  The sky-RMS is the simplest model-independent characterization of a
cosmological anisotropy signal. The RMS temperature fluctuations determined
from the $COBE$-DMR four-year sky maps are frequency independent, consistent
with the hypothesis that they are cosmological in origin, with a typical
amplitude at 7 degrees of ~ 35 \pm\ 2 uK and at 10 degrees of ~29 \pm\ 1 uK. A
joint analysis of the 7 deg and 10 deg "cross"-RMS derived from the data in
both Galactic and Ecliptic coordinates is used to determine the RMS quadrupole
normalization, $Q_{rms-PS}$, for a scale-invariant Harrison-Zel'dovich power
law model. The difference in the inferred normalizations either including or
excluding the quadrupole is a consequence of the sensitivity of the method to
the Galaxy contaminated observed sky quadrupole. Whilst there are variations
depending on the data selection, all results are consistent with an inferred
\qrms\ normalization of ~18 \pm\ 2 uK.
