My high school history teacher liked to illustrate the fallacy of averages with this vivid example: "Say I had two steaks for dinner, and you had none. On average, we each had a steak. Isn't that great?" I remembered his words when I came across the article on the flaw of averages. The author mentioned another metaphor that is both funnier and more tragic: "A humorous example involves the statistician who drowned while wading a lake that was, on average, only three feet deep." The article uses a hypothetical investment scenario to drive home the point that using averages may get you in a lot of trouble.
Average is a useful mechanism for compressing data to simplify the picture. It's common for Swivel to show averages on graphs. For example, this graph shows average distance from the Super Bowl host city to the winner's city (highest seven between 1967 and 2005):
LA is the "winner" here: you could probably guess that most of the time the winning team isn't from there. Of course, it's only a guess because the average hints at what's going on but hides the real picture. It's actually possible in Swivel right now to change the display of data to highest or lowest values (just click in Edit button and play with the 'Display' drop-down list) but what's needed to get a better view is the range of values. A box plot is one way to show it. Our graphing engine, Ploticus, supports box plots, so we'll just need to make them look nice and add the option to the user interface. I love long to-do lists, there's never a worry that you'll run out of things to work on.
So next time you see a graph on Swivel showing average data, remember the drowned statistician.
(UPDATE: this blog post fell victim to a sorting bug: bar graphs occasionally lose sort order, so I had to update the embedded graph. Apologies to those of you who've had the same problem with Swivel graphs. We're on this bug and will fix it soon.)
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see that has axis values, nice one
Posted by: Anton | February 08, 2007 at 07:48 AM