I am proud to say that I never taken a statistics course in my entire life, and I have never intentionally studied it. Why? Because I hate how statistics tries to mascarade as if it is a real math subject while it is not.
Does statistics use math? Of course. But so does string physics and quantum field theory. And so does electrical engineering. But we all understand that modern physics uses mathematical concepts, very often quite advanced mathematical concepts, to solve problems related to physics, and we understand string physics to be physics, and not math just because it heavily uses math. (By the way, the math used in modern physics is actually interesting unlike the math used in boring statistics).
Statistics is a science for collecting and interpreting numerical information. Just because it uses calculus and probability theory does not suddenly transform it into a math discipline.
Many statisticians like to identify statistics with probability theory as if they are one and the same. No, this is false. Probability theory is a real branch of mathematics. In fact, till the 1920's most mathematicians did not even acknowledge probability theory as a legitimate branch of mathematics. It was the work of Soviet mathematicians, mostly that of Kolomogrov, who were able to built probability theory on a solid mathematical foundation. And since that time probability theory has been accepted as a legitimate branch of mathematics.
But this legitimacy problem has never been addressed in statistics. All what statisticians do is collect numbers, draw them on various charts and graphs, and then attempt to make predictions about them. Which is why doing this is a science.
The sad thing is that the course I am teaching this semester has a little bit of statistics in it, near the end of the semester. But I hope to skip over that if I could. I really do not want to go through the pain of teaching how to draw a histogram or a pie chart. I rather have more fun time working on probability problems.