective

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

Vocabulary

rebuttal

Essential Concepts:

Lesson 6 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

What method of transportation would you use for your daily school commute? Would you walk, ride in a car, take the bus, ride a bike, etc.? Using the method you chose, estimate how long it would take you to get to school (in minutes).
You have learned important features of distributions that will allow you to make decisions when working with data. More specifically, you will be able to use your knowledge of measures of center and measures of spread to compare two distributions in order to make a decision.

Read the “Background” portion of the handout. Then in your IDS Journal, write down what statistical question(s) the student in the scenario is trying to answer. Also in your IDS Journal, answer the question at the bottom of the handout.
Complete the Comparing Commute Times with Dotplots handout.

Click on the document name to download a fillable copy of the Comparing Commute Times with Dotplots handout (LMR_2.8).
You will now imagine that you will debate your classmates about which is the better travel option: freeway or street. For this Active Debate, you will have to argue both sides. Imagine you are in two teams: Team Freeway and Team Street. The best way to do this is to write a two-column list. In your IDS Journal, make a two-column table. Label one colum Team Freeway and the other Team Street.
In the Team Freeway column, write down the benefits of freeway travel using the information you see in the boxplot. Use your knowledge of distributions to list as many reasons as you can that support the claim that freeway travel is better.
In the Team Street column, write down the benefits of street travel using the information you see in the boxplot. Use your knowledge of distributions to list as many reasons as you can that support the claim that street travel is better.
Spend time comparing and contrasting the benefits of Freeway vs. Street Travel. Rank the benefits of each column from strongest to weakest. Put the number 1 next to the strongest reason, 2 next to the second-best reason, and so on. Then, decide if you are Team Freeway or Team Street.
Next, you will prepare a rebuttal of the other team's argument (the one you did not choose). A rebuttal is a way to argue back against someone's claims. For example, if you chose Team Freeway, look at the Team Street column and look for weak spots. You can ask, "Where does the dotplot show a certain benefit?" or "Where is the evidence for one of the claims?" Write your rebuttal of the other team's benefits/claims in your IDS Journal. Below is a rebuttal frame that you can use.

Those who disagree believe that __ travel is the best way for the Data Science student to commute. However, the data show that __ travel is a better way to commute. First, the data show that __. Next, the visualization shows that there is __. Although it is true that __ shows that __ , that point is weak because __. For these reasons, __ travel is the best way for the student to commute to school.
Finally, go over both columns and your rebuttal one last time. Make sure that your claims, reasons, or benefits are supported by the data and the dotplot. It should not include your own opinions.
Refer back to your recommendation for the best route (freeway or street) and answer the following questions in your IDS Journal:

Did your initial choice when you completed the handout change after arguing both sides? Explain why or why not.
Complete the Comparing Exam Scores with Histograms handout. Read the “Background” portion of the handout. Then, in your IDS Journal, write what statistical question(s) the student in the scenario is trying to answer. Also in your IDS Journal, answer the question at the bottom of the handout. Make sure you have clearly stated which exam was easier using the histograms to support your claim.

Click on the document name to download a fillable copy of the Comparing Exam Scores with Histograms handout (LMR_2.9).
Repeat the "debate process" (Steps 4 - 10). You should be precise when estimating values of means, medians, MAD, and IQR. You should also be able to comment on when it is most appropriate to use each measure of center and spread.

For example: If a distribution is symmetric, it is best to use the __ as a measure of center and the MAD as a measure of spread. If a distribution is ____, or has outliers, it is best to use the median as a measure of center and the IQR as a measure of spread.
In your IDS Journal, do a quickwrite explaining why is it important to debate two sides using data as evidence to support the arguments.

Reflection

What are the essential learnings you are taking away from this lesson?

Homework

Complete the Comparing Fuel Efficiency with Boxplots handout by answering the question at the bottom. Make sure your claims are supported by the information contained in the boxplots.

Click on the document name to download a fillable copy of the Comparing Fuel Efficiency with Boxplots handout (LMR_2.10).