Data traffic by application

Sorry, no.

Look at this:

https://itunes.apple.com/us/app/onavo-count-data-usage-manager/id543547474?mt=8

That's as good as it gets in regards to the info you want.

Start by deleting any apps you've added in the last week.

While that app looks like it provides the service they claim, it also appears to do something else that may or may not be an issue for the users. In order to identify what apps are using the data, it appears to route all of your internet traffic from your iPhone through their web based VPN services. This means that they see all of your web traffic and could mine it for data, and potentially could sell your usage patterns or worse, your personal information (web accounts etc.) since it has to pass through their servers in order for them to give you the detailed usage you want.

If you are only concerned about what apps are using data, and not what information on you the app providers might be harvesting, then this app may be the answer for you. Regretfully, based on the iOS design, this is the only way to get the information you seek, but you are then relying upon the honesty and integrity of the app provider to have your best interests in mind. Since the app vendor is not charging you for the service they are providing, they have to be making their money somehow to pay for the services you are using. How do you think they are making that money if you aren't the one paying? Most likely, you are the one being sold to someone else...