Exercise: Deadly doctors

deadly doctors
Goal: demonstrate that extreme results are not necessarily out of the ordinary
Materials needed: two dice per person, sheets of paper labelled clearly 2 to 12
Time: 10 minutes
If a journalist wants to uncover a story, they need to follow any suspicious lead they find.  But how do we decide when a figure is out of the ordinary, rather than just at the extreme?
Give everyone in the class two dice, and congratulate them on becoming surgeons.  You are playing the role of the hospital administrator.  A roll of both dice determines how many patients died on their operating table this year.  Lay the sheets of paper numbered 2-12 on the floor in order, and have students line up behind the sheet showing their score.  (The students will form a histogram showing a normal curve.)
"Ask if the people at the far end (11 & 12) should be struck off.  Most students will say yes.  You can bolster your case by using a histogram to show that the chance of seeing this many patient deaths is very small."
Repeat once or twice without allowing the struck-off surgeons to roll.  Observe that previously good doctors are now rolling high numbers.
"Why do some people experience higher death rates?  Why, having removed the worst doctors, are more replacing them at the upper end of the scale?  Could anyone score highly? As an administrator, if I keep firing those high rollers, how long until I lose all my doctors?"
The lesson here is that although 12 is high, it is not unexpected or improbable.  Extremes are normal.  Get the students thinking about what range of figures they should expect to see in day to day life (i.e. the spread of data), rather than focussing on the highest number.
Image “Dicing with Death” CC Wellcome Images

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