  Redundancy of experimental data is the basic statistic from which the
complexity of a natural phenomenon and the proper number of experiments needed
for its exploration can be estimated. The redundancy is expressed by the
entropy of information pertaining to the probability density function of
experimental variables. Since the calculation of entropy is inconvenient due to
integration over a range of variables, an approximate expression for redundancy
is derived that includes only a sum over the set of experimental data about
these variables. The approximation makes feasible an efficient estimation of
the redundancy of data along with the related experimental information and
information cost function. From the experimental information the complexity of
the phenomenon can be simply estimated, while the proper number of experiments
needed for its exploration can be determined from the minimum of the cost
function. The performance of the approximate estimation of these statistics is
demonstrated on two-dimensional normally distributed random data.
