rule of five (statistics)

The rule of five is a rule of thumb in statistics that estimates the median of a population by choosing a random sample of five from that population. It states that there is a 93.75% chance that the median value of a population is between the smallest and largest values in any random sample of five. This rule can be used to save data collection time in order to make a quicker business decision.

In a scenario where the mid-point or median of a population is required, the rule of five can be used to approximate it. In any population, half the individuals will be above the median and half below. Therefore, the likelihood of choosing a value above or below the median is 50% either way, equivalent to the flip of a coin.  The likelihood of flipping 100% tails or heads would be 1/32 or 3.125%. So the chance of not getting all heads or tails is 100 - (3.125 x 2), or 93.75. Thus, the probability of the median sample being between the lowest and highest samples in any random sampling of five is 93.25%.

The goal of the rule of five is to reduce uncertainty without wasting resources gathering every piece of data. Rather than survey an entire population, applying the rule of five involves selecting five random members as a representative sample of the population. The results themselves may be less accurate, but finding the overall precision of an entire group is usually unnecessary. The rule of five makes it possible to achieve an acceptable level of accuracy to enable faster a decision-making process and trend prediction.

The rule of five was conceived by Douglas Hubbard, the author of "How to Measure Anything: Finding the Value of Intangibles in Business" and an established expert in risk management, metrics and decision analysis.