Jeesh, that data is aggravating. Here’s a run down of what percentile rank is: If you are at a 50% percentile, you are in the middle of the normal distribution of scores. So, it would make sense that public schools would be at the 50th percentile since the sample size is so large, it’s really a cross-section of the general population. Even if every public school child started performing exceptionally well on standardized tests, their aggregated scores would still turn up in the 50th percentile. The bell curve doesn’t change when the scores do. Homeschoolers represent a much smaller population whose scores will look differently on the frequency distribution. Also, as it clearly shows in the data, education (and presumably income, since those things are correlated) is disproportionately high among parents of homeschoolers, so it’s likely you will see higher percentiles on standardized tests when compared to the general population. A more accurate representation would be to compare public school students and homeschooled students of similar educational backgrounds and socioeconomic status. So, in other words, apples to oranges.