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On another site the issue has come up that questions may not be upvoted but answers are. I would like to get some statistical support for this. Are there already existing apps that can do this kind of analysis?

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This is not something you could obtain from the API. The API basically exposes some of the features of the site (e.g. search, writing posts, voting itself) in a programmatic way. For analysis like this, you'll need SEDE, the Stack Exchange Data Explorer and support for that is on Meta Stack Exchange; there's even a chatroom dedicated to SEDE.

That said, the answer to your question is about 55% on Music Stack Exchange, as this relatively simple SEDE query shows. If you're interested, you should definitely read the tutorial.

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