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Law of Large Numbers

What is the Law of Large Numbers?

The Law of Large Numbers is a theorem within probability theory that suggests that as a trial is repeated, and more data is gathered, the average of the results will get closer to the expected value. As the name suggests, the law only applies when a large number of observations or tests are considered. The false idea that a small amount of observations will reach a near expected value is sometimes referred to as the gambler's fallacy.


Example of the Law of Large Numbers

Imagine a coin toss, wherein one wanted to determine the probability of tossing a heads versus a tails. The law of large numbers states that the more the coin is tossed, the cumulative number of both head and tails values will even out, as the true probability of a value in a coin toss is 50%.

Additionally, the law works as a metric for understanding business growth as well. For example, if Company A brings in 500 million dollars and Company B brings in 10 million dollars, it would require much more money for Company A to increase their profit by 25% than it would for Company B to do the same. The law of large numbers helps inform investors examining companies with high market capitalization as they tend to have associated difficulties related to stock appreciation.