MSD averaging question


I have a question about how LAMMPS averages the MSD for a group of atoms.

According to the online manual for the compute msd command, the "4th component is the total squared displacement ... summed and averaged over atoms in the group". My question is: what is the error associated with averaging over all atoms in the group? Does LAMMPS report or record the standard deviation (error) due to averaging over all atoms in the group? If not, is there a way to output the msd for every atom at each timestep so that I can compute the standard deviation in post-processing?

I am asking because I want to report the error in my msd calculations as accurately as possible.

Example of relevant lines from my input file:

group Li type 1
compute msd Li msd com yes
fix msd Li ave/time 1 1 ${th} c_msd[4] file msddumpfile

I have searched the listserv archives, online manual and tried to look through the LAMMPS sourcecode to find the answer. If I have missed something obvious, please direct me to the correct place.

Thank you for your time,

Compute msd does not calculate a variance. The compute displace/atom
command essentially calculates an MSD on a per-atom basis,
which can then be dumped and post-processed.