Should Probability and Basic Stats Replace Calculus in the High School Curriculum?
Don't get me wrong, I love calculus. I use calculus every day. If you're a bright young student with dreams of becoming a mathematician, physicist, engineer, or economist, a good foundation in calculus is just what you need to get started. For everyone who isn't that kid, calculus may be something they learn once and then never use again.
Probability, on the other hand, is something that we all deal with all the time, and it's something that humans have a remarkably hard time grasping intuitively.
Take the famous Monty Hall problem, for instance, which fools even very smart people:
People don't understand this problem because they use unconditional probabilities when they should be using conditional probabilities. People make other mistakes, too, like the prosecutor's fallacy, which is another confusion about conditional probability.
Here's an example of how conditional probabilities come into play in everyday life (I've made up the numbers). Say you're a 60-year-old male and you'd like to plan for your retirement. You know that 90% of males in your country have died by the age of 85, so you figure if you have enough assets to keep paying your living expenses until age 85, there's only a 10% chance you will run out of money before you feel death's sweet embrace. Wrong! You've actually got a better than 10% chance of surviving past 85 because that 90% statistic includes all the people who didn't make it to 60. The relevant statistic is the number of people who made it past 85 given that they had made it to 60. A high school class on basic probability could really help people plan their lives.
The other reason I would put probability and statistics in the curriculum is to help people not to be fooled by the kinds of misleading statistics thrown around by politicians, journalists, and careless or malicious academics. In the latest episode of Jim Pethokoukis' podcast, he and Richard Burkhauser discussed the misleading data from a study by two French economists, Piketty and Saez, whose statistical analysis seemed to indicate that middle-class incomes had remained stagnant over the past twenty years while the richest 5% had gotten dramatically wealthier. Burkhauser showed that Piketty and Saez' results were very sensitive to their assumptions, and that with better data and better assumptions median income growth was not 3% over 20 years as Piketty and Saez claimed, it was more like 36%, and inequality isn't growing out of control but has remained fairly constant since 1992.
Believe it or not, I saw the graph from Piketty and Saez' study pasted to a sign at my local Occupy rally earlier this year (I was a passerby, not a participant). There are people in this world who went out and slept in tents and were a general nuisance to everyone on the basis of bad data. A little bit of statistical knowledge might not be enough to have every single Occupy person debunk a study that most economists failed to see through, but it would at least teach them that statistics are often misleading and shouldn't be taken unquestioningly as facts.
If I were designing a high school statistics course, I wouldn't just transfer "Intro to Statistics" from university to grade 12 (I was a TA for "Intro to Statistics" this past term; it's frightfully boring). When you teach someone to drive, you show him the brake before you show him the gas pedal. When you teach someone to use a gun you tell him not to point it at his face before you show him how to take the safety off. In statistics we do the opposite. Sure, there's the obligatory speech about how correlation is not causation, but that is quickly forgotten in the rush to show the students all the amazing things they can do with statistics. It's not until grad school that students are taught how to really think critically about statistics and to question the assumptions of statistical models.
However, you don't need four years of stats courses to start questioning assumptions. Thomas Sowell, in his many books, critiques bad statistics and the inferences drawn from them in terms that anyone can understand. There are some statistical pitfalls that really do require years of statistical training to understand, but people should at least know that they exist and that statistical "facts" are few. What's key is for people to develop a healthy scepticism towards statistics, so they can't be easily manipulated by politicians and intellectuals who may not have their best interests at heart.