I recently ran across an article describing how to find a rough estimate of the standard deviation of a population, given a number of samples, which seems that it would be suitable for Fermi estimates of probability distributions.
First of all, you need a large enough population that the central limit theorem applies, and the distribution can therefore be assumed to be normal. In a normal distribution, 99.73% of the samples will be within three standard deviations of the mean (either above or below; a total range of six standard deviations). Therefore, one can roughly estimate the standard deviation by taking the largest value, subtracting the smallest value, and dividing the result by 6.
This is useful, because in a normal distribution, around 7 in 10 of the samples will be within one standard deviation of the mean, and around 19 in every 20 will be within two standard deviations of the mean.
That would also work, and probably be more accurate, but I suspect that it would take longer to find the 15th and 85th percentile values than it would to find the ends of the range.
I recently ran across an article describing how to find a rough estimate of the standard deviation of a population, given a number of samples, which seems that it would be suitable for Fermi estimates of probability distributions.
First of all, you need a large enough population that the central limit theorem applies, and the distribution can therefore be assumed to be normal. In a normal distribution, 99.73% of the samples will be within three standard deviations of the mean (either above or below; a total range of six standard deviations). Therefore, one can roughly estimate the standard deviation by taking the largest value, subtracting the smallest value, and dividing the result by 6.
Source
This is useful, because in a normal distribution, around 7 in 10 of the samples will be within one standard deviation of the mean, and around 19 in every 20 will be within two standard deviations of the mean.
If you want a range containing 70% of the samples, why wouldn’t you just take the range between the 15th and 85th percentile values?
That would also work, and probably be more accurate, but I suspect that it would take longer to find the 15th and 85th percentile values than it would to find the ends of the range.