Yao is Irrelevant

Don Boudreaux links to Bryan Caplan's clear explanation of the danger of misinterpreting averages, and writes about an example he uses in Econ 101:

I use average height to explain to my students the problem with taking averages at face value. Suppose the average height of my class of 200 students is calculated and turns out to be 5�8�. Then let Yao Ming walk into the classroom. Because he is 7�6� tall, he will increase the average height of people in the classroom � but do nothing to the heights of any individual in the classroom.
The logic makes sense to me, and is a good point to make, but adding one person with an extreme attribute to a large group will usually have little effect on the resulting mean value.

I made that point when measuring the average hourly pay of Wal-Mart workers. Adding in the $10 million salary of WM's CEO H. Lee Scott increases the hourly wages of a million Wal-Mart employees by about half a cent an hour. This is irrelvant for almost all purposes. As I wrote, the median and the mean are close enough for all but nit-picking.

I'll make the same point with adding Yao to Econ 101. 7�6� Yao Ming will raise the mean height of Don's 5�8� 200 student class by approximately .11 inches. The new mean is 5�8.1��. All this means is that whether or not Yao is added is irrelevant for almost all purposes of measurement -- but is extremely important for fielding a basketball team from Don's students.

(Here's the arithmetic: 200 students at 5'8'' yields 13600 total inches. Adding in 7'6'' Yao yields 13690 inches. Dividing by 201 yields 68.11 inches on average -- or 5'8.11'')

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This page contains a single entry by Kevin published on March 29, 2005 11:02 AM.

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