The Tomato Diaries

Sven is endlessly curious about math and frankly I'm a little worried that school next year won't give him enough to bite into. So he's signed up for 8th grade math in the fall and we've been doing a little math over the summer to make sure he had all the 7th grade bases covered. (He tested into 8th grade math, but these things aren't linear.)

I bought the school district's math book, Everyday Math and it's, how do I put this politely? A steaming pile of crap.

So we've pretty much had to write our own math book. The first unit to cover was probability and statistics. Everyday Math had a table of actual US immigration data and a series of measurements of an (imaginary) girl's head. The reader was expected to understand that one set of measurements was dominated by noise, whereas the other had inconsequential measurement error. I'm not sure why 8th graders are supposed to intuit this, given that many scientists have trouble with these concepts. But more importantly, all of the problems were boring.

So we decided to make some measurements of our own, so we'd have some data that we had a real feel for. What to measure? I figured nuts from the store, but a pine nut weighs around 3 grams, and our scale reports only to the whole gram. So we would have been overwhelmed by measurement error, which isn't normally all that much fun.

Sven thought of tomatoes from the garden. Much better. More variation than pine nuts anyway, and a light tomato is 25g. So good.

At right is our combined data from the first two harvests, conveniently of exactly 12 tomatoes each. X is tomato weight in 5g buckets. Y is count per bucket. Sven is predicting the third harvest will drive up our average weight and standard deviation. We've been looking at the data to see if it has an approximately Gaussian shape. We'll get more formal about that in a little while.

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