Related to this question, I discovered a new rule for Fermi estimates.
If you want to estimate the mean value of a lognormally distributed random variable, giving the middle order of magnitude will be wrong as these are skewed.
There is a simple rule for getting this right that I discovered: take your middle order of magnitude (i.e. if you think it’s between 10 and 100, the middle is 10^1.5) and add 1.15 times the square of your estimate of the standard deviation in log-space. So in this case that’s something 1.5 +1.15 × 0.5^2. Then do 10 to the power that. This gives you about 60 - twice the answer you would have gotten with the middle order of magnitude.
This applies to things like “how big is a country” and “how many miles of track is there for a country of a given size” which might both be lognormally distributed.
Related to this question, I discovered a new rule for Fermi estimates.
If you want to estimate the mean value of a lognormally distributed random variable, giving the middle order of magnitude will be wrong as these are skewed.
There is a simple rule for getting this right that I discovered: take your middle order of magnitude (i.e. if you think it’s between 10 and 100, the middle is 10^1.5) and add 1.15 times the square of your estimate of the standard deviation in log-space. So in this case that’s something 1.5 +1.15 × 0.5^2. Then do 10 to the power that. This gives you about 60 - twice the answer you would have gotten with the middle order of magnitude.
This applies to things like “how big is a country” and “how many miles of track is there for a country of a given size” which might both be lognormally distributed.
https://www.lesswrong.com/posts/LEntkjvDSxStdGN39/shortform?commentId=soxf4Ynakr7aSjM3m