Executive summary: Apparently unrelated personal preferences may guide the difficult choice between calculus and statistics.
Explore your limits or take your chances. Neither is comforting advice when faced with a tough decision. Yet these are the options that about a million students are given each year in the US as they grapple with a notorious choice: calculus or statistics?
If you like explosions, you’ll love the stats on AP Stats. Since AP Statistics was introduced 25 years ago, its enrollment has grown to surpass Calc BC’s by 50%, and another 50% surge in the years ahead will likely take it past Calc AB’s. For homework, run the numbers, and you’ll see this is a significant rate of change! Meanwhile calculus courses remain a steady staple at high schools, colleges and universities, with maybe three-quarters of a million Americans taking some type of calculus class at any given time.
Will my later career
really be enhanced by the choice I make today?
Partly because statistics is perceived as a replacement (an easier alternative?) for calculus, and partly to keep the cognitive load under control, few students take both calculus and statistics, and fewer still take both simultaneously. This is a pity, because the two disciplines are (or at least should be) intertwined. Statistics without calculus is somewhat elementary, austere and simplistic. Maybe that’s the idea!
There’s a lot of great, expert advice available online about choosing between calculus and statistics, including very helpful insights from professional mathematicians and brilliant university educators for whom I have tremendous respect. I would recommend anyone faced with this choice to dip into some of these writings, as they are offered by strong intellectuals with profound personal experience of both subjects.
The treatments I have found seem to dwell on three main angles.
Firstly, almost everyone gives competent (or better) descriptions of what the subjects are. We learn that calculus is the mathematics of quantities that change, taking us to infinitesimal limits to deliver useful results in the real world. We learn that statistics is the mathematics of managing data, harnessing notions of probability to power inferences about large sets. Great, but I worry that these summaries don’t really tell you much: frankly, you would have to do the courses to properly understand what the summaries mean.
look closely at yourself to help make this decision
The second type of advice focuses on the relative difficulty of the two subjects, often gently slanting you towards statistics if you want the “easier” option. One day I’ll devote a whole essay to this, but, as anyone who knows me knows, I have difficulty with difficulty. What is difficulty? Where does it reside? Is it one-dimensional? What does it mean to say one thing is more difficult than another? Would everyone agree? In 2019, the mean scores for Calc AB and Calc BC were 2.97 and 3.80 respectively, while the mean for AP Statistics was 2.87. Which is more difficult now?
The third main mode is to discuss the perceived value of calculus versus statistics for the later studies and careers of the students who take them. Careful readers may discern a certain teleology in this approach. Will my later career really be enhanced by the choice I make today? Should it be? Might my confidence in later life be improved by my choosing (say) calculus today, discovering I don’t like it, then marching forward into a great future where I use statistics every day? Again, it’s imponderable.
I would advocate a different approach – look closely at yourself to help make this decision. If you love shape, symmetry, geometry and design, and if you appreciate metaphor, consider studying calculus. On the other hand, if you like people, organization, information and prediction, and if you respect precision in language, then statistics may be a better match for you.
The bottom line: Modern gurus give great guidance on this important question, but perhaps the sages – St Francis, Emerson, Thích Nhất Hạnh to name but three – have it right: The Answer Lies Within!