  We investigate the notion of uncertainty region using the variance based sum
uncertainty relation for qubits and qutrits.We compare uncertainty region of
the qubit (a 2-level system) with that of the qutrit (3-level system) by
considering sum uncertainty relation for two non-commuting Pauli-like
observables, acting on the two dimensional qubit Hilbert space. We identify
that physically valid uncertainty region of a qubit is smaller than that of a
qutrit. This implies that an enhanced precision can be achieved in the
measurement of incompatible Pauli-like observables acting on the 2-dimensional
subspace of a qutrit Hilbert space. We discuss the implication of the reduced
uncertainties in the steady states of Lambda, V and Cascade types of 3-level
atomic systems. Furthermore, we construct a two-qubit permutation symmetric
state, corresponding to a 3-level system and show that the reduction in the sum
uncertainty value -- or equivalently, increased uncertainty region of a qutrit
system { is a consequence of quantum entanglement in the two-qubit system. Our
results suggest that uncertainty region can be used as a dimensional witness.
