Extropy, as a complementary dual of entropy, has been discussed in many works of literature, where it is declared for other measures as an extension of extropy. In this article, we obtain the extropy of generalized order statistics via its dual and give some examples from well‐known distributions. Furthermore, we study the residual and past extropy for such models. On the other hand, based on Farlie–Gumbel–Morgenstern distribution, we consider the residual extropy of concomitants of m‐generalized order statistics and present this measure with some additional features. In addition, we provide the upper bound and stochastic orders of it. Finally, nonparametric estimation of the residual extropy of concomitants of m‐generalized order statistics is included using simulated and real data connected with COVID‐19 virus.