Frequently in physics one comes across situations where quenched randomness plays an important role. Any physical property X of such a system, would require an averaging over all disorder realisations. The system can be completely described by the average [ X ] where [...] denotes averaging over realisations (“averaging over samples”) provided the relative variance R X = V X / [ X ] → 0 as N →∞, where V X = [ X ] − [ X ] and N denotes the size of the realisation. In such a scenario a single large system is sufficient to represent the whole ensemble. Such quantities are called self-averaging. Away from criticality, when the larger lattice is built from smaller blocks, then due to the additivity property of an extensive quantity, the central limit theorem guarantees that R X ~ N thereby ensuring self-averaging. On the other hand, at the critical point, the question whether X is self-averaging or not becomes nontrivial, due to long range correlations.