I wonder how much statistics someone can understand without calculus. For example, how do you explain what a continuous probability density function (such as the Gaussian) is without calculus?
I teach introductory quantitative research methods to communication undergrads, most of whom have no calculus. (Which is essentially optional in the UK as it's taught at A Level after most students have specialised away from maths).
They don't seem to have a problem intuiting what a plotted PDF is showing. I think that's because in some sense it can be read analogously to a histogram. Of course, they don't have the tools to generate or manipulate one. But that's honestly not something that applied social science researchers have to do often when using traditional methods.
