Which end of a barrel connector is positive
The answer may be a bit unusual, but it's neither!
Barrel connector doesn't have a defined polarity. Instead, what you'll have is the polarity set by the device that you want to use, if the device is using DC in the first place.  Near the receptacle for the barrel connector, you might see a sign with something like this:

Take note of the signs marked on your device where the + and - symbols are drawn.
On the example above, the + sign is connected to outer shell in this example, meaning that the outside of the connector is positive and the - sign is connected to the black dot in the middle, meaning that the inside connection is negative.
If the symbols are the other way round, the opposite is true. If the line touching the tip in the centre has a + (plus) symbol, this means the tip is positive, and the outer shell is negative.
In any case, you need to research this for your particular device. There is no general rule.