I want to know what makes you conclude the second point? Particularly the second half.
Besides, what does ‘scores’ on your x-axis include? histogram does present their causality…
Anyway, I think whatever your kids have, they will be fine… More attention from you would be better than private school…
If you can afford private without compromising your time with them, going private can be a good idea… Since you showed that lower tail of private is still better than public (if this is justifiable).
But if you need to sacrifice your time with them in order to get enough money for private, I don’t think it’s worthy doing so.