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Friday, May 27, 2005

Where visuals fail

Some of us couldn’t possibly forget the 1969 draft lottery, the new and supposedly “fair” system to pick who was going to be sent to Vietnam. My Algebra 2 class is studying probability and was remarkably interested in learning about the lottery. Everyone wanted to find out what “their” number would have been — even the girls, who of course wouldn’t have been called anyway. They were particularly interested in whether their number was less than 196, since those born on the first 195 birthdays that were “randomly” selected ended up being drafted. After describing the system and pulling some sample birthdays, I showed the class a scatterplot of the numbers drawn for each date of birth:

At first glance this distribution looks fair. In fact, it looks totally random. At second glance, some see a tiny bit of a pattern, but it still looks quite random.

So then we looked at the numbers. Taking the two extremes, we calculated that the probability that a young man born in January would be drafted was only 14/31, or 45%, but the probability that one born in December would be drafted was a shocking 25/31, or 81%.

Usually a picture is worth 1000 numbers, but this is a dramatically counterintuitive example where plain numbers have more impact than a scatterplot.

By the way, my number was 205.

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