Is the word "representativity" possible?

Solution 1:

1. It is a morphologically valid construction. For example, see the same pattern in relative/relativity (where the latter is a rather recent derivative of the former)
2. It is commonly used in the field of statistics (see Google Scholar searches for “representativity + statistics” or related terms).
3. Examples of its use in academic writing include the following (found using the Corpus of Contemporary American English), both in and outside of the field of statistics:

A school based sample of 5,500 Norwegian 16 to 19 year olds (92% response rate) with good population representativity was analyzed. Same-sex experiences included “necking” / “making out”, petting, intercourse, and oral sex. Compared to heterosexual young people, young people reporting same-sex sexual experiences only were more socially integrated into their peer group and consumed more alcohol.

^{(K. Hegna, Journal of Drug Issues, 2007, vol. 37, p. 229)}  

The conventions of representation are bankrupt, for their legitimacy rested on representativity as much as on resemblance or mimesis. Abstract art used to register the bankruptcy, but, abstract art has long been assimilated and has lost its critical edge.

^{(T. De Duve, People in the image/people before the image, 1998)}

Solution 2:

There's nothing morphologically wrong with the construction, but it might not be in wide use.

Solution 3:

Representativity is valid morphologically and semantically. As for the "representativity" or representativeness debate, think of how wrong some of these word would sound ie "flexibileness" (sic) or intelligiblness (sic) or illegibileness (sic). No, adding -ness as an ending is not a panacea, and yes, the English language is more creative and adaptable than some readers might want to think.