  In this paper, we establish a truncated non-integrated defect relation for
meromorphic mappings from a complete K\"ahler manifold into a projective
variety intersecting a family of hypersurfaces located in subgeneral position,
where the truncation level of the defect is explicitly estimated. Our result
generalizes and improves previous ones. In particular, when the family of
hypersurfaces located in general position, our theorem will implies the
previous result of Min Ru-Sogome. In the last part of this paper we will apply
ours to study the distribution of the Gauss map of minimal surfaces.
