  With the space-borne missions CoRoT and Kepler, a large amount of
asteroseismic data is now available. So-called global oscillation parameters
are inferred to characterize the large sets of stars, to perform ensemble
asteroseismology, and to derive scaling relations. The mean large separation is
such a key parameter. It is therefore crucial to measure it with the highest
accuracy. As the conditions of measurement of the large separation do not
coincide with its theoretical definition, we revisit the asymptotic expressions
used for analysing the observed oscillation spectra. Then, we examine the
consequence of the difference between the observed and asymptotic values of the
mean large separation. The analysis is focused on radial modes. We use series
of radial-mode frequencies to compare the asymptotic and observational values
of the large separation. We propose a simple formulation to correct the
observed value of the large separation and then derive its asymptotic
counterpart. We prove that, apart from glitches due to stellar structure
discontinuities, the asymptotic expansion is valid from main-sequence stars to
red giants. Our model shows that the asymptotic offset is close to 1/4, as in
the theoretical development. High-quality solar-like oscillation spectra
derived from precise photometric measurements are definitely better described
with the second-order asymptotic expansion. The second-order term is
responsible for the curvature observed in the \'echelle diagrams used for
analysing the oscillation spectra and this curvature is responsible for the
difference between the observed and asymptotic values of the large separation.
Taking it into account yields a revision of the scaling relations providing
more accurate asteroseismic estimates of the stellar mass and radius.
