Plan: Talk about term paper. Median (in Excel). Histograms. Mean, median and mode. Probably more than we can do!
Didn’t talk about the term paper at all. Did do a lot of Excel work – reviewed mean for Wing Aero using Excel, then computed the median.
I asked “what fraction of the values would be less than the median?” for an arbitrary data set. One student said (as the light went on) “half!” I said I’d ask that question on an exam and most would get it wrong. So another student asked why I would ask a question that most students would get wrong. Good question. Questions everyone can do or questions no one can do are not diagnostic. Exams should consist of a range of questions from almost trivial to almost impossible. There’s a distribution of difficulty lurking there which I’m tempted to make into a problem for the exam (or at least for the text). Then students who read this blog would have a little head start. (But none do.)
Built the histogram, then talked about the mode. Two or three of the students hung around after class saying “that’s interesting”, really understood how summary information did and didn’t shed light on the full data set. For the rest of the class (which was again quite small…) I think a lot was learned, but not nearly as much.
When building the histogram we counted bucket contents by hand. I said we could check by counting the entries. When we did there were 15 and I said right away “something is wrong” and changed COUNTing entries to SUMming entries. Then I backtracked and reviewed my thought process – when I saw the 15 I knew something was wrong because I knew I expected to see 30 – the number of employees. Without an idea of what the answer should be I wouldn’t have recognized a wrong answer. In this case the error was in my method. When I replaced COUNT by SUM the answer was 27. That was still wrong, because we’d counted one of the categories incorrectly. (I knew that too, because I knew the numbers in the book.) We fixed the count, changing one 7 to a 10. Then the total was right. (I noted that there still might be an error, if we overcounted one bucket and undercounted another, but we weren’t going there. Nor were we going to the complicated instructions needed to have Excel count the bucket contents.
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