Skip to main content
law of large numbers

law of large numbers

1 5.9
When a sample gets larger, its average gets closer to the average of the whole group
  • noun
  • /lɔː ʌv lɑrdʒ ˈnʌmbərz/
  • Specialized
translation icon : ley de los grandes números
  • This is also what the weak law of large numbers tells us.

It sizes the bets to ensure that the player basically just stays in the game long enough for the law of large numbers to work.

Autoplay Next

Examples

  • The best we can do is give a statistical estimate of its half-life and allow the law of large numbers to do its work.

    Blog text (2)
  • One can also see this from the binomial formula and the law of large numbers, which shows that the bulk of the sum comes from the region.

    Blog text (23)
  • People who lived in small countries did not understand the law of large numbers.

    Fiction book (1993)
  • OK, this is a kind of law of large numbers for random events.

  • In probability theory, the law of large numbers is a theorem that describes the result of performing the same experiment a large number of times.

  • It sizes the bets to ensure that the player basically just stays in the game long enough for the law of large numbers to work.

  • The first equality of (12) is a consequence of the law of large numbers (for stationary processes).

    Academic text (2018)
  • So, most of the value of combining the areas comes from the law of large numbers: variance rises roughly half as fast as the mean, so that low output events would be reduced by very, very roughly 50%.

    Blog text (6)
  • But as Williams points out, we can circumvent this problem by a clever combination of Bernoulli's "law of large numbers" and a second direct inference.

    Academic text (2001)
  • The law of large numbers explains why a larger sample yields a mean closer to the population average.

Synonyms

law of averages
vslaw of large numbers
1 3.9

The idea that after many tries results tend to match what is expected on average

is a precise statistical principle rather than an informal expectation about trials
Kolmogorov's strong law of large numbers
vslaw of large numbers
  • Specialized
9.9

A theorem that says the average of many independent random results almost certainly equals the true average

is a general statistical principle about averages approaching the population mean
strong law of large numbers
vslaw of large numbers
  • Specialized
9.1

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

is the broader statistical rule about averages getting closer to the population mean
Bernoulli's law
vslaw of large numbers
  • Specialized
9.5

The average of a large random sample gets close to the true value for the whole group

is the general statistical statement about averages becoming nearer the population mean

Surface Forms

Morphology

law + of + large + number

The phrase transparently composes 'law' (a rule) with 'large numbers', so a learner who knows the words can infer it is a rule concerning large quantities of numbers. However, the precise statistical meaning about sample means converging on the population mean is technical and not fully derivable from the constituents alone, so prior statistical knowledge is needed.

Etymology

Law of large numbers comes from a simple picture: if you flip a coin many times, the results settle near the true average. The words large and numbers mean 'a lot of cases' and the 'law' shows it is a dependable rule, so the phrase explains why averages become 'predictable' as the sample grows.