This question came up when answering Find the pH of an amphiprotic salt dissolved in water at room temperature. If we dissolve $\ce{NaHA}$ in water, the species $\ce{HA-}$ can act as acid or base:

$$ \begin{align} \ce{H2A &<=> AH- + H+}\\ \ce{HA- &<=> A^2- + H+} \end{align} $$

The $\mathrm{pH}$ of the solution can be estimated as

$$\mathrm{pH} = \frac{\mathrm{p}K_\mathrm{a1} + \mathrm{p}K_\mathrm{a2}}{2}$$

My question is how accurate this estimate is, depending

1. on concentration of the amphiprotic salt (as the concentration approaches zero, the $\mathrm{pH}$ should approach 7),
2. on the average of the $\mathrm{p}K_\mathrm{a}$ values (the closer these are to neutral, the smaller the difference between $[\ce{H2A}]$ and $[\ce{A^2-}]$), and
3. on the difference between the $\mathrm{p}K_\mathrm{a}$ values (the bigger the difference, the lower the percentage of $\ce{NaHA}$ undergoing acid or base reactions).

So depending on these three variables, how accurate is the estimate? My guess is that high concentration, average of $\mathrm{p}K_\mathrm{a}$ near neutral and difference between $\mathrm{p}K_\mathrm{a}$ low would give good estimates. When any of these parameters a very different from those "ideal" conditions, the estimate probably gets worse.