How can I track statistics on my site's user population?
Other than the option you present, I think you have two choices.

One is to wire up a hook_menu(), and create a path that accepts role, gender, and the other field value.  You would then pass this into a db_select() or EntityFieldQuery(), and return the results in HTML table form.

The other option, and the one I would recommend, would be to make up a View over your users, add in your roles and fields, and then use Views Data Export to export as XLS or CSV.  You can then analyze your data in a third-party tool like Excel.

Why do I recommend the later?  Leverage your tools for their strengths.  Drupal is good an managing and serving up content (raw data counts).  Tools like Excel are great at analyzing data.  These three fields are what you need to look at now, but this could change in the future.  Having a full export of the raw data will make this much easier down the road.