For a number of reasons, the properties of integrated stellar populations are distributed. Traditional synthesis models usually return the mean value of such distribution, and a perfect fitting to observational data is sought for to infer the age and metallicity of observed stellar populations. We show here that, while this is correct on average, it is not in individual cases because the mean may not be representative of actual values. We present a simple mathematical formalism to derive the shape of the population's luminosity distribution function (pLDF), and an abridged way to estimate it without computing it explicitly. This abridged treatment can be used to establish whether, for a specific case, the pLDF is Gaussian and the application of Gaussian tools, such as the χ^2 test, is correct. More in general, our formalism permits to compute weights to be attributed to different properties (spectral features or band luminosities) in the fitting process. We emphasize that our formalism does not supersede the results of traditionally synthesis models, but permits to reinterpret and extend them into more powerful tools. The reader is referred to the original paper for further details.