High-school senior that is highly curious.
Most PhD programs don’t publish their admissions rates. Of the ones that do, the lowest number I’ve seen is around 5% (Stanford’s PhD in economics program) and the highest one I’ve seen is around 20%. I’d imagine that most PhD programs have admissions rates in that range.
However, do note that admissions rates for PhD programs have to be read differently than undergrad programs, and because of that they don’t matter as much.
Some fields simply attract more PhD applicants than others. The humanities, for example, produce a surplus of PhDs every year. Math and computer science fields produce fewer, likely because it’s pretty easy to get a good job with a BA or MA in those fields. So the acceptance rates to statistics programs may seem higher - almost deceptively - simply because there are fewer people competing for slots.
That said, acceptance rate kind of doesn’t matter for PhD programs, because so much of what counts for admissions is holistic and quite nebulous. All kinds of factors go in - things that come from you like your letters of recommendation, your past research experience, your research interests and fit with the department, but also things that come from the department like who’s taking students, who’s retiring/taking sabbatical the next year, yield management, etc. For example, the year I entered my PhD program the program unexpectedly had a much higher yield than they anticipated (yay, recession!) so there were 12 people in my cohort, which is about twice the size of a normal PhD cohort in my department. So next year, the program admitted fewer people to ensure they brought in a smaller cohort, which probably artificially depressed the acceptance rate that year and made it more difficult for people to get in! A person who may have been admitted in the year I applied might have been rejected the following year.
Furthermore, just because the acceptance rate is low doesn’t mean anything for individual students. A superstar with an outstanding application package will have a good shot even at programs in the 5-10% range. Meanwhile, a student without the requisite experience would have a difficult time getting admitted even to PhD programs with 20%+ acceptance rates.
I say this because I’ve seen students who are prepping for PhD programs spend a lot of time trying to track down acceptance rates for individual programs or find out stats for recently accepted students, and honestly I don’t think that’s time well spent. Instead, when you get to college, talk to your professors in the math/stats department about your performance and competitiveness as a student. That’s a far better gauge as to where you should apply than random bits of information you can dig up. (Knowing the average GPA and GRE scores of a place might be mildly helpful, but even then, you can have one or two “off” pieces of an otherwise outstanding package and still get in. For example, my undergrad GPA was a 3.42, but my major GPA was a 3.67 and I had an otherwise great package and great fit with my department.)
One last thing. I think planning ahead is good - I’m a planner, and I decided I wanted a PhD in my freshman or sophomore year of college (my mom says it started even earlier, which I don’t remember). I finished mine in 2014, so I made that goal come true.
However, I do urge you to consider whether or not you actually need a PhD, because it’s a pretty big sacrifice of time and potential money. While I won’t say I regret doing a PhD, I think that with the benefit of hindsight I may not have done one - I wasn’t aware how many research careers in my field one could have with a master’s (and even how many research-related jobs there were that I could’ve done with a BA!) and how many there were outside of academia and the public sector. So, explore some careers and do some internships in college. Even if you do end up getting a PhD, it’ll still be good because you’ll have some idea of where you could go if you wanted a non-academic career, or if you decided to drop out of your PhD program.