Averaging paradoxes
Started the class answering a homework question on finding the weights in this CPI graphic
The problem is a little harder than routine – it asks for the weights. But the hardest part was getting the students to tell the story – the idea that people ate some food at home, some out, in different proportions, and that the percent increases in the two kinds of food were different. Then think a little qualitatively – if almost all was eaten out the average would be nearer the 2.7%. Then we worked on finding the actual weight. Guess and check was the first strategy of choice. I did point out that you could do the problem with algebra – but that you shouldn’t use that strategy unless you liked algebra. Guess and check will serve you well even in places where algebra fails.
The really interesting stuff came next – the paradoxes. No one made progress even starting
Alice and Bob are both students at ESU. In September they start a friendly competition.
In June they compare transcripts. Alice had a higher GPA for both the Fall and Spring
semesters. Bob had a higher GPA for the full year.
(a) Explain how this can happen, by imagining their transcripts.
(b) Who wins?
But we were able to do it collectively. The clue, of course, is that they can have very different credit course loads in the two semesters.
Finished with “on average your friends have more friends that you” and the average class size paradox (teachers see a smaller value than students). Some of them enjoyed it. I did.
On to Excel next time.
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