Experience First

To start this lesson, you might want to check that students know what Skee Ball is all about. It might even be worth showing them this quick video.  

 

In this activity, students must predict which Stats Medic will win the Skee Ball game, based on probability and expected value (mean). We really like this activity because students will get contradictory evidence as they work through the activity, ultimately revealing a need for expected value. Question #3 suggests that Mr. Wilcox will win. Question #4 shows that they will tie. Question #5 should reveal that Ms. Gallas is more likely to win (true story).

 

Students will need access to a computer or device for this activity to use the “Discrete Random Variables” applet at www.statsmedic.com/applets. 

 

In question #4 of the activity, students calculate the mean of X and the mean of Y. We fully expect students to use the incorrect mean formula they already know (add ‘em up and divide by the number of number). What students are missing here is the fact that each X value has a different weight (it’s probability) and this must be accounted for in the calculation. 

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Formalize Later

When debriefing question #5, point out that the mean from the applet does not match the mean calculation from the previous question. This is now your opportunity to talk about probabilities acting as weights and the correct formula for calculating the mean. 

 

While the third learning target calls for students to “calculate” the standard deviation, we felt this was unnecessary to do by hand with a formula. We are much more interested in the interpretation of the standard deviation. Therefore, we suggest having students use the applet to “calculate” the standard deviation.