I doubt many people lose sleep over statistics. But I did. I keep wondering why the Law of Large Numbers is. The LLN says that the average weight of a series of samples bags of pebbles taken from a beach is a more accurate measure of the the weight of all the individual pebbles on the beach than one large bag of pebbles.

I know the formula and I know the proof, but something has never gone from my rational sphere to my gut, even after 50 years as a statistician.

Everyone who teaches math says you can't prove a geometric theorem, like all angles of a triangle total 180 degrees, by cutting out and measuring triangles. People would laugh if you did. But that is geometry and that theorem is really a syllogism based on the definition of triangle and the definition of degrees.

The law of large numbers is the real world. So I did the equivalent of cutting out triangles. I made a list of 100 numbers from a random number table, the average of my list is 46.9. I did an average of every ten numbers on the list. The average of those ten averages is 46.9. The theoretical average for a column of random two digit numbers is 50. The LLN doesn't show anything in my test. Now my gut still has to depend on my rational sphere.

(*A reader, Gene, below found an error in my calculations, right away. It is now corrected. Thanks Gene.*)

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