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Law of large numbers The statistical principle that the larger the sample the more likely it is that the frequency of events within the sample will approximate to the event's true frequency or put another way: the larger the sample observed, the more confident one can be that a statistic derived from it (e.g., a mean or a proportion) is closer to its true value – with small samples greater variability should be expected and with larger samples less variability.
For example, imagine a fair coin is tossed four, sixteen, one hundred, or ten thousand times. Even though the expected number of ‘heads’ is ½ for a single toss, the expected outcome for, say, sixteen tosses is not certain to be eight ‘heads’. Because each toss is an independent event having a 50/50 probability there is variance in the proportion of heads yielded in any set of tosses. However, as the number of tosses increases, this variance of proportion decreases. The greater the number of trials, the closer the proportion of heads gets to ½. (see also: Bayes' theorem, Laws of Probability » Probability theory, Gambler's fallacy, Sample size, Sample size error, sample bias, pattern-seeking, distribution, probabilistic, generalizability»generalization, survey, Regression towards the mean, statistical decision-making)
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