A-Mazing Inferential and Descriptive Statistics!

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Objective

Students will be able to participate in a study, discuss the data collection technique, and lay the foundation for descriptive and inferential statistics.

Big Idea

This is an A-Mazing opportunity for the students to learn about descriptive and inferential statistics!

Disguised Data Collection!

10 minutes

Begin class by handing out the maze (face down).  The students will likely be a little dumbfounded that they are starting math class by doing a maze – but little to their knowledge, it is a form of data collection!  Prior to instructing the students to begin the maze, project a timer on the board for everyone to see.  Tell the students that everyone will begin the maze at the same time.  Once a student completes the maze they should record their time at the bottom of the sheet.  Ready – Set – GO!

While the students complete the maze, I hand out sticky notes for them to privately record their time on.  We will use these times to create our data table.  Once everyone is complete and has recorded their time and gender on BOTH their maze sheet and their sticky note, I collect the sticky notes and create the class data table.  

Class Discussion

20 minutes

At this point in the lesson, the students will likely be highly engaged and full of energy.  If the guys appeared to be faster – they will be letting the girls hear about it!  (Likewise if the girls appear to have completed it faster!)  This is a perfect time for a class discussion!

I begin by asking the students about the maze test:

  • What did you notice about my data collection?
  • Did you initially know you were taking part in a study?
    • How do you think this impacts our results?
    • What might this study seek to infer?
    • What things do you notice about our data? 
      • Have a discussion centered on the outliers… BE CAREFUL channel the conversation around outliers and NOT let the students say, “Well, a couple of smart kids finished in 2 minutes and a couple of dumb kids finished in 10 minutes.”  THIS KILLS A CLASSROOM CULTURE!
      • What impact do these outliers have on our data, and how do you think we will deal with them?

THESE ARE JUST A FEW POSSIBLE DISCUSSION POINTS!  THERE ARE COUNTLESS OTHERS.  As long as you are careful about the direction of the conversation, it is an awesome platform to discuss many important data collection issues.  The students will also likely make connections to the flaws and fallacies lesson, which is great!  The students may not be able to explicitly say that we have independent random samples with equal variances, and that the distributions of the maze completion times for males and females are approximately normal, but they WILL leave with the foundational understanding of these important concepts.  We will discuss them more in upcoming lessons.

Wrapping up the discussion:  (4-5 minutes) To wrap up the discussion, I ask the students what types of statistical calculations they are familiar with, and how we can use them to look at our data.  This is where the students will give answers like “mean, median, and mode” – low level tools of statistical analysis.  As the students give me examples of each, I write them on the board.  When we have exhausted the students’ prior knowledge I ask them “Does anyone feel a little inadequate with this small little list that we have created?”  Although these are good starting points, there are so many more powerful tools at our disposal!  Remember those things that we defined as outliers?  They can really kill a good mean calculation.  In the coming days we will look at ways that we can analyze the data as objectively as possible. 

 

Histogram of Data Set

10 minutes