A finite element 3D polycrystalline aggregate made of 216 grains is subjected to a mean axial deformation up to 1%. The heterogeneities inside the polycrystal are due to the crystallographic orientations of the grains - this appears at the scale of the mean responses per grain - and to the local interaction between neighbouring grains - this appears at the intragranular scale. The intragranular heterogeneity is measured as a function of the distance to the grain boundary, inside a single grain and for all the points of the microstructure. It is characterized by dispersions of the local responses due to grain boundaries. These measurements correspond to dispersions - variances -; the statistical errors have also been determined.