In this paper a numerical study of Chu and Hotelling's  method of approximating to the moments of the sample median will be made. With an introductory outline of their method in Section 2, we will proceed to apply it to various distributions, and will evaluate the degree of accuracy that can be conveniently obtained by means of it in each particular case. The numerical results will be presented in tabular form.
"Approximations to the Moments of the Sample Median." Ann. Math. Statist. 33 (1) 157 - 168, March, 1962. https://doi.org/10.1214/aoms/1177704720