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Reversion to the Mean


Reversion to the mean, also called regression to the mean, is the statistical phenomenon stating that the greater the deviation of a random variate from its mean, the greater the probability that the next measured variate will deviate less far. In other words, an extreme event is likely to be followed by a less extreme event.

Although this phenomenon appears to violate the definition of independent events, it simply reflects the fact that the probability density function P(x) of any random variable x, by definition, is nonnegative over every interval and integrates to one over the interval (-infty,infty). Thus, as you move away from the mean, the proportion of the distribution that lies closer to the mean than you do increases continuously. Formally,

 int_(mu-i)^(mu+i)P(x)dx>int_(mu-j)^(mu+j)P(x)dx

for i>j>0.

The Season 1 episode "Sniper Zero" (2005) of the television crime drama NUMB3RS mentions regression to the mean.


See also

Mean

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Cite this as:

Weisstein, Eric W. "Reversion to the Mean." From MathWorld--A Wolfram Web Resource. https://mathworld.wolfram.com/ReversiontotheMean.html

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