# Autarchy of the Private Cave

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## Mean or median?

16th September 2006

Mean is just a mathematical average of all the data point values; median is the value, which divides the continuum of data point values into two equal parts: values of the “left” part are all smaller than the median, values of the “right” part are all bigger than the median. Comparing mean and median, they usually say that

• mean is optimal for standard deviation calculation in the sense that it is the only measure of data points range, when standard deviation is the smallest possible;
• median is much less sensitive to the extreme values (outliers), which often are the result of error, and thus presents a more fair idea about the data set.

Here’s a popular comparison example for mean and median:

Suppose 19 paupers and one 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 (that is, \$109) there. The total is then \$1,000,000,095. If that money is divided equally among the 20 persons, each gets \$50,000,004.75. That amount is the mean (or “average”) amount of money that the 20 persons brought into the room. But the median amount is \$5, since one may divide the group into two groups of 10 persons 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 no one present—pauper or billionaire—brought in an amount approximating \$50,000,004.75.

More can be found here and here.

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