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Extremely metal‐deficient (XMD) galaxies, by definition, have oxygen abundances ≤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 luminosity–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‐luminosity XMD galaxies are consistent with those expected from the  L – Z  relation, other XMD galaxies are deviant, and more so as the luminosity and/or metal‐deficiency increases. 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, and in fact, nine of the galaxies lie below the 99.5 per cent confidence interval about the  L – Z  relation.  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. This suggests that some process, peculiar to XMD galaxies, has resulted in their low measured metallicities. 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. In isolated dwarf galaxies, the outer parts of the stellar envelope probably do not participate in the star formation, but are still generally included in the calculation of effective yield. This results in an overestimate of the 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.

When are extremely metal‐deficient galaxies extremely metal deficient?