I thought I would share a tactic I have personally used at billion dollar orgs in social media. It is free and incredibly powerful.
Install a Facebook pixel on your site
Wait for it to collect enough people to make a custom audience (the minimum is 100)
Make a custom audience from your site visitors (you can also do this from an email list)
Facebook gives very limited insights on these audiences, but here's the workaround:
4.1 Go to ads manager and create an ad.
4.2 Choose your custom audience and then look at the estimated reach. That will be the denominator in your fraction below.
4.3 Then choose "narrow audience" and add whatever you like (demographics, interests, HHI etc). See how the audience size shrinks. Thats your numerator.
4.4 With both numbers, you can now estimate what your audience is comprised of!
Whats powerful about this is that Facebook has a ton of information, so you can 'query' just about anything you are interested in.
There is of course caveats to this and a bunch of nuance. If people are interested, I am happy to share in a larger post.