What is Molar-mass averages?

For a sample containing $N_i$ chains of molar mass $M_i$, the number-average molar mass and the mass-average molar mass are

where $w_i$ is the mass fraction of the chains of mass $M_i$. The dispersity $\text{\DH} = \bar M_w/\bar M_n$ is at least 1, and equal to 1 only if all chains have the same mass. The averages $\bar X_n$ and $\bar X_w$ of the degree of polymerisation are defined in the same way.