  In practice, we often encounter situations where a sample size is not defined
in advance and can be a random value. The randomness of the sample size
crucially changes the asymptotic properties of the underlying statistic. In the
present paper second order Chebyshev--Edgeworth and Cornish--Fisher expansions
based of Student's $t$- and Laplace distributions and their quantiles are
derived for sample median with random sample size of a special kind.
