100% agreed. I always found statistics to be a bunch of weird maths that did… something? But not for reasons anyone could explain to me, just memorise the formula.
Then someone explained to me that statistics is about determining the likelihood that a model corresponds to reality. So you need to have a model and you need to have some experiment, and you’re trying to make sure that the experiment samples enough of the space that each new sample can (ideally) eliminate some alternative models and give confidence to your model.
And, once I understood that, a bunch of statistical techniques made sense because they’re just trivial applications of probability. And those weird formulae are just reusable partial applications, like the quadratic equation formula that is just the result of completing the square on a quadratic where all of the variables are symbolic.