Sounds like an interesting thesis subject. There is something special going on here and it’s growing leaps and bounds around the Arduino platform. The fact that it is based on open source software and hardware makes it somewhat unique.
Also the fact that the platform is useful for raw beginners in programming and electronics all the way to professional embedded engineers makes it unique I think. The entry costs can be very low, but still hard to out grow the capabilities and applications one can handle with this platform.
There are now 3rd party vendors in all continents manufacturing processor boards and/or accessory shield boards that support this platform.
Now how to get a handle on user population and number of processor boards sold? That’s kind of hard to get I would think. The member population of this forum is one metric, but don’t know how inclusive it would be. There are so many manufactures now that I’m sure getting them all to give you units shipped to date would be difficult, but maybe worth some e-mails. A quick look on E-bay using Arduino as a search word will show a growing number of listings over time. Of course goggle can give you a count of site hits using a Arduino search word.
I don’t know, it’s your thesis, so I guess you have all the hard stuff to figure out. I do know that it’s a very interesting dynamic going on around the Arduino community and I think it has legs.