  In quantum physics, all measured observables are subject to statistical
uncertainties, which arise from the quantum nature as well as the experimental
technique. We consider the statistical uncertainty of the so-called sampling
method, in which one estimates the expectation value of a given observable by
empirical means of suitable pattern functions. We show that if the observable
can be written as a function of a single directly measurable operator, the
variance of the estimate from the sampling method equals to the quantum
mechanical one. In this sense, we say that the estimate is on the quantum
mechanical level of uncertainty. In contrast, if the observable depends on
non-commuting operators, e.g. different quadratures, the quantum mechanical
level of uncertainty is not achieved. The impact of the results on quantum
tomography is discussed, and different approaches to quantum tomographic
measurements are compared. It is shown explicitly for the estimation of
quasiprobabilities of a quantum state, that balanced homodyne tomography does
not operate on the quantum mechanical level of uncertainty, while the
unbalanced homodyne detection does.
