Intervening objects giving rise to absorption lines in the spectra of distant QSOs provide one of our best probes of the conditions in the Universe at early epochs. In particular, damped Lyman alpha (Lyalpha) systems are generally assumed to be due to the progenitors of today's normal galaxies, seen at an early phase in their evolution. Several groups have reported on the metallicity deduced for such absorbers, noting that they are significantly lower than present day metallicities measured in the interstellar gas of typical spiral galaxies such as our own. This is expected, in general terms, from chemical evolution models, but the required rate of evolution appears higher than expected from these models. However, in order to interpret these results correctly, we need to consider the average metallicity seen on a random line of sight through a galaxy, subject only to the constraint of a minimum gas density. Much of the covering factor on the sky may be the result of the outer parts of large discs or of numerous small systems, either of which are likely to have low abundances. In this paper we attempt to model random lines of sight, taking these factors into account. We find that such an area-weighted mean metallicity may be much less (by nearly 1 dex) than would be obtained by simply adopting the figures given for the central parts of giant spirals. For a range of plausible galaxy populations this mean is only about one third of the solar metallicity, even today. Relatively little evolution is therefore required in order to account for the low abundances seen in the Lyalpha absorbers.