Hey anthonye.

In your interpolation based approach, are you using the interpolation and then solving for when you get half way (in terms of finding the limits that give this constraint)?

Remember the median is the middle value and so if you setup an interpolation function, you have to find the corresponding value that is closest to the middle of your curve (in terms of intercepting with an x-value) and compare that against your calculated median. We also assume your interpolation function is non-decreasing.