Median: ill-defined as fallback?

According to the recent ISDA consultation, the fallback spread above RFR will be based on median historical spread over a lookback period of 5 years. One issue that I did not raised in my answer to the consultation is the definition of median (it was so obvious to me that a median would not be selected, that I did not bother; I know, I was wrong again).

The median of a random variable is (see for example the Wikipedia definition) is any real number m that satisfies the inequalities
P(X ≤ m) ≥ 0.5 and P(X ≥ m) ≤ 0.5.

The tricky part is in the "any" for discrete distribution (like an historical distribution). If there is an even number of days in the 5-year lookback period (the exact meaning of 5-years is still unclear), there are infinitely many of such numbers. With the 7 decimals on LIBOR (5 decimals when expressed in percent) and the composition on many days on irregular period for the overnight part, it is very unlikely that the two numbers in the middle will be exactly the same. 

It will be interesting to see how median will be defined in the actual legal wording. I'm torn between simply median (and then it will be up to the user to define what it means in practice, including potential lawsuit) and a redefinition of median (for the fallback computation purposes, median means xxx). In both cases, it will be up to some third party (Bloomberg again?) to decide what the meaning of the consultation is.

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