Take all the most expensive and exotic ingredients in the world, boiled'em up in a big pot….. and it tastes like brown soup.
It’s amazing how fast things converge on the bell curve.
Take a uniform 0,1 distribution. Graph it, it looks like a rectangle.
Take the average of two samples…. it’s a triangular distro.
Take the average of three, it is already looking neatly curved and very “Bell"ish.
But the really fun thing is the fine print.
It only works with distros with finite variance.
The average of samples from a distro without finite variance (eg. power law) may equally rapidly start to look like a Bell curve….. but still have a long tail!
So the average of the weight of the people reading this follows remarkably closely the bell curve.
The average of the wealth looks very bell curvish…. but still has a long tail.
I call it “The Brown Soup Theorem”.
Take all the most expensive and exotic ingredients in the world, boiled'em up in a big pot….. and it tastes like brown soup.
It’s amazing how fast things converge on the bell curve.
Take a uniform 0,1 distribution. Graph it, it looks like a rectangle.
Take the average of two samples…. it’s a triangular distro.
Take the average of three, it is already looking neatly curved and very “Bell"ish.
But the really fun thing is the fine print.
It only works with distros with finite variance.
The average of samples from a distro without finite variance (eg. power law) may equally rapidly start to look like a Bell curve….. but still have a long tail!
So the average of the weight of the people reading this follows remarkably closely the bell curve.
The average of the wealth looks very bell curvish…. but still has a long tail.