If you Google for [unanswered tag site:data.stackexchange.com](https://www.google.com/search?q=unanswered+tag+site:data.stackexchange.com) you can find some already existing Data Explorer queries for this. For example:


 * [Unanswered Questions by Tag](http://data.stackexchange.com/mathoverflow/query/42823/unanswered-questions-by-tag): Shows the number of unanswered questions by tag for the most popular tags. 
 * [Unanswered Questions by Tag](http://data.stackexchange.com/mathoverflow/query/50761/unanswered-questions-by-tag): Shows all tags with at least 3000 questions, their total questions and of those, how many are unanswered. 
 * [Unanswered Questions by Tag with at least 100 questions](http://data.stackexchange.com/mathoverflow/query/77412/unanswered-questions-by-tag-with-at-least-100-questions)
 * [Unanswered Questions by Tag](http://data.stackexchange.com/mathoverflow/query/50761/unanswered-questions-by-tag): Shows all tags with at least 3000 questions, their total questions and of those, how many are unanswered. 

You can probably find more or modify those queries for your purposes.

You should be aware that the notion of *unanswered question* has some ambiguity to it. On SE network usually a question is considered unanswered even if it has some answers, but none of them is upvoted or accepted, see [here](http://blog.stackoverflow.com/2008/09/ok-now-define-answered/). (For example, the questions on the [unanswered tab](http://mathoverflow.net/questions?sort=unanswered) or the questions that are bumped by the [Community User](http://meta.stackoverflow.com/questions/19738/who-is-the-community-user) are questions fulfilling these criteria.)