Saturday, September 26, 2009

Bill Gates Walked into a Bar

I’ll get around to the punch line after a little bit, but one of the concepts that has become important in our work is the difference between the mean and median averages. For those of you who have forgotten your Fifth Grade Math, here’s an explanation from

Mean and Median

The arithmetic mean, also called the average, of a series of quantities is obtained by finding the sum of the quantities and dividing it by the number of quantities. In the series 1, 3, 5, 18, 19, 20, 25, the mean or average is 13 – in other words, 91 divided by 7.

The median of a series is that point which so divides it that half the quantities are on one side, half on the other. In the above series, the median is 18.

The median often better expresses the common –run, since it is not, as is the mean, affected by an excessively high or low figure. In the series 1, 3, 4, 7, 55, the median of 4 is a truer expression of the common-run than is the mean of 14.
Most of us are used to dealing with the mean, and that’s usually what we mean by “average”, but as the explanation suggests, the median is often a more useful way of thinking about something.

At one point a few years ago we hired a consultant to do a study of a zip code in the City of Dallas where we were doing some work. He calculated both the mean and median income of people living there. The mean family income was $94,000 per year, while the median family income was $14,000 per year—barely above the poverty level even for a single person.

The consultant told us this area was the most unusual that he had ever seen. Think about what the difference in the numbers tells us about the people who live there. If the median is $14,000, and the mean is $94,000, then the top fifty percent in income of the people living in the area had to average at least $174,000 in yearly income. Half the people living there make less than $14,000 while the other half make almost $175,000 income.

That’s an unusual disparity in income—the particular zip code included both a federal housing project and some extremely high income areas where a number of multi-millionaires lived. It isn’t unusual for a large disparity, if not quite that large, to exist between the mean and median incomes in a city, a neighborhood or even a particular census track, and that disparity changes how we need to think about neighborhood revitalization. What needs to be done to improve a neighborhood is very different is everyone in a neighborhood is middle class or the neighborhood has a few very rich people and a lot of very low income people.

“So Bill Gates walks into a bar, suddenly on average everyone in the bar is a millionaire.”

But you won’t have any more money than you did before Bill Gates came in.

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