The correct idiom is happy medium and not happy median. The confusion of a phrase based on its pronunciation is called an eggcorn.
Medium is the middle term for size, in between large and small. It is also the name for people who believe they can channel thoughts from the dead, and the term for materials used by an artist.
Median is the middle of a set of numbers, as well as the divider in a road.
But while happy median does make logical sense, the standardphrase, which has been in use since at least the eighteenth century, is happy medium meaning to have a balance or satisfactory compromise.
Since the phrase is describing the middle of something, it has no plural.
But surely there is a happy medium between desperately seeking someone, anyone and leaving it all up to fate. [Washington Post]
Alloa and Livingston offer best value at £190 and £180 in the second tier while Falkirk strike a happy medium at £250. [Scottish Daily Record]
Of course, what is too hot or too cold will depend on each individual’s heat sensitivity and thus, the ideal face-washing temperature is your own happy medium. [Vogue Australia]
Now of course, they have the Champions League to contend with which has forced the Kop boss to alter his plans – but he hopes to find the happy medium soon. [Daily Star]
And yet for some A-listers, there is no happy medium between being dressed to the nines and slummin’ it. [E! Online]