"Happy median" versus "happy medium"

Which is more correct and/or common "Happy Median" or "Happy Medium"? Any history on the two would also be interesting.

The phrase is happy medium. Here is NOAD's take:

happy medium noun a satisfactory compromise : you have to strike a happy medium between looking like royalty and looking like a housewife.

Etymonline says:

Happy medium is the "golden mean," Horace's aurea mediocritas.

So apparently it comes to us through classical scholarship.

It is medium, not median.

Here's a dictionary.com link.

The earliest example of the phrase that I've been able to find of that particular phrase is an article in the Perth Magazine of Knowledge and Pleasure, published in 1772. The use of the word "medium" as a bridge between two extremes goes back to the late 16th century.

Median is primarily a mathematical term, but is sometimes confused with medium due to its similar sound and somewhat similar meaning. Interestingly, they also both come from the same Latin root, "medius," which simply meant "middle".