Statistically speaking, we don’t use calculus By Dave Gammon
An article in a local op-ed piece today (Roanoke Times) claims:
“Quantitative skills are highly sought after by employers, and the best time to learn these skills is in high school and early college. And we all know the best math students should eventually learn calculus.
Or should they? Maybe it’s statistics, not calculus, that is a more worthy pursuit for the vast majority of students.”
This reminds me of the trouble I got into when, as a graduate student at the University of Pennsylvania, I supplemented my fellowship in philosophy by leading some recitation classes in statistics at the Wharton school. Although it was vaguely suggested that I not assign homework problems that required calculus, since many of the exercises in the sections of the text (on business statistics) that I was to cover required, and were illuminated by, calculus, (and given that the text was written by a Wharton statistics professor [de Cani]), I went ahead and assigned some of them, and promptly was reported by the students[i]. The author of this article appears to have no clue that statistical methods depend on calculus and the “area under a curve”.
It’s not that learning calculus is pointless. Calculus applies integrally to physics, engineering, space exploration, satellite positioning, complex building projects and several other lines of work. If your career ambitions fit within one of these domains, by all means, learn calculus. Most of us, however, are destined for careers other than physics, engineering or mathematics.
Statistics weave deeply throughout the fabric of our society. Remember all those political polls last fall? Every one of them reported a “margin of error” and a “sample size” as part of the results. Without statistical training, it is easy to misinterpret their results — especially when you encounter conflicting poll results….
Because of the news media and the Internet, we face a daily bombardment of quantitative information. This deluge is growing exponentially with each passing year and each technological innovation, becoming a virtual river into which our vessels are thrust. A citizen without a working knowledge of statistics is rafting that river without a paddle.
Can you remember the last time you saw in the newspaper a story that focused on the area under a curve, or the slope of a line? Yeah, neither can I. If you ever stumble upon such a story, then calculus might be your best friend.
To most students, however, statistics will be of far more use than calculus, especially if they select career paths that require them to analyze risk, evaluate trends, confront randomness, deal with uncertainty or extract patterns from data…
Not once in my professional career has calculus been particularly relevant.
Statistics, however, has been my bread and butter. Nearly every major project I have attempted required the use of statistics. I wish someone had told me this secret when I was younger……
Ultimately, it will take time for our educational systems to adapt to the shifting needs of society. Students will benefit right now, however, if they expose themselves to more statistics. Parents and academic advisers everywhere should take heed and help promote this valuable discipline.
Admittedly, a lot of the statistics we read about remains stuck at a shallow level; and perhaps the “virtual river into which” this author’s vessel is thrust will never have to scratch far below the surface. Else, he might have to discover that statistical methods are based on areas under curves.
[i] I made up “recipe sheets” for the rest of the semester.
Can you recommend articles, websites or textbooks that illuminate statistics using calculus? I’ve been looking for more “proof-like” explanations of statistics for a while.