Friday, January 6, 2012

Average vs Median

Argh, sometimes people drive me nuts as evidenced with following (paraphrased) quote:
"But it is statistical fact that you cannot have more than half the population above the average and thus the statement cannot be true."
Can I say for the record this is entirely false. You can trivially prove via the following set: {1, 2, 1000, 1001, 1002, 1003}. The average of that is 668.16 which means that 4 of the 6 elements are above the average, i.e. more than half the population.

Of course, had they talked about the median I would have been OK with the statement as written.

I didn't realize that this was a common rant around my house until I mentioned it to my non-math major wife and she replied, "Of course the median and the average aren't the same. Look at a skewed normal distribution" which is a surprisingly good rebuttal.

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