It depends greatly on what you're doing. For Facebook or Twitter, in typical use? Hundreds or thousands, but not hundreds of thousands.

For, I don't know, a podcast app, it could be dozens for most users, low hundreds for power-users.

There exist very lucrative mobile apps where the answer is likely single digits. (In addition to some which make no requests at all, of course.)

I should have been more clear. I was looking at how many API calls a typical app would make when gathering data. Is it in the hundred, thousands? On average. Or that too wide of a question to get an accurate metric?

There's no clear metric because it's dependent on how many requests each individual API the app has integrated or built.

To find out you would probably have to test a lot of apps yourself and extrapolate from that.