Yes. About 15%. It's like taking Dash as a feat. However, iirc the barbarian's elevated movement does not work if it is wearing heavy armour.
If you really want to test it out, set up a race between your barbarian and a character that does not have a boost to speed (e.g. not a barb, not a monk, does not have Dash). The barb will be faster.
The fastest character is a high level monk, as monks receive a movement boost every three levels.
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