Use the adverb reputedly for things that are said by many to be a certain way, like the unpromising-looking pizza place that's reputedly the best Italian restaurant in your neighborhood.
When people generally believe that you're really fast at reading, you're a reputedly speedy reader. And if the creepy old house next door is reputedly haunted, that means that everyone says ghosts live there. Another way to think of reputedly is meaning "by reputation." In fact, the two words share a Latin root, reputare, "to count over, reckon, or think over."