Today I Learned: The Rule of 5

I was reading the (so far) very interesting book, How to Measure Anything by Douglas W. Hubbard, and he mentioned the rule of five. Essentially, if you collect 5 data points at random the median of that distribution will be within the biggest and smallest sample value with a probability of 0.9375. This follows from the definition of the median, i.e., that 50% of the probability mass is on each sides. So there is a 125=0.03125 probability that all data points are above the median (assuming independence). It is equally probable that all sample points are below the median. This gives you a very quick way to get a rough, back-of-the-napkin style estimate of things like average commuting times (the example from the book) and other things were you can easily get hold of five new data points. This all assumes independence.