A vast majority of graduate students are not from low income backgrounds. Graduate students by definition already have a college degree, and statistically college graduates come from families that make substantially more than he average income.
You're making a poor assumption however. The college graduates that go on to pursue a graduate degree are not randomly selected.
Sure. But aren't they even more likely to be well-off? Are people who can afford to forgo getting a job for 4-5 years after getting their college degree more or less likely to be from a lower-income household?
I'm not certain, but to offer a counter argument, aren't the more wealthy students likely to be content to get a Bachelor's degree of an MBA and move into the workplace? Possibly using their connections to supplement their other qualifications?
What is the poor assumption that s/he is making?
Sorry to clarify, the poor assumption is that the fact that the people going to college being generally wealthier means that the people going to graduate school are generally wealthier. A uniform randomness would be required to determine which students choose to continue advancing which is not the case as those choosing to pursue a graduate degree are being influenced by other factors - how fast they need to begin acquiring income, how lucrative they think immediate employment may be, interests...