Draft:Rule of Five (statistics)
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In statistics the rule of five is a statistical rule of thumb used to quickly estimate the median of a population. It states that there is a 93.75% chance that the true median of a population lies between the smallest and largest values in any random sample of five taken from that population.
The rule of five offers a way to reduce uncertainty and make faster business decisions without extensive data collection. Instead of surveying an entire population, the rule of five involves selecting a random sample of five members to represent the population. This statistical tool is used across disciplines like business research[1], software engineering[2], statistical computing[3], data analytics[4], and social research[5].
How it Works
[edit]The rule is based on the probability of randomly selecting values above or below the median of a population. There's an equal chance (50%) of picking a random value above or below the median, similar to a coin flip. The probability of selecting five values that are all above the median (akin to flipping five heads in a row) is . The same probability applies to selecting five values all below the median.
Therefore, the probability of all five values being either above or below the median is . Consequently, the probability that at least one value is above the median and at least one is below (meaning the median falls within the range of the sample) is .
Usefulness
[edit]The rule of five is valuable when:
- A quick estimate of the median is needed.
- Resources or time are limited, making extensive data collection impractical.
- An acceptable level of accuracy is sufficient for decision-making or trend prediction.
- It can be particularly useful when there are high levels of uncertainty to begin with.
Limitations
[edit]- Randomness is critical: The selected sample of five must be truly random to avoid bias and ensure the rule's validity.
- The rule provides an estimate of the median and may not replace the need for thorough data analysis in all situations.
- The range might be very wide with a sample size of only five.
History and Origin
[edit]The rule of five was conceived by Douglas W. Hubbard, an expert in risk management, metrics, and decision analysis. He introduced it in his book "How to Measure Anything: Finding the Value of Intangibles in Business".[6] Hubbard chose the number five because it’s memorable and the smallest sample size that provides a probability greater than 90%.
References
[edit]- ^ Amadio, William J.; Pelletteri, Barry M.; Krall, John S. (2014-05-27). Modern Data Analytics for Decision Making (PDF). Global Conference on Business and Finance Proceedings. San Jose Costa Rica: The Institute for Business and Finance Research. Retrieved 2025-02-28.
- ^ Dartus, Pierre‑Marie (2024-03-04). "The Rule of Five - Making good calls from limited data". Retrieved 2025-02-28.
- ^ Jacobs, Jay (2014-11-16). "Simulating the Rule of Five". Retrieved 2025-02-28.
- ^ "Definition: rule of five (statistics)". 2018-12-01. Retrieved 2025-02-28.
- ^ Fisher, Natalie (2015-04-13). "The Rule of Five. A quick and easy way to reduce uncertainty in business". Retrieved 2025-02-28.
- ^ Hubbard, Douglas W. (2010). How to Measure Anything. New Jersey: John Wiley & Sons, Inc., Hoboken. p. 150. ISBN 978-0-470-53939-2.
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