  We show that with respect to the q-Plancherel measure on partitions of size
n, the irreducible characters of an Hecke algebra $H_q(S_n)$ are concentrated
around the normalized trace of $H_q(S_n)$. More precisely, we prove that the
deviations of the values of the q-characters $\chi^\lambda_q$ are
asymptotically gaussian, and we give an explicit formula for the covariances of
the limit normal laws (the other results were already in arXiv:1001.2180). Our
proof involves Sniady's theory of cumulants of observables of diagrams and a
M\"obius inversion formula for additive class functions on symmetric groups.
