What type of format was the original data? For example, were you provided individual lists of each profession or a list of addresses and all the professions at the given address?
All geocoding does for you is provide a spatial data point. How you work with it is a whole different story. You mention hygenists per population; do you have data to support such a relationship? You could do that by simply getting a count of licenced hygenists in a given region (city, county or state) and then getting the population for you chosen region. Simple math and perhaps a relevant analysis, but not terribly challenging or truly spatial.
What if you had public transportation route data and you figure out how many hygenists are within a half mile of a bus route? Or if you get demographic data and you look at neighborhood income and the number of offices within a particular income threshold.
There are hundreds of analyses you can perform if you have the data. The trick with GIS data is we get to see the spatial relationships between our various data in the form of a map. Anyone with with a spreadsheet can produce rows and columns of data; halfway through the presentation of your results, your audience is in dreamland.
My suggestion is to give this more thought. Then you can figure out what sort of additional data you need; obtain it and see if you can answer your questions.
That should just about do it....
