Suggestion regarding updates for deleted application
Look in the "receipts" folder which has a list of files pertaining to applications and updates which have been installed. It's in the main library folder: I.E. imac/library/Receipts
Search for one that pertains to the deleted application. Delete it. You may need to authenticate.
I believe this shouldn't do any harm and might eliminate your problem.
Also you could delete the plist preference file for the application which would be in the in the user library preferences folder. I.E. imac/users/username/Library. You can get to the user Library by holding the option key and selecting Library from the list in the "Go" menu in the finder. Search for a plist file that pertains to the problematic application. For example the plist filename for Microsoft Excel is "com.microsoft.Excel.plist"
Don't go nuts deleting things if you're not sure. If you're not comfortable deleting these files - just move them to a temporary folder somewhere.
Probably best to reboot after deleting or moving the files and try the update process again.
I believe deleting the receipt file will "fix" the problem. If this was an app store installed application - the fix might be different.