  A generalized definition of average, termed the q-average, is widely employed
in the field of nonextensive statistical mechanics. Recently, it has however
been pointed out that such an average value may behave unphysical under
specific deformations of probability distributions. Here, the following three
issues are discussed and clarified. Firstly, the deformations considered are
physical and may experimentally be realized. Secondly, in view of
thermostatistics, the q-average is unstable in both finite and infinite
discrete systems. Thirdly, a naive generalization of the discussion to
continuous systems misses a point, and a norm better than the $L^1$-norm should
be employed for measuring the distance between two probability distributions.
Consequently, stability of the q-average is shown not to be established in all
the cases.
