Bernoulli's law

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Definition

Noun: 1. A statistical principle: Bernoulli's law, also known as the Law of Large Numbers, states that as the size of a random sample from a population increases, the sample's average (or other statistical properties) will get closer and closer to the true average (or properties) of the entire population.

Usage
  • Bernoulli's law is a fundamental concept in probability and statistics.
  • According to Bernoulli's law, flipping a fair coin many times will result in a proportion of heads very close to 50%.
  • The reliability of opinion polls is based on Bernoulli's law; a larger sample size typically yields more accurate predictions of the overall population's views.
Advanced Usage
  • Distinction from "Law of Averages": It is important to distinguish Bernoulli's law from the common misconception of the "law of averages." Bernoulli's law describes a long-term tendency, not a short-term compensation. For example, it does not mean that after several "heads" coin flips, a "tails" becomes more likely on the next flip.
Variants and Related Words
  • Law of Large Numbers: This is the more common modern name for Bernoulli's law.
  • Bernoulli's Theorem: Another name for the same principle.
Synonyms
  • Law of Large Numbers
Noun
  1. (statistics) law stating that a large number of items taken at random from a population will (on the average) have the population statistics

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