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The number-average molar mass weights each molecule equally. For counts $n_i$ with molar masses $M_i$,A mass-proportional SEC detector response requires conversion to counts before determining this average.

A SEC detector response must be specified before interpreting a peak area. Ultraviolet absorbance depends on a species' response factor and concentration, as described by the Beer-Lambert law; differential refractive index detection depends on how the dissolved species changes refractive index. Equal amounts need not produce equal signal areas across unlike species.

Even a calibrated mass-proportional trace is not a chain-count probability distribution. In an original two-population example, equal recovered masses of chains with molar masses $20,000$ and $80,000\mathrm{g}\mathrm{mo}{\mathrm{l}}^{-1}$ contain four times as many chains in the lighter population. Thus equal signal areas, assuming equal response per unit mass, correspond to number fractions $4/5$ and $1/5$: their number-average molar mass is $32,000\mathrm{g}\mathrm{mo}{\mathrm{l}}^{-1}$, while their weight-average molar mass is $50,000\mathrm{g}\mathrm{mo}{\mathrm{l}}^{-1}$. Converting a continuous trace additionally requires response correction and the appropriate change of variables between elution and molar mass bins.

Suppose a synthetic polymer population contains three chains of molar mass $10000\mathrm{g}\mathrm{mo}{\mathrm{l}}^{-1}$ for every one chain of molar mass $40000\mathrm{g}\mathrm{mo}{\mathrm{l}}^{-1}$. Multiplying both chain counts by any common factor leaves the averages unchanged. Substitution into the existing number-average molar mass and weight-average molar mass definitions givesThe larger chains are only one quarter of the chain count but supply $40000/70000=4/7$ of the mass. Thus a weighted mean that emphasizes mass gives a larger result than one that weights each molecule equally. Total mass divided by total chain amount of substance gives $M_n$, while $M_w/N_{\mathrm{A}}$ is not the mean mass of a randomly chosen chain. Inferring chain counts from size-exclusion chromatography still requires the existing SEC detector response and SEC molar mass calibration assumptions.