What's your context for averaging multiple rotations?
Averages are something that you can do with sums, where order of composition doesn't matter.
Rotations don't commute, so the concept of average as we understand it doesn't normally apply to them.
If you're holding a phone: rotate the screen away from you 180° (so you'd be seeing the back), then clockwise 90° relative to the ground (around vertical axis).
Your camera will be facing your left.
Now hold the phone normally, and do the same rotations in the opposite order. Your camera will now be facing your right.
Question: where should the camera be facing in the "average" of these two rotations?
There's no single answer — it depends on what you need from the average.
Averages are something that you can do with sums, where order of composition doesn't matter.
Rotations don't commute, so the concept of average as we understand it doesn't normally apply to them.
If you're holding a phone: rotate the screen away from you 180° (so you'd be seeing the back), then clockwise 90° relative to the ground (around vertical axis).
Your camera will be facing your left.
Now hold the phone normally, and do the same rotations in the opposite order. Your camera will now be facing your right.
Question: where should the camera be facing in the "average" of these two rotations?
There's no single answer — it depends on what you need from the average.