  We propose a direct measure of tripartite quantum correlation in an arbitrary
symmetric pure state of N correlated two-level atoms (qubits). We compute the
third order moments of the collective pseudo-spin operators in terms of the
individual atomic operators of the atoms in the assembly and find that all the
bipartite quantum correlation terms among the atoms cancel out leaving only the
all possible tripartite quantum correlation terms among them. We observe that
the third order moments are made up of solely the tripartite quantum
correlations among the atoms. This helps to extract out only the tripartite
quantum correlations among the N atoms and propose a measure and quantification
of these correlations. We also propose the necessary and sufficient condition
for the presence of tripartite quantum correlation in such multi-atomic
systems. We conjecture the way of determining the third order moments of the
pseudo-spin operators of the two-level atoms in the assembly, experimentally.
