Not calculus; statistics!

So what’s the most important math course?  What top-level course should most people be aiming for?  How about calculus?

Or maybe not calculus.  Maybe it should be statistics.  Several people have sent me links to this video:

I think this is a good idea.  Sure, calculus is important for engineering and advanced business courses.  But statistics is key to allocating the use of limited resources (for example in health care), to mitigating risk, to epidemiology, even to understanding the environment - to lots of stuff.  It would be generally useful to a huge section of the public.

Suppose your doctor told you that your blood sugar was μ+σ.  Would you be reassured or should you start pricing insulin plans?  How about if you applied for a marriage license and your HIV test came back positive: you’d be concerned of course, but should you totally freak out?  Would there be rational hope that a more advanced test might turn up negative?

More importantly, if (as a culture) we could communicate in statistical terms, might that be a political game-changer?  There could be whole classes of idiotic rhetoric that politicians and journalists just couldn’t get away with anymore.  To say nothing of what it would do to the gambling and lottery industries.  That thought makes me smile.

NOTES:

Posted by George on 07/05/09 at 09:54 PM

  1. Yes, but 50% of people are below average wink

    They can’t even do arithmetic. Stats are maybe only for the upper quartile.

    Posted by Stu  on  07/06/09  at  03:33 AM

  2. I wonder if the reason many people can’t even do arithmetic could be that it’s never given them a sense of advantage to do so.

    Posted by George  on  07/06/09  at  06:33 AM

  3. Hmmm. Arent’t we bombarded every day with statistics which are, for all practical purposes, massaged for some political/economic agenda? In other words, statistics are one of the preferred tools for liars, cheats and thieves.

    Was it Mark Twain who said, “There are lies, there are damned lies, and there are statistics”?

    How about we just tell the truth and let the chips fall where they may? Wait. No. That’s an idiotic idea. Let’s stick with lies.

    Posted by gerry rosser  on  07/06/09  at  07:17 AM

  4. Gerry, you’re not suggesting that ignorance of statistical methods would be some kind of defense against that onslaught of lies, are you?  I think it makes us more vulnerable.

    Journalists and politicians can get away with spewing that bilge because they know most people doesn’t have a well-equipped baloney detector.

    Posted by George  on  07/06/09  at  07:24 AM

  5. Stats are maybe only for the upper quartile.

    Once I started learning stats in my grad class I thought it was one of the easier forms of math. In that class we were taught what formulas were showing and what the data meant rather than how to memorize formulas. Sadly it seems until higher education, too much of our education seems to be about memorizing facts and plugging through 100s of formulas over and over again. But do they REALLY understand it? We need to do a better job of teaching students what a standard deviation is rather than questioning who to plug and chug values.

    And Mark Twain and I would differ. Stats don’t lie, people who twist the stats do.

    Posted by webs05  on  07/06/09  at  09:06 PM

  6. Jane read this and asked me ‘So how much statistics should people learn?’

    My suggested answer : Enough to be able to do SPC - statistical process control - .

    What would you guys answer?

    Posted by Stu  on  07/07/09  at  02:08 AM

  7. For most people - the ones who can’t do arithmetic now - I’d be happy if they could understand concepts and not be so impressed when politicians and journalists recite what they feel is the meaning of a self-selected poll.  (Of course I would say that, being not much above that level myself.)

    Normal distribution, median vs. mean, standard deviation, error bars and significance would be a good start.  How to figure out what variables you’re really looking at.

    Your aunt Hattie smoked a pack a day her whole life and was active til she slipped on a banana peel at 93. What’s an “outlier”?  Isn’t pretty much every lottery winner an outlier? (Hint: they’re a lot further from μ than your aunt Hattie is). 

    And probability comes naturally from that.  Flip a coin five times, and it comes up heads each time.  What’s the probability it will be heads on the next flip?  What’s the probability of getting six heads in a row?  Why are those probabilities different? 

    And data gathering techniques are important to understand.  Why are internet polls useless?  How could the wording of a question affect poll results?  How can random sampling be useful and what are the challenges of achieving randomness?  Why is it easier on an assembly line than stopping people on the street? 

    School districts would call my stats course “Citizen statistics” or some happy-talk like that.  Mathematicians would call it “Bone-head statistics”, and be closer to the truth.

    Posted by George  on  07/07/09  at  06:47 AM

  8. I’ve found statistics to be an excellent entry point on bias and logical fallacies.

    Even while I remain a horrible statistician, looking at bad statistics is an excellent trainer on bias.

    Posted by Patness  on  07/08/09  at  05:52 PM

  9. I think a course in bonehead statistics would be useful. Way toomany people I know (read: argue with on the interwebs) quote internet polls like gospel (often whilst actually quoting gospel).

    Math held my interest until the 8th grade when I got a truly sadistic teacher (and I mean that - he used to hit students with a friggin ruler, and pick out the ones he thought deserved help and ignore the rest. I stopped showing up after sitting there for half a semester with my hand in the air. He gets numerous complaints every year, but those who actually *do* get help like him, so they won’t fire him. Did I mention that he works as a prison guard during the summer?) and dropped out.

    I took a remedial course the summer after tenth grade (different system here, school is mandatory 1-10th grades, after that it’s 4 years of “college” and then uni) and finished near the top of the class.

    Statistics are easyto manipulate and I’ve learned to always take statistical results with a grain of salt. It’s the old joke: if you have one foot in boiling water and the other in ice water, on average you’re comfortable. Reading statistics should be a mandatory course for anyone, and of course knowing how they are compiled is part of that.

    Posted by Tina St.Sebastian  on  09/26/09  at  10:34 AM

  10. Tina, it’s staggering to think of accounting the damage that teacher has done in his career.  Of such my dad used to say; “He doesn’t have twenty years teaching experience, he has one year twenty times.”

    Glad you overcame!

    Posted by George  on  09/26/09  at  11:01 AM

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