Any question answered...

But what if you're talking about olive oil exports in the nineteenth century...? :)

For better or worse, I think the current standard usage is that "data" and "media" are both singular. But I'm not sure whether economics still clings to the more prescriptive usage.

I am not a native english speaker, its my 2nd language, but at university (in The Netherlands) we were taught when writing business reports to refer to Data (plural) , group of collected information. And Datum (singular) individual record from the group. However in practice no one ever used the word datum, simply always referring to data.

The same is true for criteria

several criteria ,or one criterion (people just never use this, as they are un familiar with it so commonly also refer to one criterion as a single criteria, in fact a mistake).

And The dictionary says:

USAGE Strictly speaking, [B][B]the singular form (following the original Greek) is criterion and the plural form is criteria[/B][/B]. It is a common mistake, however, to use criteria as if it were a singular, as in : a further criteria needs to be considered.

And for Data it says:
USAGE Data was originally the plural of the Latin word : datum, 'something (e.g., a piece of information) given.' Data is now used as a singular where it means 'information': : this data was prepared for the conference. It is used as a plural in technical contexts and when the collection of bits of information is stressed: : all recent data on hurricanes are being compared. [B][B]*[B]Avoid : datas and : datae, which are false plurals, neither English nor Latin.*[/B][/B][/B]

I think you can conclude that you can use data for both the singular and plural correctly, as long as you do it consistently throughout the paper, and your target audience are not scholars of latin, or english but concerned with the content of the paper I do not think it would be an issue.

Very Long answer but I hope this helps give you peace of mind.