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Deceptive Per Captia Rankings for Brain Cancer

We're working on a project to produce a report on the ratings that students give to their professors at the end of the semester. There is a big concern by the math people on the committee that we will give some professors an unfair bad (or good) rap because of the variability in these rankings. They don't want to report the ratings as a mean (average). Instead, they want to plot an uncertainty range. 
I was reading a book this week (How Not to Be Wrong by Jordan Ellenberg) that provided a great example of the risk of ranking things when there is uncertainty. It can lead to erroneous conclusions. Here is a summary of his argument that appeared in an NPR interview. Perhaps this sort of example will be helpful for the committee to share when teaching the general faculty about the new instrument.
If you take a rare disease like brain cancer and you look at its rate of incidents in different states, there are very big differences. And so you might say, "Well, I should go wher…