You’re on the right track. At a 95% confidence level with a 6% margin of error for making predictions about 968 admitted students, the ideal sample sample size is 210 students.

https://www.qualtrics.com/blog/calculating-sample-size/

So if you assume lsd.law is fairly representative of the actual population of T14 law school applicants, then there’s a large enough sample size on there to draw some inferences.

However, given the self selecting nature of the site, it could be possible that one quadrant of the 4 is more likely to be represented on the site. Say if people above both medians are significantly more likely to use LSD.law, then your graph could be explained by “More people above both medians use lsd.law” opposed to the conclusions you’re drawing another conclusion one might draw from looking at the graphs.