Welcome back! For Laurel- Farm size versus ownership

I was gone trotting around Portland for two weeks, which meant that I had to leave you all scatter plot-less.
I hope this wasn't too sad.
So, today, I present the first of a series of scatterplots, requested by Laurel, centered around farming and the like. Specifically, she asked me about the link between non-corporate farming and farm output. I think. More or less.
So, thank you to http://www.ers.usda.gov/StateFacts/ , I have been able to start digging into this question. There will be more digging!
The first thing I wanted to look at was farm size versus private ownership. I would think that in the states where agriculture is a big business, farms would be larger and less privately owned.
I was, it seems, wrong. Farm size seems to be a lot more related to population density than anything else. Also, farm ownership seems to be pretty uniformly in the range of 80-90% private, across the board. Of course, some of those might be very small hobby farms. A median farm size would be an interesting thing to know.
Anyway, since this research wasn't very conclusive, I will play with more of the numbers in the coming days.