Sorry - I misunderstood your original question, and then our posts crossed each other. In my opinion the only sensible way to preserve data between installations is to use cloud storage, and that usually also requires some form of user registration. If you want to save data on the device then you need user assistance before they decide to uninstall, and they need to be knowlegeable about where it is stored and how to retrieve it after they have reinstalled the app.
This post explains the procedure, but it is not in my opinion very satisfactory for the use you have in mind.