In this work, we present a measure of quantum correlation for a multipartite system, defined as the sum of the correlations for all possible partitions. Our measure can be defined for quantum discord (QD), geometric quantum discord or even for entanglement of formation (EOF). For tripartite pure states, we show that the multipartite measures for the QD and the EOF are equivalent, which allows direct comparison of the distribution and the robustness of these correlations in open quantum systems. We study dissipative dynamics for two distinct families of entanglement: a W state and a GHZ state. We show that, for the W state, the QD is more robust than the entanglement, while for the GHZ state, this is not true. It turns out that the initial genuine multipartite entanglement present in the GHZ state makes the EOF more robust than the QD.