In my second post, I gave the mathematical definitions of median and arithmetic mean (average). These were pretty *useless*, like all mathematical definitions, because I did not explain when to *use* median salary vs. average salary.

O.K., time for everyone to cringe: remember “word problems” from 4th grade mathematics? It turns out life is a word problem. A computer can do math calculations for you (including calculus), but computers are really bad at turning word problems into meaningful answers. A human has to decide which is the best equation to solve a word problem.

To choose between median and mean, we have to get to the underlying word problem. At PayScale, a common word problem we are asked is, “what is the *typical *salary for job X?”

Time for a little side trip into word use: *typical* is a common dictionary definition for the word *average*. In fact, people often ask us, “what is the *average *salary for job X?” Unfortunately, *average* also has the specific meaning in statistics of the arithmetic mean. Because of this linguistic overlap, people often expect the arithmetic mean to be a good way to measure what people *typically* earn. It isn’t.

The median salary is often much closer than the arithmetic mean to what common intuition would give for the typical salary. Strangely, people, political parties, newspapers, even statisticians continue to calculate the arithmetic mean and present it as a “typical” salary answer, when median salary would be much closer to what people want to know.

I have to get back to my day job for today. Over the next few posts, I will spell out why the median salary is a better measure of typical salary, give a historical justification for why peoppeople often expect the arithmetic mean to be a good way to measure what people *typically* earn. It isn’t.le use the mean anyway, rant about why both Democrats and Republicans mislead through careful use of both the median and the mean, and talk about even better ways to measure what is a typical salary.

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