January 15, 2007

mean, median & mode

I just read an interesting post at good math, bad math about statistical averages (aka measures of central tendency). Though one with little experience in statistics may think that there is only one concept for average, there are really three: the mean, median and mode. His post is very brief and offers simple, clear explanations for these concepts and shows how they are each computed. But, most importantly, I like his post because he offers examples of how people commonly misuse each type of average with the purpose of deceiving others:

"For example, it's a pretty common trick when talking about incomes to talk about how the mean income of a large group of people has increased - when in fact, the typical member of the group did not get any raise - instead one or two outliers got huge raises, and everyone else got nothing. Suppose that you had ten employees, and you gave them pay-changes of -2%, -2%, 0%, 0%, 0%, 0%, 1%, 1%, 3%, 20%. The mean salary change would be +2%. But half of the employees saw either no change or a decrease; and in fact, almost all of the increase went to just one person. Take that one person out, and the average raise drops by nearly a factor of 20 to 0.11%."

These are basic statistical concepts and it's important for people to understand them, so I recommend this post for those who may need a little brush up.

(On a side note, it would be interesting to see if he will write about measures of variability like the standard deviation and variance in the future, with a discussion of how they are used/misused.)

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