 Further, mean-unbiasedness is not preserved under non-linear transformations, though median-unbiasedness is (see ); for example, the sample variance is a biased estimator for the population variance, but its square root, the sample standard deviation, is an unbiased estimator for the population standard deviation.These are all illustrated below.Suppose we have a statistical model, parameterized by a real number "θ", giving rise to a probability distribution for observed data, formula_1, and a statistic formula_2 which serves as an estimator of "θ" based on any observed data formula_3.