  In this paper we have considered a difference of Jensen's inequality for
convex functions and proved some of its properties. In particular, we have
obtained results for Csisz\'{a}r \cite{csi1} $f-$divergence. A result is
established that allow us to compare two measures under certain conditions. By
the application of this result we have obtained a new inequality for the well
known means such as arithmetic, geometric and harmonic. Some divergence
measures based on these means are also defined.
