Draft:Rule of Five (statistics)

• Comment: This is a borderline decline on what could be a decent article, so please don't give up on working on it. The problem with the sources that have been added is that they are personal webpages and/or blogs. This means that they don't qualify as reliable sources because they are self-published and/or user-generated (see WP:RSSELF and WP:UGC).
  The book that you originally added is an example of an in-depth reliable source. However, it isn't independent of the subject because the author conceived the subject (the 'Rule of Five' in this case). It also wouldn't be able to be the only source for the article.
  If you could find academic sources and/or other books, they would be a great way of guaranteeing reliability. However, reliability isn't limited to only sources as strong as those ones if you can other types that meet WP:RS.
  Something that would help us with reviewing the article (but isn't necessarily a reason for decline) would be if you could use the sources you find to cite the content in the "How it Works" section to help us verify that the content is accurate. MangoMan11 (talk) 10:27, 29 April 2025 (UTC)

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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, software engineering, statistical computing, data analytics, and social research.

How it Works

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 $({\tfrac {1}{2}})^{5}=3.125\%$. 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 $3.125\%+3.125\%=6.25\%$. 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 $100\%-6.25\%=93.75\%$.

Usefulness

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

• 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

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". Hubbard chose the number five because it’s memorable and the smallest sample size that provides a probability greater than 90%.