Intuitively, if the weight average molecular weight is w, and you pick a random monomer, then the polymer it belongs to will have a weight of w on average.
The weight average molecular weight can be determined by light scattering, small angle neutron scattering (SANS), and by sedimentation velocity.
An alternative measure of molecular weight for a polymer is the number average molecular weight; their ratio is called the polydispersity index.
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