How quickly do experience orbs travel?

This is given that the player's movement speed is 4.317 blocks per second and their Motion, which i used to test this, is 0.0784 This means that a Motion value of 1 would be 55.064 blocks per second.

That being said, I did some testing, and the velocity of an experience orb is roughly modeled by -5.91561 * sin(0.19495 * x) + 5.89166 where x is the distance from the player

For the exact values, here's the graph I plotted: https://www.desmos.com/calculator/5wgkjjukzl

It's somewhat difficult to get the exact 'average' speed as there is a falloff as the orb gets farther away and it is hard to find an exact endpoint where the xp orb no longer moves toward the player.
This means that technically the slowest that the orb can move without being stopped is infinitesimally greater than 0.

There is also no real 'median' because the function is continuous, but if you want to know the speed when you are half way between the maximum and minimum distances, that would be 2.5935 blocks per second at the distance 3.05 blocks

To answer your question

After some calculus, the average value of the function I defined earlier is 1.508 blocks per second. It won't be exact as the values I got didn't perfectly match the function but it's extremely close