When are extremely metal-deficient galaxies extremely metal-deficient?

Extremely metal-deficient (XMD) galaxies, by definition, have oxygen abundances \le 1/10 solar, and form a very small fraction of the local gas-rich, star-forming dwarf galaxy population. We examine their positions in the luminousity-metallicity (L-Z) and mass-metallicity (M-Z) planes, with respect to the L-Z and M-Z relations of other gas-rich, star-forming dwarf galaxies, viz., blue compact galaxies (BCGs) and dwarf irregular (dI) galaxies. We find that while the metallicities of some low-luminousity XMD galaxies are consistent with those expected from the L-Z relation, other XMD galaxies are deviant. We determine the 95 per cent confidence interval around the L-Z relation for BCGs, and find that its lower boundary is given by 12 + log(O/H) = -0.177 M_{B} + 4.87. We suggest that a galaxy should be regarded as XMD, in a statistically significant manner, only if it lies below this boundary in the L-Z plane. Of our sample of XMD galaxies, we find that more than half are XMD by this criterion. We also determine the gas mass fractions and chemical yields of galaxies in all three samples. We find that the effective chemical yield increases with increasing baryonic mass, consistent with what is expected if outflows of metal-enriched gas are important in determining the effective yield. XMD galaxies have lower effective yield than BCG/dI galaxies of similar baryonic mass. Motivated by the fact that interactions are common in XMD galaxies, we suggest that improved (tidally-driven) mixing of the interstellar media (ISM) in XMD galaxies leads to a lowering of both, the measured metallicity and the calculated effective yield. We suggest that XMD galaxies are deviant from the L-Z relation because of a combination of being gas-rich (i.e., having processed less gas into stars) and having more uniform mixing of metals in their ISM.