<p>If you Google for <a href="https://www.google.com/search?q=unanswered+tag+site%3adata.stackexchange.com" rel="nofollow">unanswered tag site:data.stackexchange.com</a> you can find some already existing Data Explorer queries for this. For example:</p>

<ul>
<li><a href="http://data.stackexchange.com/mathoverflow/query/42823/unanswered-questions-by-tag" rel="nofollow">Unanswered Questions by Tag</a>: Shows the number of unanswered questions by tag for the most popular tags. </li>
<li><a href="http://data.stackexchange.com/mathoverflow/query/50761/unanswered-questions-by-tag" rel="nofollow">Unanswered Questions by Tag</a>: Shows all tags with at least 3000 questions, their total questions and of those, how many are unanswered. </li>
<li><a href="http://data.stackexchange.com/mathoverflow/query/77412/unanswered-questions-by-tag-with-at-least-100-questions" rel="nofollow">Unanswered Questions by Tag with at least 100 questions</a></li>
<li><a href="http://data.stackexchange.com/mathoverflow/query/50761/unanswered-questions-by-tag" rel="nofollow">Unanswered Questions by Tag</a>: Shows all tags with at least 3000 questions, their total questions and of those, how many are unanswered. </li>
</ul>

<p>You can probably find more or modify those queries for your purposes.</p>

<p>You should be aware that the notion of <em>unanswered question</em> 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 <a href="http://blog.stackoverflow.com/2008/09/ok-now-define-answered/">here</a>. (For example, the questions on the <a href="http://mathoverflow.net/questions?sort=unanswered">unanswered tab</a> or the questions that are bumped by the <a href="http://meta.stackexchange.com/questions/19738/who-is-the-community-user">Community User</a> are questions fulfilling these criteria.)</p>