Statistical regularity is a notion in

statistics Statistics (from German language, German: ', "description of a State (polity), state, a country") is the discipline that concerns the collection, organization, analysis, interpretation, and presentation of data. In applying statistics to a s ...

and

probability theory Probability theory or probability calculus is the branch of mathematics concerned with probability. Although there are several different probability interpretations, probability theory treats the concept in a rigorous mathematical manner by expre ...

that random events exhibit regularity when repeated enough times or that enough sufficiently similar random events exhibit regularity. It is an

umbrella term Hypernymy and hyponymy are the wikt:Wiktionary:Semantic relations, semantic relations between a generic term (''hypernym'') and a more specific term (''hyponym''). The hypernym is also called a ''supertype'', ''umbrella term'', or ''blanket term ...

that covers the

law of large numbers In probability theory, the law of large numbers is a mathematical law that states that the average of the results obtained from a large number of independent random samples converges to the true value, if it exists. More formally, the law o ...

, all

central limit theorem In probability theory, the central limit theorem (CLT) states that, under appropriate conditions, the Probability distribution, distribution of a normalized version of the sample mean converges to a Normal distribution#Standard normal distributi ...

s and

ergodic theorem Ergodic theory is a branch of mathematics that studies statistical properties of deterministic dynamical systems; it is the study of ergodicity. In this context, "statistical properties" refers to properties which are expressed through the behav ...

s. If one throws a

dice A die (: dice, sometimes also used as ) is a small, throwable object with marked sides that can rest in multiple positions. Dice are used for generating random values, commonly as part of tabletop games, including dice games, board games, ro ...

once, it is difficult to predict the outcome, but if one repeats this experiment many times, one will see that the number of times each result occurs divided by the number of throws will eventually stabilize towards a specific value. Repeating a series of trials will produce similar, but not identical, results for each series: the average, the standard deviation and other distributional characteristics will be around the same for each series of trials. The notion is used in

games of chance A game of chance is in contrast with a game of skill. It is a game whose outcome is strongly influenced by some randomizing device. Common devices used include dice, spinning tops, playing cards, roulette wheels, numbered balls, or in the case ...

, demographic statistics,

quality control Quality control (QC) is a process by which entities review the quality of all factors involved in production. ISO 9000 defines quality control as "a part of quality management focused on fulfilling quality requirements". This approach plac ...

of a manufacturing process, and in many other parts of our lives. Observations of this phenomenon provided the initial motivation for the concept of what is now known as

frequency probability Frequentist probability or frequentism is an interpretation of probability; it defines an event's probability (the ''long-run probability'') as the limit of a sequence, limit of its Empirical probability, relative frequency in infinitely many E ...

. This phenomenon should not be confused with the

gambler's fallacy The gambler's fallacy, also known as the Monte Carlo fallacy or the fallacy of the maturity of chances, is the belief that, if an event (whose occurrences are Independent and identically distributed random variables, independent and identically dis ...

, because regularity only refers to the (possibly very) long run. The gambler's fallacy does not apply to statistical regularity because the latter considers the whole rather than individual cases.

References

* * {{cite book , last=Whitt , first=Ward , year=2002 , title=Stochastic-Process Limits, An Introduction to Stochastic-Process Limits and their Application to Queues , location=New York , publisher=Springer , isbn=0-387-95358-2 , chapter=Experiencing Statistical Regularity , chapter-url=http://www.columbia.edu/~ww2040/scalingchno.pdf Statistical laws

See also

References