When users struggle for appropriate jargon, I often misunderstand what they're after. I feel like if I had a dental appliance, I could encourage more precise questions on this site. Nonetheless, I do not have such a tool.

If I can't understand such a question, and I answer correctly and find out I'm wrong, do I delete my answer?

At least sometimes, yes, but not always. Consider a couple of cases:

  1. If the question was later edited to make it clear, or you conclude your own reading of it was mistaken (so that other people are unlikely to have read it as you did), then I think deletion or wholesale rewriting to address the new understanding of the question are usually reasonable choices.

  2. If the question was, and remains, ambiguous and can be taken two ways -- even if you no longer think that your original interpretation is the correct one (perhaps from reading another answer, say) -- then there can be value in leaving the answer there, because other people looking for help on the question you thought you were answering may put it in a similar way to the posted question. Another alternative would be to retain the original answer and also answer the question as you now think of it (possibly with the original answer coming second), highlighting that there's two possible ways to take the question.

    If you do either approach in 2., you may want to add a note at the start of your answer describing your changed view of the question but explaining why the answer is staying there. [Possibly the question should also be put on hold as unclear, but that is not itself a reason to delete the answer.]

I think it's up to you. You can (and I have) delete your answer if you don't think it's relevant or contributes to the thread.

On the other hand, you can also modify your answer to put a short note at the top:

I understood the question to be asking ____. In light of that, I provided the answer below. However, it now appears that the question is asking ____ instead, which my post does not address.

This may be a reasonable strategy for a couple reasons. Others may have the same understanding you originally had. Your post adds to the clarity and value of the thread as a whole. Likewise, a future reader may come across the thread looking for your answer based on the same misunderstanding of the question. Moreover, someone might learn an additional fact serendipitously despite / because your answer is different.

It depends... If it is a short answer about some basic topic and you wouldn't cry after it, it may be a good idea to delete it. However if you made some effort for answering the question (and sometimes got upvoted for it!) than it may be better to leave it because it still can be helpful. Recall when you search the site, the search results refer to both questions and answers -- in the future someone may be searching for your answer.

What you could do is alternatively:

  1. rephrase it, so it fits to the question as it was initially understood by you and to the true question (not always possible),
  2. add lead, as proposed by @gung, that describes as you understood the question,
  3. break your answer into two paragraphs with "old" and "new" answer, with some description of why the question can be understood in different ways, so it could lead to different answers (mixed strategy with 2),
  4. add another answer that answers "the" question, with providing the lead to the initial one (mixed strategy with 2).

So leave what could be helpful, but make sure that your answer is not misleading (by re-phrasing or providing a new one).

You can post the "wrong" interpretation as a separate question and move the answer there (by deleting the original answer and reposting the answer).

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