  We consider the inverse Calder\'on problem consisting of determining the
conductivity inside a medium by electrical measurements on its surface.
Ideally, these measurements determine the Dirichlet-to-Neumann map and,
therefore, one usually assumes the data to be given by such map. This situation
corresponds to having access to infinite-precision measurements, which is
totally unrealistic. In this paper, we study the Calder\'on problem assuming
the data to contain measurement errors and provide formulas to reconstruct the
conductivity and its normal derivative on the surface. Additionally, we state
the rate convergence of the method. Our approach is theoretical and has a
stochastic flavour.
