  A modified definition of quantum mechanical uncertainty D for spin systems,
which is invariant under the action of SU(2), is suggested. Its range is shown
to be h^2j<D<h^2j(j+1) within any irreducible representation j of SU(2) and its
mean value in Hilbert space computed using the Fubini-Study metric is
determined to be mean(D)=h^2j(j+1/2). The most used sets of coherent states in
spin systems coincide with the set of minimum D uncertainty states.
