In this paper, we introduce a notion of mean on irreducible symmetric cones, based on the product decomposition between the determinant one hypersurface and the determinant. Irreducible symmetric cones and their determinant on surfaces form an important class of spaces for statistics and data science, since they encompass positive definite self-adjoint operators as well as Lorentz cones and hyperbolic spaces. By construction, log-extrinsic means have similar equivariance properties as those of the Fr\'echet means. Moreover, the two means coincide under some symmetry assumption on the distribution. However, the log-extrinsic mean admits an explicit expression and is much simpler to compute. Numerical experiments show that the log-extrinsic means are a relevant alternative to log-Euclidean means. Furthermore, along with the log-extrinsic mean, we introduce a corresponding notion of Gaussian distributions, called log-extrinsic Gaussians. A classification experiment on stereo audio signals demonstrates the practical interest of the log-extrinsic framework.