  Randomized measurements constitute a simple measurement primitive that
exploits the information encoded in the outcome statistics of samples of local
quantum measurements defined through randomly selected bases. In this work we
exploit the potential of randomized measurements in order to probe the amount
of entanglement contained in multiparticle quantum systems as quantified by the
multiparticle concurrence. We further present a detailed statistical analysis
of the underlying measurement resources required for a confident estimation of
the introduced quantifiers using analytical tools from the theory of random
matrices. The introduced framework is demonstrated by a series of numerical
experiments analyzing the concurrence of typical multiparticle entangled states
as well as of ensembles of output states produced by random quantum circuits.
Finally, we examine the multiparticle entanglement of mixed states produced by
noisy quantum circuits consisting of single- and two-qubit gates with
non-vanishing depolarization errors, thus showing that our framework is
directly applicable in the noisy intermediate-scale regime.
