In terms of statistical fluctuations , stellar population synthesis models are only asymptotically correct in the limit of a large number of stars , where sampling errors become asymptotically small .
When dealing with stellar clusters , starbursts , dwarf galaxies or stellar populations within pixels , sampling errors introduce a large dispersion in the predicted integrated properties of these populations .
We present here an approximate but generic statistical formalism which allows a very good estimation of the uncertainties and confidence levels in any integrated property , bypassing extensive Monte Carlo simulations , and including the effects of partial correlations between different observables .
Tests of the formalism are presented and compared with proper estimates .
We derive the minimum mass of stellar populations which is required to reach a given confidence limit for a given integrated property .
As an example of this general formalism , which can be included in any synthesis code , we apply it to the case of young ( t \leq 20 Myr ) starburst populations .
We show that , in general , the UV continuum is more reliable than other continuum bands for the comparison of models with observed data .
We also show that clusters where more than 10 ^ { 5 } M _ { \odot } have been transformed into stars have a relative dispersion of about 10 % in Q ( He ^ { + } ) for ages smaller than 3 Myr .
During the WR phase the dispersion increases to about 25 % for such massive clusters .
We further find that the most reliable observable for the determination of the WR population is the ratio of the luminosity of the WR bump over the H \beta luminosity .
A fraction of the observed scatter in the integrated properties of clusters and starbursts can be accounted for by sampling fluctuations .