Wednesday, November 14, 2007

On being average

There's nothing wrong with being average. Most people are. Another word for average is "normal" and certainly there's nothing wrong with being normal.

I have recently heard a couple of jokes about "average" that bear repeating.

One claims that a national leader expressed dismay upon learning that half of all Americans are below average.

Another claims that 80% of university professors surveyed rated themselves above average as professors.

What makes these jokes funny is that, in any population, half are below average and half are above average. That's just what "average" means. In particular, 80% of the population cannot be above average; exactly 50% are.

Suppose you look at an entire population and measure any naturally occurring property (height, weight, intelligence, bank balance, etc.). Suppose you then count the number of people with each possible measurement. Now graph the values of the property across, from smallest to largest value. Finally, show the number of individuals at each measurement as the height of the graph. When you do this, the graph will look something like this:

Image courtesy Wikipedia.

This graph is called the "normal distribution" by statisticians. You may recognize it as the "bell curve," so called because of its shape.

The vertical line at the very center is labeled with the Greek letter mu, which is the symbol used for the "mean value" (which is what statisticians call the average measurement).

This is the highest point in the graph, which means that there are more people who have the average measurement than any other measurement. Fully 68% of the people are "close" to this average measurement. Most people will be close to normal.

And, as I have said, 50% of the people have measurements above average; the other 50% are below average.

To indicate how far a measurement is from average, statisticians use the term "standard deviation," indicated by the Greek letter sigma. Only about one in a thousand people will be more than three standard deviations above average.

More than 2/3 of the individuals in the population will be within one standard deviation of the average measurement. Only one in six will be abnormally above or below average. Of these, only one in fifty will be "way" above (or below) average. And, as mentioned earlier, only one in a thousand will be off the chart.

Almost everyone is average. That is normal. And being normal is nothing to be ashamed about.

Disclaimer: The statistics here are simplified, as this is just meant to be thought-provoking.


Anonymous said...

What could be better than simplified statistics? And thank you for letting us know that it is okay to be normal, average people like we are!

Andrew said...

New study shows 50% of people are below average!

Andrew said...

I love those jokes. It's also interesting to think that 50% of doctors, lawyers, etc. graduated in the bottom of their classes.