Thank you. I mean randomly dropped, for example poured using another bucket. Or another example maybe if using a computer you randomly generated the position of the particles in mid-air in a volume (with walls i.e. bucket), then you let the spheres settle (according to gravity), and began shaking.
This might be helpful: http://en.wikipedia.org/wiki/Kepler_conjecture "Experiment shows that dropping the spheres in randomly will achieve a density of around 65%". I think how much they settle down would depend on the size of the balls and the diameter of the bucket.