The Rule of Five

When needing to approximate the median of a certain population, it requires only 5 random samples to identify with 93.75% confidence that the value is between the smallest and the largest of those samples.

The Explanation
The chance to random pick a value that is above the median is 50%, same as flipping a coin. The chance of hitting heads five times in the row is 1/32 or 3.125%. The chance of not to get all heads or tails is 100 - 2 x 3.125 = 93.75

Varied Amounts
How about if we vary the amount of samples?

It seems that we are getting diminishing returns after the 5 samples.


What are scenarios that this tool proved to be valuable?