My questions are:
- Is this a problem?
- Should we attempt to do something about it?
- If we should do something about it, what should be done?
My questions are:
As quid pointed out, it's impossible to accept an answer where none exists. So the issue should be separated into two:
It't not necessary to write queries for this, the site search gives the same information (with the help of search parameters). E.g., one can look at the posts that are 3 months old with
created:3m, or at all posts in 2015 with
created:3m so that the very recent posts, many of which are on their way to deletion, do not distort the picture.
So, more than half of questions with an answer have an accepted answer.
For year-to-year comparison, the numbers from 15 months ago:
It's remarkable how similar the numbers are, except for the first one. A major factor here is that abandoned questions (0 score, 0 answers, 0-1 comments, low views) are automatically deleted after a year. Presumably, this is also the fate of many of the 16,233 questions created 3 months ago.
More generally, I don't see a reason to ever worry about acceptance. The question author probably posted the same question on five sites, got an answer on three, of which they read one (not the one on Math.SE), and went on about their life. If other users care about the answer, they'll upvote.
If nobody cares about the answer... you still had fun writing it, haven't you? If it isn't fun any more, stop doing it.
I'm not sure if that's already included in your statistics, but there are a lot of relatively easy questions that have an answer which is stated as a comment. This will be ok for the one who asks the question, but I also want to point out, that this habit is a bit unnerving for someone who wants to answer an unanswered question only to find, that there is an answer already.