  In this article we present very intuitive, easy to follow, yet mathematically
rigorous, approach to the so called data fitting process. Rather than
minimizing the distance between measured and simulated data points, we prefer
to find such an area in searched parameters' space that generates simulated
curve crossing as many acquired experimental points as possible, but at least
half of them. Such a task is pretty easy to attack with interval calculations.
The problem is, however, that interval calculations operate on guaranteed
intervals, that is on pairs of numbers determining minimal and maximal values
of measured quantity while in vast majority of cases our measured quantities
are expressed rather as a pair of two other numbers: the average value and its
standard deviation. Here we propose the combination of interval calculus with
basic notions from probability and statistics. This approach makes possible to
obtain the results in familiar form as reliable values of searched parameters,
their standard deviations, and their correlations as well. There are no
assumptions concerning the probability density distributions of experimental
values besides the obvious one that their variances are finite. Neither the
symmetry of uncertainties of experimental distributions is required (assumed)
nor those uncertainties have to be `small.' As a side effect, outliers are
quietly and safely ignored, even if numerous.
