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On my reasonably flat commute I average around 16 mph on my road bike, but your average speed is dependent on many different factors. A general rule of thumb is that if you are switching from a mountain bike with knobbies to a road bike you will be between 15-20% faster at the same watts/effort.
It depends more of your legs than of the bike. On a typical road bike most clubs rate rides as relaxed (<12mph), slow (12-15mph), moderate (15-18mph), or brisk (>18mph). A pro racer average on the flat will be over 25 mph.