The book by Griffith on elementary particles reads:
A typical experiment starts out with beam of particles whose spin orientations are random, and simple counts the number of particles in a given direction.In this case the relevant cross section is the average over all initial spin configurations and sum over all final spin configuration.
I do not understand this explanation. If we do not know the spins of both initial and final particles shouldn't we take average for both? Why do we sum for final particles?
