A closed-form approximation for the median of the beta distribution
  A simple closed-form approximation for the median of the beta distribution Beta(a, b) is introduced: (a-1/3)/(a+b-2/3) for (a,b) both larger than 1 has a relative error of less than 4%, rapidly decreasing to zero as both shape parameters increase. 
Jouni Kerman
math.ST stat.CO stat.TH