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Marathon of Numbers

Great article, Do the Math: Our Problem with Numbers, on being a critical consumer of statistics as “hard facts”.  The Chicago Tribune stated a rough estimate of crowd size at the Chicago marathon as being 1.7 million people.  So what would this look like along a 26.2 mile route?  Would this mean a dense crowd 10 people deep along the entire course, or a more sparse intermittent crowd of a couple people here and there?  In effect we are asking you to create a new scale, replacing miles with “people” as a measure of distance.  If you had people stand side by side along both sides of the entire route how many could you fit?  Questions like this gave my students fits!  It was much harder than I imagined, given that the author actually walks through a computation for us.

Chicago marathon

It starts easily enough, 1.7 million people over 26.2 miles is about 65,000 per mile or 32,000 people per mile on each side.  Already the “each side” is starting to clog up my students’ short term memory, making the next calculations even harder to follow.  A mile is then divided into full blocks (one-eight of a mile), or 16 short blocks, each 110 yards long.  We have quickly introduced 2 rates in terms of people per mile (or people per mile both sides), and 4 different units for distance.  The full block is given as a fraction of mile while the short block is introduced as the number in a mile, and only the short blocks are converted to yards.

Now the author does try to simplify all of this by saying: “Divide those 32,000 people per mile by 16, and we get 2,000 spectators in a block 110 yards long. Allow 2 to 3 feet of space per viewer. To get 2,000 spectators in those 110 yards would require packing them in, shoulder to shoulder, 12 to 18 people deep!”  But once again so much is packed into these sentences that my students were not able to process everything meaningfully.  The density of 2-3 feet per viewer was particularly challenging, especially translating that into 12-18 people deep.  Before proceeding, and definitely before assigning this article :O), compute the 12-18 people deep from the 2-3 feet per viewer.

I asked the following questions and my students struggled mightily.  The first one could have been solved with a simple proportion (1.7 million is 1.7 times 100,000)!  The second question where I ask them to run the computation in reverse was like watching  people try to run a marathon in reverse, pretty comical.

Quiz 7 Marathon Numbers

  1. In the article, Do the Math: Our Big Problem with Numbers[1], the author converts the total number of spectators into how “deep” the crowd would have to be if everyone stood shoulder to shoulder (2-3 feet of space per viewer).
    1. Assume the actual number of viewers is only 100,000. Perform a similar calculation to compute how deep the crowd would be.
    2. If the crowd is 2-3 feet deep how many total spectators would this predict if we run the author’s computation backwards?
    3. If instead of crowd depth, we measure the crowd by the number of spectators per short block and average 50 spectators per short block. How big is the total crowd?


[1] http://www.chicagotribune.com/news/opinion/commentary/ct-chicago-marathon-numbers-spectators-false-perspec-1013-20161012-story.html












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