Can "mode" be used as "mean" and "median" are?

The question can be restated as "Can mode be used as an adjective?" for which one just needs to look in a dictionary.

OED lists mode as a noun and a verb, but not an adjective.

However, there is an adjective modal, for which OED gives

6. a. Statistics. Of, relating to, or of the nature of a mode; (of a value, etc.) that occurs most frequently in a particular sample or population. Cf. mode n. 13.

and there is a citation which exactly mirrors your example, although it appears the BBC thought it necessary to explain the word:

1968 Listener 25 July 101/1 The administrators we saw..had averaged only 2·8 years in all their completed jobs in the class; in fact, the modal (most frequently occurring) period in completed jobs was two years.

Neither mean, median, nor mode are likely to occur in casual conversation or writing. They are statistical terms, and would really only be used in a technical context. What you'd actually find in "regular" writing would be statements such as:

The average ticket price was $56.50.

(In nontechnical usage, mean has too many other, well, meanings, so "average" is used instead.)

The middle of the range of ticket prices was $61.

(This one is debatable: people do use median in nontechnical contexts, but you can never tell whether they're using it correctly, or whether they're using it as a synonym of average.)

The most common ticket price was $40.

(While it's true that mode has the adjectival form modal, almost nobody would know what you mean by "modal ticket price". Heck, I have a degree in math, and if I encountered that in a magazine or blog, I wouldn't know what it meant. In those rare cases when you need to talk about the mode, you're much better off describing the meaning in nontechnical terms, such as the "most common" phrasing I used above, or if you want to be slightly more accurate, something like "most frequently occurring".)