I am wondering if anybody knows good exact bounds for the Median of a Hypergeometric distribution:
$$ X \sim \text{Hypergeometric}(N,K,n) $$
One exact bound could be given by exploiting the inequality between Mean, Median and Standard Deviation.
Another direction might be the Binomial approximation of Hyperbolic distribution, because there is an explicit bound for the Median of a Binomial distribution. Further, there are explicit bounds for the Total variation distance between Hypergeometric and Binomial distributions. These might be combined to a tighter bound than one obtained by Mean and Standard Deviation.
Is anybody aware of a formula or reference that would yield a tight explicit expression for such bounds?