One sense of “medium” is “a channel of communication,” such as television, radio, or the internet. The plural of this sense of “medium” is “media”:
We gathered data from a variety of media.
However, when referring to communication channels, we also use “media” as a mass noun. This is why we say “the media” when talking about TV, radio, and news sources. The plural “media” also applies in other cases, including:
Electronic files that can be played (e.g., an MP3 is a type of “digital media”)
Intervening substances, especially in the sciences (e.g., air and water are “media” through which sound is transmitted)
Artistic materials (e.g., paint and charcoal are “artistic media”)
It is thus correct to use “media” as a plural in any of these situations.
As a professional ghost hunter, I have worked with many mediums.
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This is the only sense of “medium” where “media” is not an accepted plural.
In addition, we can use “mediums” for artistic materials. In this case, “mediums” and “media” are interchangeable, so we could say either of the following:
Paint and charcoal are artistic mediums.
Paint and charcoal are artistic media.
However, you will still want to use one term consistently in each document.
Summary: Media or Mediums?
The correct plural depends on the kind of “medium” you are discussing:
If discussing means of mass communication, the correct plural is media.
For an intervening substance, the correct plural is media.
If you are discussing psychics or spiritualists, the correct plural is mediums.
For artistic materials, you can use either media or mediums.
The key is remembering to use “mediums” when referring to psychics. In all other cases, “media” is the preferred plural. And don’t forget to have your written work proofread if you’d like more help with your word choices.