I'm from the US, and have no idea why rich/poor entered this discussion. My parents were very poor, but reasonably educated. I never picked up on any hint of a correlation between wealth and good grades.
HOWEVER, I saw an enormous correlation between wealth and going to university.
I also belong to the poor-but-educated-parents so I know what you're saying. I would assume the explanation for people with poor parents doing worse is because the parents have less time to be involved. But if you want to know more there are numerous studies. :)
HOWEVER, I saw an enormous correlation between wealth and going to university.