# The Rule of Five

When needing to approximate the median of a certain population, it **requires only 5 random samples** to identify with **93.75% confidence** that the value is between the smallest and the largest of those samples.

**The Explanation**

The chance to random pick a value that is above the median is 50%, same as flipping a coin. The chance of hitting heads five times in the row is 1/32 or 3.125%. The chance of not to get all heads or tails is 100 - 2 x 3.125 = 93.75

**Varied Amounts**

How about if we vary the amount of samples?

// 2 samples

1 - 1/4 * 2 = 0,5

// 3 samples

1 - 1/8 * 2 = 0,75

// 4 samples

1 - 1/16 * 2 = 0,875

// 5 samples

1 - 1/32 * 2 = 0,938

// 6 samples

1 - 1/64 x 2 = 0,969

// 7 samples

1 - 1/128 x 2 = 0,984

It seems that we are getting diminishing returns after the 5 samples.

## Examples

What are scenarios that this tool proved to be valuable?

TBD

- Source: L. How to Measure Anything
- Tags: #statistics #estimations #tools