  This paper tackles challenges in pricing and revenue projections due to
consumer uncertainty. We propose a novel data-based approach for firms facing
unknown consumer type distributions. Unlike existing methods, we assume firms
only observe a finite sample of consumers' types. We introduce
\emph{empirically optimal mechanisms}, a simple and intuitive class of
sample-based mechanisms with strong finite-sample revenue guarantees.
Furthermore, we leverage our results to develop a toolkit for statistical
inference on profits. Our approach allows to reliably estimate the profits
associated for any particular mechanism, to construct confidence intervals, and
to, more generally, conduct valid hypothesis testing.
