Statistical regularity is a notion in

statistics Statistics (from German language, German: ''wikt:Statistik#German, Statistik'', "description of a State (polity), state, a country") is the discipline that concerns the collection, organization, analysis, interpretation, and presentation of ...

and

probability theory Probability theory 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 expressing it through a set o ...

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

umbrella term In linguistics, semantics, general semantics, and ontologies, hyponymy () is a semantic relation between a hyponym denoting a subtype and a hypernym or hyperonym (sometimes called umbrella term or blanket term) denoting a supertype. In other wor ...

that covers the

law of large numbers In probability theory, 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 shou ...

, all

central limit theorem In probability theory, the central limit theorem (CLT) establishes that, in many situations, when independent random variables are summed up, their properly normalized sum tends toward a normal distribution even if the original variables themselv ...

s and

ergodic theorem Ergodic theory (Greek: ' "work", ' "way") is a branch of mathematics that studies statistical properties of deterministic dynamical systems; it is the study of ergodicity. In this context, statistical properties means properties which are expres ...

s. If one throws a

die Die, as a verb, refers to death, the cessation of life. Die may also refer to: Games * Die, singular of dice, small throwable objects used for producing random numbers Manufacturing * Die (integrated circuit), a rectangular piece of a semicondu ...

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, or numbered balls drawn from ...

, 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 places ...

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 as the limit of a sequence, limit of its relative Frequency_(statistics), frequency in many trials (the long-run probability). Probabi ...

. This phenomenon should not be confused with the gambler's fallacy, 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