Maybe homeschoolers aren't interested in Princeton. ;)
Seriously, though, education is not a contest and we don't need to compare success with admission standards. Colleges are beginning to recognize the quality that home schooling can give to students, and many are revising their standards to make themselves more attractive to these kids. Homeschoolers are now being sought out by some colleges, maybe not in the % that they "should" but I am not big on % or "shoulds." Kids who get a good home education have the world open to them. They aren't forced into the traditional tracks. Many go on to work or apprenticeships or even starting their own businesses. Some take time to travel and explore their options. Many start college while still in high school and would show up as transfer students rather than as freshmen. Also, some home schoolers are registered under public school programs or private schools. In CA, all indepedent home schools are private schools, and you don't have to declare yourself as a home schooler. They would show up in the private school %. Some kids homeschool for only a part of their education, and might finish only the last few years in a public program. So I bet there are a lot more than just 2%.
Sure, I'll bite. First off, Princeton is probably much smaller than you realize. It'd be tough to get statistical accuracy on that 2%. That 2% probably amounts to about a dozen students, believe it or not. Princeton's pretty small. I'm a product of a public school and I teach in a public school. I've taught in a Christian school before as well, and I have friends who have home-schooled. My daughter is one of my students, currently a junior, and is considering Princeton since it has a chemical engineering major. The numbers you throw out there sound realistic. The 30% private schools is a very large percentage, but many of the "prep schools" specifically prepare students for IV league schools, so that number shouldn't be surprising. Those students would have high SAT scores (Princeton doesn't use ACT). It also doesn't surprise me that homeschoolers make up 2%. As I said before, there is probably a good deal of statistical slop in that number, but at any rate, some home schoolers are exceptionally bright and receive fantastic educations. I'm sure some score brilliantly on the SAT. Others get a great education at what they're exposed to but aren't exposed to a lot of variety. Still others receive a pathetic education. It runs the gamut. As far as 9% religiously based, they're basically private schools and some are getting great educations and have parents driven to demand educational excellence. That number sounds fair. Here's the thing, though......MOST of Princeton's students are products of public schools. That says to me, underrepresentation or not, that people driven to strive in the public schools still have plenty of room to succeed. Which is good news for the poor folks like me.
From what I understand, schools like Harvard, Yale and Princeton, consider many factors that are out of the child's control like whether the parents attended college there and the quality of the child's high school. I mean that is out of your control if you are a high school student and your parent did not attend there and you are attending a not very high quality high school. Most of the high schools in my state are not very good (our state is rated about 45th or so in quality), so you lose admission points for that. I think it is probably better overall to be a homeschooler than to be attending a low-quality high school (and the schools in our town are rated Ds in quality by the state so that is probably true in our case). But if you have wonderful schools in your area then you have a different situation.
Some of the admissions policy for those colleges are so unfair, that it is almost unrealistic I think to expect to attend those colleges. But I guess for the 1800 or so that do attend in that class, they are guaranteed wonderful jobs afterward so it is great for them. But I feel sorry for the 17,000 or whatever that don't make it; I hope they do have realistic expectations when they apply! And they probably will still get accepted into perfectly fine colleges and will get perfectly acceptable jobs!
Yeah, but homeschoolers are fairly represented. That is AWESOME! Public schoolers will always be underrepresented at top schools because public schools were never designed to thoroughly educate ALL their students (unlike homeschools & most other private schools). John Gatto has a great discussion of this in "The Underground History of American Education".