Eighteen lines of code to find the middle one or two elements in a sorted list is a bit mighty, would you agree? When a small problem becomes complex code, it becomes a big problem, transforming the problem and the solution. This is counter productive, to say the least.
Scratch what you have. Nobody is going to analyze it. It's too far fetched. Start over.
What is the given? => A sample space
What is the constraint? => Sample space is sorted
What is the objective? => The middle one (data point) or average of middle two, by parity
This does not take a lot of logic to perform. Give it another go and see if you don't reduce your code substantially.
Given a list that we care nothig about in the global scope, we can sort in place the input.
The single object came in, and now goes through a simple transformation. But whatever object that may have been, unless the argument was a list literal, it too will undergo the same transformation. Lists are reference objects that do not get copied to functions, only referenced. If the list was indeed a defined object, it just got sorted.
That all aside, we now have an iterable object with a length. We know that it has order from lowest to highest. The median is right at hand.
n = len(x)
m = int(n / 2)
m will be the middle index, or the index of the lowest value of the top half.
return x[m] if n % 2 else float(x[m - 1] + x[m]) / 2