The Rule of Five


“The Rule of Five estimates the median (middle point) of a population. Half of the population is above a certain measure, half is below. 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.

How the Rule of Five works

The change of randomly picking a value above the median is, by definition, 50%- the same as a coin flip resulting in ‘heads’ or ‘tails’. The change of randomly selecting five values that happen to be all above the median is like flipping a coin a 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 chance of not getting all heads or all tails is then 100%-3.125% x 2 (=6.25%), 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 the median is 93.75%. To improve on this result you can adjust your method to account for certain types of bias.

The Rule of Five approach proves that you need far less data than you think. How much data is needed to reduce uncertainty sufficiently for some given problem can be estimated with a particular type of calculation. It can be surprising how much reduction in uncertainty can be achieved from just a little bit of data. This is particularly true when there are high levels of uncertainty to begin with.

So, don’t assume that the only way to reduce your uncertainty is to use an impractical, expensive or sophisticated method. Sometimes knowing something is a great deal better than knowing nothing, and often it doesn’t take much data collection to gather that information. Douglas Hubbard believes that measurement is iterative. Start measuring it, make an attempt, and be sure the questions you are asking are well formed and relevant. You will realize that that something that seems immeasurable, something that is ‘intangible’ can be measured to a point at which your uncertainty is at least reduced.”

The information contained in this blog was sourced from How to Measure Anything in Business, Douglas Hubbard, 2010 as provided by NSF Consulting.