Home-schooling is an industry in itself, with prepared materials and curricula for parents to follow while teaching their children. The results are pretty easy to find as many studies have been done that have conclusively demonstrated the advantages of homeschooling by comparing achievement in quantitative studies, here a write up from The Washington Time that is very informative: http://www.washingtontimes.com/news/2009/aug/30/home-schooling-outstanding-results-national-tests/ - especially the quote "Five areas of academic pursuit were measured. In reading, the average home-schooler scored at the 89th percentile; language, 84th percentile; math, 84th percentile; science, 86th percentile; and social studies, 84th percentile. In the core studies (reading, language and math), the average home-schooler scored at the 88th percentile.

The average public school student taking these standardized tests scored at the 50th percentile in each subject area. "