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Bernoulli's law

Bernoulli's law

9.5
The average of a large random sample gets close to the true value for the whole group
  • noun
  • /bərˈnuːliˌz lɔː/
  • Specialized
translation icon : ley de Bernoulli
  • According to Bernoulli's law, averages become more accurate with larger samples.

Examples

  • Researchers referenced Bernoulli's law when analyzing data collected from a large, random population sample.

  • In probability theory, Bernoulli's law underpins the idea of reliable long-term statistical trends.

  • According to Bernoulli's law, the average result becomes more predictable as the sample size increases.

  • Many statisticians rely on Bernoulli's law for their analyses.

  • According to Bernoulli's law, the average result becomes more predictable as the sample size increases.

  • Researchers referenced Bernoulli's law when analyzing data collected from a large, random population sample.

  • In probability theory, Bernoulli's law underpins the idea of reliable long-term statistical trends.

Synonyms

law of large numbers
vsBernoulli's law
  • Specialized
1 5.9

When a sample gets larger, its average gets closer to the average of the whole group

is the statistical formulation emphasizing average behaviour over many random items
strong law of large numbers
vsBernoulli's law
  • Specialized
9.1

The average of many separate random results becomes almost always close to the true average

is the general statistical statement about averages rather than the technical almost sure version

Surface Forms

Morphology

Bernoulli's + law

This is an eponymous scientific name: 'Bernoulli's' only signals authorship and 'law' indicates a rule, but the specific statistical content (about averages approximating population values) cannot be inferred from the parts. A B1 learner who knows the words 'Bernoulli' and 'law' would understand it names a law but would not be able to derive the precise meaning without prior exposure.

Etymology

Bernoulli's law is named after the mathematician Jacob Bernoulli and gives a simple picture: imagine tasting many apples from a tree — as you taste more, the 'average' taste you find becomes closer to the tree's true average. So, the law means that the 'average' of a large random 'sample' will be close to the real average of the whole group.