qgis - How to get the altitude of the vector shapes from DTM raster layer?

I have a vector layer containing thousands of vector shapes/polygons and a raster layer with DTM. Every shape has its own OBJECTID in attribute table. I would like to get the altitude of every shape, weighted mean of the altitude would be the best. I suppose there should be used a script or something similar to count weighted mean of altitude of all pixels inside the polygon. I use Qgis 1.7.3.

Thanks in advance.