  A numerical illustration of a universally valid Heisenberg uncertainty
relation, which was proposed recently, is presented by using the experimental
data on spin-measurements by J. Erhart, et al.[ Nature Phys. {\bf 8}, 185
(2012)]. This uncertainty relation is closely related to a modified form of the
Arthurs-Kelly uncertainty relation which is also tested by the
spin-measurements. The universally valid Heisenberg uncertainty relation always
holds, but both the modified Arthurs-Kelly uncertainty relation and
Heisenberg's error-disturbance relation proposed by Ozawa, which was analyzed
in the original experiment, fail in the present context of spin-measurements,
and the cause of their failure is identified with the assumptions of unbiased
measurement and disturbance. It is also shown that all the universally valid
uncertainty relations are derived from Robertson's relation and thus the
essence of the uncertainty relation is exhausted by Robertson's relation as is
widely accepted.
