In my googling, it seems the proper way to find the median of a cdf of a discrete variable is to stick to the discrete values provided, even if you overshoot and end up with an x where P(X <= x) > 0.5. But is there a way to approximate an exact value such that P(X <= ) = 0.5?
A straightforward way would be to use the slope between the two points closest to 0.5 to find X. Would this be considered reasonable? If not, are there other methods that better account for the whole distribution instead of just looking at two points?
Edit: It has been made clear that a non-integer value wouldn't really make sense. However, for some context, I'm looking at how many users have converted after a certain number of free trial appointments, and how that number might be applied across many users. You can see why it feels weird to laypeople to say the median is 5 if P(X <= 4) = 0.49 but P(X <= 5) = 0.90. That's an exaggeration, but the kind of issue I face.