law of large numbers

(noun)

The statistical tendency toward a fixed ratio in the results when an experiment is repeated a large number of times.

Related Terms

Examples of law of large numbers in the following topics:

  • The Law of Large Numbers and the Mean

    • The Law of Large Numbers says that if you take samples of larger and larger size from any population, then the mean $\bar{x}$ of the sample is very likely to get closer and closer to µ.
    • NOTE : The formula for the mean is located in the Summary of Formulas (Section 2.10) section course.

  • What Does the Law of Averages Say?

    • Some people interchange the law of averages with the law of large numbers, but they are different.
    • The law of averages is not a mathematical principle, whereas the law of large numbers is.
    • 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 is important to remember that the law of large numbers only applies (as the name indicates) when a large number of observations are considered.
    • Evaluate the law of averages and distinguish it from the law of large numbers.

  • The Scope of the Normal Approximation

    • This characteristic follows with the statistical themes of the law of large numbers and central limit theorem (reviewed below).
    • The law of large numbers (LLN) is a theorem that describes the result of performing the same experiment a large number of times.
    • According to the law, the average of the results obtained from a large number of trials should be close to the expected value, and will tend to become closer as more trials are performed.
    • The law of large numbers is important because it "guarantees" stable long-term results for the averages of random events.
    • An illustration of the law of large numbers using a particular run of rolls of a single die.

  • Organization

    • A few of these laws of grouping include the laws of proximity, similarity, and closure and the figure-ground law.
    • For this reason, people tend to see clusters of dots on a page instead of a large number of individual dots.
    • The brain groups together the elements instead of processing a large number of smaller stimuli, allowing us to understand and conceptualize information more quickly.
    • The IBM logo plays on the law of closure.
    • Because of the law of proximity, people tend to see clusters of dots on a page instead of a large number of individual dots.

  • Common Law

    • Law of the United States was mainly derived from the common law system of English law.
    • At both the federal and state levels, the law of the United States was mainly derived from the common law system of English law , which was in force at the time of the Revolutionary War.
    • It has incorporated a number of civil law innovations.
    • As a result, the laws of any given state invariably differ from the laws of its sister states.
    • In response, a very large body of law was developed to regulate the conflict of laws in the United States.

  • Primary Sources of American Law

    • The primary sources of American Law are: constitutional law, statutory law, treaties, administrative regulations, and the common law.
    • At both the federal and state levels, the law of the United States was originally largely derived from the common law system of English law, which was in force at the time of the Revolutionary War.
    • However, U.S. law has diverged greatly from its English ancestor both in terms of substance and procedure, and has incorporated a number of civil law innovations.
    • Second, a small number of important British statutes in effect at the time of the Revolution have been independently reenacted by U.S. states.
    • The number of published volumes of American reports soared from eighteen in 1810 to over 8,000 by 1910.

  • Employment Policy

    • United States labor law is a heterogeneous collection of state and federal laws.
    • The Fair Labor Standards Act of 1938 (FLSA) establishes minimum wage and overtime rights for most private sector workers, with a number of exemptions and exceptions.
    • A number of states have enacted higher minimum wages and extended their laws to cover workers who are excluded under the FLSA or to provide rights that federal law ignores.
    • Local governments have also adopted a number of "living wage" laws that require those employers that contract with them to pay higher minimum wages and benefits to their employees.
    • The Worker Adjustment and Retraining Notification Act, better known by its acronym, the WARN Act, requires private sector employers to give sixty days' notice of large-scale layoffs and plant closures; it allows a number of exceptions for unforeseen emergencies and other cases.

  • Gauss's Law

    • Gauss's law is a law relating the distribution of electric charge to the resulting electric field.
    • Gauss's law, also known as Gauss's flux theorem, is a law relating the distribution of electric charge to the resulting electric field.
    • It is one of the four Maxwell's equations which form the basis of classical electrodynamics, the other three being Gauss's law for magnetism, Faraday's law of induction, and Ampère's law with Maxwell's correction.
    • Gauss's law has a close mathematical similarity with a number of laws in other areas of physics, such as Gauss's law for magnetism and Gauss's law for gravity.
    • In fact, any "inverse-square law" can be formulated in a way similar to Gauss's law: For example, Gauss's law itself is essentially equivalent to the inverse-square Coulomb's law, and Gauss's law for gravity is essentially equivalent to the inverse-square Newton's law of gravity.

  • The Third Law of Thermodynamics and Absolute Energy

    • The third law of thermodynamics states that the entropy of a system approaches a constant value as the temperature approaches absolute zero.
    • The third law of thermodynamics states that the entropy of a system approaches a constant value as the temperature approaches zero.
    • Entropy is related to the number of possible microstates according to $S = k_Bln(\Omega)$, where S is the entropy of the system, kB is Boltzmann's constant, and Ω is the number of microstates (e.g. possible configurations of atoms).
    • Physically, the law implies that it is impossible for any procedure to bring a system to the absolute zero of temperature in a finite number of steps.
    • In addition, glasses and solid solutions retain large entropy at absolute zero, because they are large collections of nearly degenerate states, in which they become trapped out of equilibrium.

  • The Law of Multiple Proportions

    • The law of multiple proportions states that elements combine in small whole number ratios to form compounds.
    • The law of multiple proportions, also known as Dalton's law, was proposed by the English chemist and meteorologist John Dalton in his 1804 work, A New System of Chemical Philosophy.
    • The law, which was based on Dalton's observations of the reactions of atmospheric gases, states that when elements form compounds, the proportions of the elements in those chemical compounds can be expressed in small whole number ratios.
    • In CO2, the ratio of the amount of oxygen compared to the amount of carbon is a fixed ratio of 1:2, a ratio of simple whole numbers.
    • Dalton's law of multiple proportions is part of the basis for modern atomic theory, along with Joseph Proust's law of definite composition (which states that compounds are formed by defined mass ratios of reacting elements) and the law of conservation of mass that was proposed by Antoine Lavoisier.