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