How Does It Compare?

Given 2 data sets, students will be able to: 

1. Compute measures of center (mean, median, mode).
   • Advanced students can compare different measures of center and when they are used.
2. Compute measures of spread (Range, IQR, Q1 and Q3).
   • Advanced students can talk about the advantages and disadvantages of using range vs. IQR. Including standard deviation can also significantly increase the difficulty of this project.
3. Choose a visual to aid in the comparisons of centers and spreads.
   • Lower level students should focus on being given the template of a box and whisker plot.
   • More advanced students should be put into a position to choose their representation of data and be prepared to defend it OR discuss the nuances of data collection techniques.

This project allows students to look at relevant questions about comparing 2 data sets. Examples of topics might include comparing 2 basketball players, determining which side of town has better prices, or who builds a more reliable car. This project is a good project to do at the end of a statistics unit in an Algebra 1 or Algebra 2 class as students will have the power to apply the measures of center and measures of spread that they have learned to 2 data sets. More advanced students will have the ability to compare different measures and even use the comparisons to justify their comparisons.

One of the central areas of statistics is to be able to represent measures of center and measures of spread visually to make meaningful comparisons across data sets. Technology can be used to enhance these comparisons. More tech savvy and tech interested students can explore online statistical programs or even a program like Microsoft Excel to articulate their comparisons with data. Other students might like creating a poster or a printed representation to compare their data.

The project as written includes 5 data sets over diverse topics to provide students choice and build insight into relevant problems: 

• Is Lebron James better than Steph Curry?
• Does the Northside of Indianapolis or South Side of Indianapolis have better gas prices?
• Are Fords faster than Chevys?
• Is Carmel more expensive than Herron Morton place?
• Has IU or Purdue had a better basketball program these past few decades?

It is encouraged that teachers use the templates of these data sets to include items of local and student interest to enhance perceptions of relevance for this project.

Students will be evaluated on their knowledge of the center and spread by their work on the poster/PPT and how it fits into the developmental rubric. Good projects have accurate computations of mean, median, mode, and IQR. Graphs should be well labeled and include a title.

Exemplary projects include analysis such as the impact of outliers on their data or a discussion on the data collection and perceived limitations.

• Project Expectations/Rubric – This was used in a summer school credit recovery Algebra 2 class in a virtual setting. In an in person Algebra 2 class in a previous semester, I added a discussion of sampling methods as that was a skill covered in the statistics unit. A few additions for more advanced students:
  • Include standard deviation in measures of spread. 
  • Take out descriptions of data or have students search their own data sets so they can formulate their own analysis about the data collection process.
• Stats Project Help Video – In this 17-minute video I show a sample comparison of car companies and reliability.
  • For Pre-Requisite Skills, some of the following videos might be helpful:
    • Measures of Central Tendency
    • Measures of Spread

• Example Work – This document looks at examples of Advanced Statistical Thinking and Tech Integration. 
• Google Form Project Proposal – Make sure to recreate/copy this form so you are the owner before you share it with your students. You won’t have access to the answers/results if you don’t.
• Video Note taking Guide

It is assumed that lessons on centers and spreads have been taught prior to this current lesson.

Part I

Stats Project Help Video (20 minutes)

Phase 1: Introduce the Stats Project Help Video. You might want to use this video notetaking guide to help out. The video note taking guide can be used in 2 ways: 

• For a class with more dependent learners, consider showing the video and periodically pausing the video to ask cold call questions. Have the students write down the computations from the video in the video note taking guide.
• For a class with more advanced and/or independent learners, you might want to consider having the students work through the Consumer Reports dataset as a bellwork in a think, pair, share format. Perhaps, in a partnership, one student can do the measures of center and one student can do the measures of spread. The questions in the video note taking guide might be good for discussion in partnerships or a whole class setting. 

Part 2

Project Roll Out (15 minutes)

Introduce the project to the students by going through the project expectation document. It would be good to cover the rubric and introduce the 5 data sets. After you go through the project expectations, have students fill out the Google Form Project Proposal for their project proposal and answer any questions they might have. Be sure to make your own copy of this form as you will not have access to the results if you don’t.

Take time to go over commonly asked questions. You might want to consider showing the Google Form responses in class.

Part 3

Work Time on the Project (60 minutes + homework for the next class)

As students are working on their proposal, they should do their computations first before doing any graphics. Make sure students are defining key vocabulary like mean, median, mode, Q1, Q3, IQR, range, and standard deviation (if applicable). Then, students can think about their writeup or final product. This writeup can be done on a posterboard, PPT, or a Google Doc.

Observations during work time

• Dependent/lower level learners will need some support with concepts like IQR, Q1, Q3 and will struggle with the concept of spread. It might be helpful to have a worked out data set that shows the steps in the computations of these that they can work off of and apply to their own data. 
• Advanced students should be pushed to analyze and evaluate different computations. Such questions to deepen knowledge levels include: 
  • Is the mean or the median working better in your situation?
  • How are outliers affecting your dataset?
  • What could be done to strengthen the data and arguments the next time research is done on this issue?

Encourage students to evaluate themselves using the language and checklist of the rubric.