  We construct a multi-observable uncertainty equality as well as an inequality
based on the sum of standard deviations in the qubit system. The obtained
equality indicates that the uncertainty relation can be expressed more
accurately, and also can be used to detect the mixedness of the system.
Meanwhile, the new uncertainty inequality can provide a tighter lower bound,
and the tightness can be maintained at a high level even in an open system.
Furthermore, the deficiency of the uncertainty relation, that the lower bound
of the product form uncertainty relations can be null even for two incompatible
observables, can be completely fixed by the new uncertainty relation.
