Your articles and statistics always talk about averages. That means California's sewage dump is averaged with schools where every kid goes to college and many on scholarships. Many years ago, the NAEP showed a significant drop in the average test scores. Guess where one of the high schools they used was located? Baltimore MD. That one school was so bad it dropped the nationwide average.
Let me ask you something, if I gave you a math test right now, and told you just to do your best, how well do you think you would do? Now, let's say I tell you that in two weeks, I am going to give you a test on math you should know from high school, and I'll give you $5 for every one of the 100 questions you get correct, would you study up, or just take your chances.
When I was teaching, grades were calculated of four quarters of work averaged with a final exam, meaning the final was worth 20% of the grade. I made the final out of tests from all 4 grading periods during the year, so I knew they should know the material. I probably had a passing rate of about 20%. Why, you ask? The kids knew they had already passed, and the final would likely only mean a letter grade difference in their grade for the year, so they didn't give a shit!
The same thing goes for tests like the ACT. All juniors were required to take the test at the end of the year, no matter what. the grades were used for school accountability, to see if our children learned anything. Because that was the only incentive, most students either "Christmas-treed" their answers or simply took a nap for that testing session. They had zero incentive to do well on any part of the test. Homeschoolers like to compare their kids to public school student's scores and claim their kids did better, when public school students are required, whether they are going to college or not. If a parent feels their homeschooler will do poorly or isn't going to college, they simply don't take the test.
The few homeschoolers that took the test were motivated to do well, while public school students rally didn't give a rat's ass. How do you think that impacted the comparison?