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# What is the law of averages?

Question #77788. Asked by rixbix. (Mar 25 07 9:18 AM)

Sofie

The law of averages is a lay term used to express the view that eventually, everything "evens out." For example: Two very similar people who drive similar cars in similar circumstances over a long period of time will have roughly the same number of accidents. The more children one has, the more likely one has an equal division of boys and girls. The longer one flips a coin, the more likely the number of heads and tails will equalize.

Thus every outcome in a fair game exhibits identical probabilities equal to the underlying probability of the game. In order to understand this it is important to realize that no outcome in a fair game is at any point, in any way whatsoever affected by any other past or future outcome within the game.

The formal mathematical result that supports the law of averages is called the law of large numbers. It states that a large sample of a particular probabilistic event will tend to reflect the underlying probabilities. For example, after tossing a "fair coin" 1000 times, we would expect the result to be approximately 500 heads results, because this would reflect the underlying 0.5 chance of a heads result for any given flip.

Note, however, that while the average will move closer to the underlying probability, in absolute terms deviation from the expected value will increase. For example, after 1000 coin flips, we might see 520 heads. After 10,000 flips, we might then see 5096 heads. The average has now moved closer to the underlying 0.5, from 0.52 to 0.5096. However, the absolute deviation from the expected number of heads has gone up from 20 to 96.

http://en.wikipedia.org/wiki/Law_of_averages

 Mar 25 07, 9:48 AM

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