Consider for example a methyl group which is rotating during dynamics. If you average the coordinates, you will notice that the C-H bond distances shrink, although all in each frame the distance is ~1A. Looking at a planar analog:
X (Z) X'
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A
If atom X is observed at positions X and X', the average position is
Z, and we can see that
( d(A-X) + d(A-Y) ) / 2 != d(A-Z)
The measurement of an average structure from a trajectory is not equivalent
to the average of the same measurement on each set in the trajectory.
Long answer by Thomas Cheatham