  In this paper we define a Grassmann odd analogue of Jacobi structure on a
supermanifold. The basic properties are explored. The construction of odd
Jacobi manifolds is then used to reexamine the notion of a Jacobi algebroid. It
is shown that Jacobi algebroids can be understood in terms of a kind of curved
Q-manifold, which we will refer to as a quasi Q-manifold.
