## Monday, March 18, 2013

### Top of the Curve = Middle of the Pack

Here's a normal distribution design from a t-shirt (thanks Jun). Unlike the possible confusion we have seen from bell-curve t-shirts, this one, from shirtwoot! shows that the designer got the bell-curve's relation to the normal distribution correct. The bell-curve is not the normal distribution. The bell-curve only describes the normal distribution. The normal distribution is a specific random arrangement of measurements on a number line. This arrangement ranges from small measurements on the left of the number line, up to large measurements on the right. The curve represents the frequency or density of observations along the line. Where the curve is low, the observations have a very low density. We would expect few measurements there, occurring sparsely in those regions. Where the bell-curve is higher, we expect a dense arrangement, with observations piling up to a peak in the middle. But the location of this peak on the bell-curve lies in the middle of our number line range. The peak corresponds to the measurement that occurs most often, where its measurement is most common. It is literally the peak of mediocrity.

This shirt design gets it right. At this peak, you have not surmounted all around you to become the best. On the contrary, you've truly "reached mediocrity".