  We investigate the standard deviation $\delta v(\tsamp)$ of the variance
$v[\xbf]$ of time series $\xbf$ measured over a finite sampling time $\tsamp$
focusing on non-ergodic systems where independent "configurations" $c$ get
trapped in meta-basins of a generalized phase space. It is thus relevant in
which order averages over the configurations $c$ and over time series $k$ of a
configuration $c$ are performed. Three variances of $v[\xbf_{ck}]$ must be
distinguished: the total variance $\dvtot = \dvint + \dvext$ and its
contributions $\dvint$, the typical internal variance within the meta-basins,
and $\dvext$, characterizing the dispersion between the different basins. We
discuss simplifications for physical systems where the stochastic variable
$x(t)$ is due to a density field averaged over a large system volume $V$. The
relations are illustrated for the shear-stress fluctuations in quenched elastic
networks and low-temperature glasses formed by polydisperse particles and
free-standing polymer films. The different statistics of $\svint$ and $\svext$
are manifested by their different system-size dependence
