  The readings of a highly inaccurate "weak" quantum meter, employed to
determine the value of a dichotomous variable $S$ without destroying the
interference between the alternatives,may take arbitrary values. We show that
the expected values of its readings may take any real value, depending on the
the choice of the states in which the system is pre- and post-selected. Some of
these values must fall outside the range of eigenvalues of $A$, in which case
they may be expressed as "anomalous" averages obtained with negative
probability weights, constructed from available probability amplitudes. This
behaviour is a natural consequence of the Uncertainty Principle.
  The phenomenon of "anomalous weak values" has no non-trivial analogue in
classical statistics.
