wrongly
In an incorrect or mistaken way.
Wrongly means in an incorrect or mistaken way. When you answer a math problem wrongly, you get the wrong result, whether because you made a calculation error or misunderstood the question. When someone is wrongly accused of breaking a window they didn't break, they're blamed for something they didn't actually do.
The word describes actions, beliefs, or judgments that miss the mark. A teacher might wrongly assume a quiet student isn't paying attention when they're actually thinking deeply. A referee might wrongly call a foul when the player touched only the ball. People in the past sometimes held beliefs that were later shown to be wrongly held.
Wrongly is different from wrong, which describes something that's incorrect (a wrong answer) or morally bad (lying is wrong). Wrongly describes how something is done: it's the adverb form that modifies verbs and actions. You might spell a word wrong (adverb), but you spelled it wrongly (adverb describing your action).
When we discover something was done wrongly, people may try to correct it, whether that means fixing a mistake, apologizing, or setting the record straight.