I've been doing the MS10775A course this past week and one question that came up that the trainer couldn't answer reliably is:
Does a re-index update the statistics?
We found discussions online arguing both that it does and that it doesn't.
You can keep the following in mind when caring about updating statistics (copied from Rebuilding Indexes vs. Updating Statistics (Benjamin Nevarez)
The short answer is that you need to use
* Added by Paul White
Updates Statistics will update the stats of those columns which are not part of indexes.
If you are looking for a script then you can find one on the following link.