  We have calculated the Tsallis entropy and Fisher information matrix
(entropy) of spatially-correlated nonextensive systems, by using an analytic
non-Gaussian distribution obtained by the maximum entropy method. Effects of
the correlated variability on the Fisher information matrix are shown to be
different from those on the Tsallis entropy. The Fisher information is
increased (decreased) by a positive (negative) correlation, whereas the Tsallis
entropy is decreased with increasing an absolute magnitude of the correlation
independently of its sign. This fact arises from the difference in their
characteristics. It implies from the Cram\'{e}r-Rao inequality that the
accuracy of unbiased estimate of fluctuation is improved by the negative
correlation. A critical comparison is made between the present study and
previous ones employing the Gaussian approximation for the correlated
variability due to multiplicative noise.
