Thursday, July 26, 2007

Means and medians

The popular press seems to have a hard time understanding when a median (the 50th percentile) is better, and when to use a mean (the sum of everything in a population divided by the size of the population) is better. Both are measures of central tendency.

If one worries about large mistakes exponentially more than small mistakes, means are better. To give one example, if one is underwriting an 80 percent loan-to-value ratio loan, a small mistake in valuation matters little, but a big mistake matters a lot. Predicting house values based on a mean (likely a conditional mean, i.e., a mean based on knowlege about the characteristics of this house) thus makes more sense for underwriting than predicting house values based on a median. But if one just wants to know what someone in the middle of the homebuying pack would pay, the median is far better.

Median income is a much better reflection of middle class living standards than mean income. Reporters seem to have a hard time understanding this. But then so do some business school professors I know...


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