19 paupers and a billionaire in a room…

I’ve never had much time for mathematics, particularly being bedevilled by statistics. And so it was welcome to receive in my email this morning a fairly clear explanation, courtesy of wikipedia, of the distinction between the mean and the median. Finally!

Suppose 19 paupers and 1 billionaire are in a room. Everyone removes all money from their pockets and puts it on a table. Each pauper puts $5 on the table; the billionaire puts $1 billion. The total is $1,000,000,095. The money is then divided equally among the 20 people, each gets $50,000,004.75 – this amount is the mean (or “average”) amount of money that the 20 people brought into the room.

But the median amount is $5, since one may divide the group into two groups of 10 people each, and say that everyone in the first group brought in no more than $5, and each person in the second group brought in no less than $5. In a sense, the median is the amount that the typical person brought in.

By contrast, the mean (or “average”) is not at all typical, since nobody in the room brought in an amount approximating $50,000,004.75.

Now I need to put the distinction into practice… (I wouldn’t mind joining them in that room. Sounds like a nice room.)


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