Inferring Median from a Few Values

Holger von Jouanne-Diedrich is stuck in the middle with you:

Let us dive directly into the matter, the Small Data Rule states:

In a sample of five numerical values from any unknown population, the median of this population lies between the smallest and the largest sample value with 94 percent certainty.

The “population” can be anything, like data about age in a population, income in a country, television consumption, donation amounts, body sizes, temperatures and so on.

This is a very interesting concept. Five values won’t give you the median, but it will give you a bounded expectation with high likelihood. And check out the comments: adding a few more data points increases the expected likelihood even further.