Did Google recommend you do this? Surely no? Yes, like MHes said doing this lets Google know the links haven't been paid for also that you don't vouch for that site but adding nofollow to all your outbound links looks very unnatural. Sure you're passing link juice by linking out but at the same time you're associating your content with (I assume) authoritative content which is a good thing. You want to link out to good sites. Linking to authoritative sites will then help the other links on the same page. Win-win.
Maybe a thing to do is nofollow the less authoritative sites or simply not link out to them at all. Definitely see if you can reduce the outbound links. But do not nofollow all of them as it'll let Google know you're being manipulative. Just get a nice natural looking nofollow dofollow ratio.