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The variance (Latin variantia = "difference" or variare = "(to change) to be different"), obsolete dispersion (lat only called scatter is a measure of the scatter of the probability density around its center of gravity and can be interpreted physically as an moment of inertia. Mathematically, the variance represents the central second order moment of a random variable. It is defined as the mean square deviation of a real random variable from its expected value. It is the square of the standard deviation, the most important measure of dispersion in stochastics.
The variance is never negative and does not change when the distribution is shifted. The variance of a sum of uncorrelated random variables is equal to the sum of their variances. A disadvantage of the variance for practical applications is that, unlike the standard deviation, it has a different unit than the random variable. Since it is defined by an integral, it does not exist for all distributions, i.e. that is, it can also be infinite. The variance can be calculated using a variance estimator, e.g. B. the sample variance can be estimated.