"In a landmark U.S. national study, Rudner (1999) administered academic achievement tests to 20,760 primary and secondary homeschooled students. Results showed that homeschooled students’ achievement-test scores were significantly higher than those of their public- and private-school counterparts. Furthermore, Clemente (2006) conducted a study to determine if there was a statistically significant difference in the college aptitude of homeschooled high school seniors compared to traditionally schooled students who subsequently attended Christian colleges. Clemente’s results indicated that the homeschooled students’ mean test score on the SAT (including verbal and mathematics sections) was 1123, whereas private- and public-school students averaged 1054 and 1039, respectively."

The researchers noted that there hadn't been much study on the performance of homeschooled kids in college, so they conducted their own study. They found that "Similar to ACT composite scores, the mean SAT total score of Catholic-schooled students (1761.04) was found to be slightly lower than the total mean (1779.36). Moreover, the mean SAT total score of public-schooled students (1706.76) was found to be the lowest, and the mean SAT total score of homeschooled students (1864.94) was found to be the highest...Forty-two students were public schooled, 54 were Catholic schooled, and 68 were homeschooled...The mean major GPA of Catholic-schooled students (3.12) was still found to be slightly lower than the total mean (3.14). Moreover, the mean major GPA of public-schooled students (3.07) was found to be the lowest, and the mean major GPA of homeschooled students (3.20) was found to be the highest..."

https://files.eric.ed.gov/fulltext/EJ1005657.pdf

Though it should be noted that this study does not control for economic class or ethnicity, which may influence the results. It is possible that those who homeschool their kids come from more economically advantageous backgrounds. However, I still found the results to be surprising.