I already love this essay because I've been saying the same thing for years, and he even mentions "statistics and discrete mathematics" as something we should be doing more of; in short, calculus is useful for physicists and engineers, primarily, whereas statistics and discrete mathematics, properly taught and motivated, are useful for everybody.
For example, if there's a certain probability of people with cancer getting a positive test result, what's the probability of a positive test result meaning you have cancer? Too many people absolutely cannot approach that problem in any intelligent fashion.
(Side note: More classes should accept "there isn't enough information to give a coherent answer" as a correct result.)
You will need calculus for any non-trivial statistics though, unless you want statistics distilled into cook book style pre-canned formulas and recipes. Those are fine when you are dealing with a situation that has been anticipated 'just so'.
> You will need calculus for any non-trivial statistics though, unless you want statistics distilled into cook book style pre-canned formulas and recipes.
It's a matter of focus: The point isn't to derive statistics, any more than the point of a first semester course on differential calculus is to derive the real numbers and the infinitesimals. Calculus isn't useless, it's just not as useful unless you go into specific fields.
Statistical distributions and methods were all designed by humans for a particular purpose. If you understand calculus, you can start with a statement of the desired goal, and then work backwards to derive the formulas you need. The final form you get then makes sense, and you have some ownership of it. In a pinch you can re-derive it for yourself, but even if you look it up in a book you understand what the parts mean.
If you don’t know calculus, someone has to tell you the formulas, which will seem like mysterious completely arbitrary magic. Memorizing them will be a pain in the butt. When you try to use statistics you will make small mistakes which will lead to wrong or even entirely incoherent results, but you won’t notice because you’re just following a recipe you don’t understand.
Of course, to do real statistics you need linear algebra as well.
For example, if there's a certain probability of people with cancer getting a positive test result, what's the probability of a positive test result meaning you have cancer? Too many people absolutely cannot approach that problem in any intelligent fashion.
(Side note: More classes should accept "there isn't enough information to give a coherent answer" as a correct result.)