Sunday, March 19, 2006

Raising the Median - Averages

An average can be very misleading. For instance, knowing the average (mean) weight of ten mice and one elephant doesn't really tell you very much about each.

Yet this same measure, this average (mean) is often used to analyze economic policy and wealth, to see what effect it's having on the ordinary person, the so-called "average" person. Unfortunately, this is usually done by using the mean average, rather than the median average.

To use an extreme example, if ten people have exactly the same income, say $30,000 annually, but a change in economic policy results in just one person whose income zooms to $330,000 annually, but the rest remains the same, then policy-makers can claim that their policy was successful, as the average income doubled! Sure, great for the one guy, but the lot of the nine others hasn't changed at all. Successful policy? Or not?

A mean average can hide a multitude of sins. As Wikipedia says about a mean average ...
"It is used for many purposes and may be abused by using it to describe skewed distributions, with highly misleading results."
A much better but under-used measure for these sorts of things is, in my opinion, the median average. The median measures what change occurred for the very middle value of any array. In this case, it would show that a $30,000 annual income was still the normal value here. It definitely shows how the policy hasn't really changed the lot of the ordinary person.

So the next time you hear a news report claiming that the average (mean) has moved this way or that, ask the question - "But, what has happened to the median?" And maybe even fire them off an email. And make sure you ask the same of your politicians, and public bureaucrats. It can even be useful in your personal investing. It'll lead to better answers everywhere!

Jay Walker - Raising the Median!


The Confused Capitalist


TBU said...

wouldn't the mode be a more effective measure given your example? It gets less notice than even the median, but from an equity standpoint it may even be more useful, i.e, greatest change for the greatest number of people.

Jay Walker said...

Yes, it can be effective, but if there's a number of people clustered at one end of the spectrum, it too can give can give misleading results (since it's a measure of the highest number with exactly the same numeric).

But yes, I agree it can be effective at times too - still, all-in-all, I think the median generally does the best at measuring how a change affected a sample population.

Thanks for your comments ...