http://www.hslda.org/docs/nche/000010/200410250.asp"1. In 1997, a study of 5,402 homeschool students from 1,657 families was released. It was entitled, "Strengths of Their Own: Home Schoolers Across America." The study demonstrated that homeschoolers, on the average, out-performed their counterparts in the public schools by 30 to 37 percentile points in all subjects. A significant finding when analyzing the data for 8th graders was the evidence that homeschoolers who are homeschooled two or more years score substantially higher than students who have been homeschooled one year or less. The new homeschoolers were scoring on the average in the 59th percentile compared to students homeschooled the last two or more years who scored between 86th and 92nd percentile. "
I think in general that this is really only because the parents care more. Homeschooling takes serious effort, and most homeschooling parents are quite dedicated. There are exceptions.
And let's face it, none of the material being taught in school is any harder than what you took in school, in fact I would say quite the opposite.