From Douglas W. Hubbard, How to Measure Anything (3rd ed.) via https://lobste.rs/s/kk89vp/back_envelope_estimation_hacks#c_cffofh https://lobste.rs/s/kk89vp/bac

From Douglas W. Hubbard, How to Measure Anything (3rd ed.) via https://lobste.rs/s/kk89vp/back_envelope_estimation_hacks#c_cffofh https://lobste.rs/s/kk89vp/back_envelope_estimation_hacks#c_... > There is a 93.75% chance that the median of a population is between the smallest and largest values in any random sample of five from that population. > It might seem impossible to be 93.75% certain about anything based on a random sample of just five, but it works. To understand why this method works, it is important to note that the Rule of Five estimates only the median of a population. Remember, the median is the point where half the population is above it and half is below it. If we randomly picked five values that were all above the median or all below it, then the median would be outside our range. But what is the chance of that, really? > The chance of randomly picking a value above the median is, by definition, 50%—the same as a coin flip resulting in “heads.” The chance of randomly selecting five values that happen to be all above the median is like flipping a coin and getting heads five times in a row. The chance of getting heads five times in a row in a random coin flip is 1 in 32, or 3.125%; the same is true with getting five tails in a row. The chance of not getting all heads or all tails is then 100% − 3.125% × 2, or 93.75%. Therefore, the chance of at least one out of a sample of five being above the median and at least one being below is 93.75% (round it down to 93% or even 90% if you want to be conservative).