Variance

In probability theory and statistics, the variance of a random variable is a measure of its statistical dispersion, indicating how far from the expected value its values typically are.

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The variance of a real-valued random variable is its second central moment, and it also happens to be its second cumulant. The variance of a random variable is the square of its standard deviation.

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If ? = E(X) is the expected value (mean) of the random variable X, then the variance is

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:operatorname{var}(X)=operatorname{E}((X-mu)^2).

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That is, it is the expected value of the square of the deviation of X from its own mean. In plain language, it can be expressed as "The average of the square of the distance of each data point from the mean". It is thus the mean squared deviation. The variance of random variable X is typically designated as operatorname{var}(X), sigma_X^2, or simply sigma^2.

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