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