Use Statistics module to view published/unpublished nodes
The Drupal 7 Statistics module is for monitoring web pages. It records when pages are viewed and who viewed it. Per its documentation, "these statistics are useful in determining how users are visiting and navigating your site."

I think what you're asking for is a module that counts the content (i.e. the individual nodes). You should be able to do this with Views, by selecting the appropriate Fields (what kind of content), Field Filters (published or not), and then "Use Aggregation" (to calculate counts). I found a module called Count that might do what you want, but it's only for Drupal 6.

I'd be interested in other people's answers on your question.