It's too wide of a question because of several reasons:

1. What do you count as an API request? Do you mean requests to "external" APIs? Or do you mean requesting content from the actual app server (e.g. Facebook loading timeline content)? Which API requests are you interested in?

2. What is a "typical app"? A game? A news reader? Twitter?

Even if someone could give you an answer that answer would most likely be irrelevant. API requests are a design choice. You can build the same app making 100 requests or 1 request for the same content. Both have tradeoffs.

Obviously it also depends on how much the user uses the app.