  We present a versatile inequality of uncertainty relations which are useful
when one approximates an observable and/or estimates a physical parameter based
on the measurement of another observable. It is shown that the optimal choice
for proxy functions used for the approximation is given by Aharonov's weak
value, which also determines the classical Fisher information in parameter
estimation, turning our inequality into the genuine Cram{\'e}r-Rao inequality.
Since the standard form of the uncertainty relation arises as a special case of
our inequality, and since the parameter estimation is available as well, our
inequality can treat both the position-momentum and the time-energy relations
in one framework albeit handled differently.
