Is there a way to determine when an iOS upgrade was installed?
If you have updated iOS through iTunes, you can look in your iTunes data folder, on a Windows machine that will be: 

C:\Users\[username]\AppData\Roaming\Apple Computer\iTunes\iPhone Software Updates\

Then check out the timestamp on the iPhone..._Restore.ipsw file. That will be the date you upgraded (or downloaded) our latest iOS update.

If you updated it directly on the device, I don't think it is possible to retrieve its date.