In those languages of the world that are inflected, the plurals of nouns are routinely formed by adding a desinence (= inflectional suffix) to the stem of the singular. English is no exception. There is thus an iconic relation between the forms of the two grammatical numbers, viz. the plural is longer than the singular.
However, English also has a set of plurals which are shorter than their singular counterparts, namely the learnèd words of Latin and Greek origin such as medium, phenomenon, criterion, etc., whose plurals (media, phenomena, criteria, etc.) are formed by replacing the desinence of the singular with –a. This is admittedly a small lexical class, but its frequency has also conditioned a change in the history of English whereby the plural forms commonly supplant the singular for both numbers. Thus media is now generally construed as a collective singular––interestingly, with no plural (singulare tantum). There are even contemporary examples of scholarly writing where this change can be observed. Cf. the stylistic barbarism in the following sentence: ”Almost from the very beginning Sologub seemed to be a curious phenomena in Russian Symbolism, for reasons other than his background, profession or appearance.” (S. D. Cioran, “Introduction,” Fyodor Sologub: The Petty Demon [Woodstock: Ardis, 2006], p. 16. This may or may not be a genuinely native solecism, given the Romanian surname of the writer, but it was evidently not caught in proof and thus counts as such all the same).
The change at issue is unidirectional: the plural form always replaces the singular for both numbers. The fact that the normal English plural desinence –s fails to be attached in such words as media can be ascribed to the residual strength of the original meaning of the plural as the marked number. Be that as it may, ultimately the change can be construed as a consequence of the principle of iconism, here dictating that the shorter of the two variants be used as the form of the singular.