Not sure how to gather data on ‘active’. It should be possible to track the number of implementations though.
I remember one platform, vBulletin I think, used the same default guidelines or text in their terms and conditions on every site. I put that into google and came up with some 50k results. Not exactly a precise figure, but something to start with perhaps. Can you find something on there that isn’t easily changed?
Tracking activity will be hard. Perhaps individually click on 100 at random (not sure how random that will be given how google ranks this stuff) and see how many are active as a percentage and then multiple by the total number of communities.
Not exactly scientific…but could be ‘something’.
(or just ask each of the forum owners how many customers they have and divide by 2 / 3