This quantity is preserved under sums if the summand random variables are all pairwise uncorrelated.
For an unbiased estimator, a lower bound on this quantity is given by the reciprocal of the Fisher information, according to the Cramer-Rao inequality. A one-sided probability calculated using the F-test can be used to determine whether this value is the same for two data sets. Powers of this quantity are used to normalize the third and fourth central moments in calculating the skewness and kurtosis, respectively. This quantity is preserved under sums if the summand random variables are all pairwise uncorrelated. FTP, name this quantity, equivalent to the second cumulant and the second central moment, a measure of statistical dispersion whose square root is the standard deviation.
For an unbiased estimator, a lower bound on this quantity is given by the reciprocal of the Fisher information, according to the Cramer-Rao inequality.
{variance}