Law of Large Numbers

Image by Thomas Wolter from Pixabay

A recent episode of the PBS program NOVA took me back to my undergraduate statistics course. It was a course I didn't want to take because I have never been a math person and I assumed that is what the course was about. I was wrong. 

The interesting episode is on probability and prediction and its approach reminded me of the course which also turned out to be surprisingly interesting. Program and course were intended for non-math majors and the producers and professor focused on everyday examples.

I suggest you watch the NOVA episode. You will learn about things that are currently in the news and that you may not have associated with statistics, such as the wisdom of crowds, herd immunity, herd thinking and mob thinking.

For example, the wisdom of crowds is why when a contestant on a Who Wants to Be a Millionaire type of programs asks the audience and out of a few hundred people 85% answer "B," then there's an excllent chance that "B" is the correct answer. And larger samples get more accurate. Why is that?

One of the things I still recall from that class that the program highlighted was the law of large numbers. The law of large numbers states that as a sample size grows, its mean gets closer to the average of the whole population. It was proposed by the 16th century, mathematician Gerolama Cardano but was proven by Swiss mathematician Jakob Bernoulli in 1713.

It works for many situations from the stockmarket to a roulette wheel. I recall that we learned about the "Gambler’s Fallacy." The fallacy is that gamblers don't know enough math, or statistics. They stand by the wheel and see that red has won once and black has now won 5 times in a row. Red is due to win, right? Wrong. The red and black is the same as a coin flip. The odds are always 50/50. The casino knows that. They even list which color and numbers have come up on a screen to encourage you to believe the fallacy.

Flip the coin or spin the wheel 10 times and if could be heads or reds 9 times. Flip or spin 500 times and it will come out to be a lot closer to 50-50.

The "house edge" for American Roulette exists because there is that double zero on the wheel. That gives the house an edge of 2.70%. The edge for European roulette is 5.26%. 

Knowing about probability greatly increases your accuracy in making predictions. And more data makes that accuracy possible.



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