A median filter is a non-linear and lossy process, so it doesn't have a closed form frequency response as would a FIR filter (say a box filter of the same length) in an LTI system.
But how closely can something similar to a frequency response of a median filter be approximated? How would this scale with the length of a median filter? Under what conditions or for what class of signals might this approximation be ballpark "close"? For what class of signals might this approximation be very inaccurate?
What kinds of frequency domain distortion or additive noise does a median filter produce?