I graded most of the exams – students seem to have done nicely. Will collect the improved versions today and see if they managed the third problem better.
Plan to start weighted averages. I should be able to do the general idea, then GPA. I’d like to get to one of the paradoxes, which I can state in voting terms: Party X can win majorities in each of two constituencies and not have an overall majority. But it’s hard to see how to write this as a weighted average other than using the artificial mathematical construct that looks at a percentage as an average of some zeroes and ones.
We’ll see what I come up with.
What happened … lots!
Weighted average of four grades of 90 and one of 70 is (4/5)*90 + (1/5)*70 = 86, four fifths of the way from 70 to 90.
Calculated GPAs with credits as weights.
Did the hard problem – what do you need to do to improve your GPA? Solved with algebra and with guess-and-check.
Time out for a rant about why spelling and grammar matter – they may cost you a job some day, they irritate fussbudgets like me enough to destroy (or at least interfere with) my ability to understand what you are saying. Also, please use “therefore” or “so” between steps when solving an equation – don’t use equals signs, or arrows. Words matter!
Back to averages – paradoxes.
- In each of Physics and English women’s average salary exceeds men’s, but it’s smaller for the faculty as a whole.
- Average car and truck prices both go up while average vehicle price comes down.
I showed how considering an extreme case might help explain – e.g. suppose last year all vehicles were trucks, this year all cars
Then I even had time for the class size paradox.
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