Our ability to accurately generalize with statistics is infuriating. With a sample of 100 or less people, measured for specific traits, a good study can make reliable assertions about the broader population in a way that we now might taken for granted. It’s all because of a concept known as the Central Limit Theorem.
Case in point: if given my weight, height, age, and miles run per week, you could refer to a sample of the same data from 100 people (totally random people) and make an excellent prediction of my 5k time. Add another 100 people to the sample, and you’ll probably get a better prediction.
It’s infuriating how accurate this is. I want to be a snowflake. I want to be special and unique. Yet, I cannot defeat the Central Limit Theorem. None of us can. It’s like fighting an ocean.
All the same, we deny the reality. That’s why we all consider ourselves above-average drivers.
It all comes back to the bell curve (i.e., the normal distribution). Central Limit Theorem states that, with enough samples, the values of practically any measure are eventually plot themselves in the shape of the bell curve. An image below shows this nicely. With progressively larger samples, a very classic bell curve is formed:
For many things, if not most, you and I populate the center peak of this curve. We practically have to. Reading comprehension? 5k time? Attractiveness? Humor? Join me in the sea of averages.
But enough self-effacement, the more important takeaway is that the central limit theorem is what helps us brush broad strokes with very little paint. This can be a force for good or bad. Central Limit Theorem emboldens fools to say very awful things (e.g., brutish stereotypes) and informs intelligent people in their quest for structural improvements (e.g., central tendencies).
More importantly, it helps us identify what truly is unique so that we can narrow our search into why.
This is where the 10,000 hour rule came from. In his book Outliers 1, Malcolm Gladwell cited research from K. Anders Ericsson that studied high performers in a variety of fields and, through the Central Limit Theorem, found that one general trait of outliers was a high degree of deliberate practice over a period of time roughly approximating 10,000 hours.
Since then, many have argued against the 10,000 hour rule. No one literally spent five years with a stopwatch clocking in their 10,000 hours to become a master. Nonsense!
Of course, what’s deeply mistaken in every critique is that we’re talking about statistics here. This isn’t calculus. There are margins of error, confidence intervals, and a few other elements that make these generalizations so … general. And deeply instructive all the same.
When it comes to statistics, we mistake these observations for some sort of rigid, reliable mathematical formula. It either works or it doesn’t. Black and white. And when we invariably get a different result, see a different (average?) observation, we immediately reject the information. “I spent 10,000 hours and I’m not a master yet. I want my money back.”
I see a recursion here. Central Limit Theorem suggests the average person has a hard time accepting general observations that apply broadly to the population. Which is to say the average person has a hard time not acting like an average person.
I write this tongue-in-cheek but it clearly this means that, if I can recognize this, I’m not average. Not at all. And if you’re reading this, you must not be average either. Let’s keep telling ourselves that.
Image from Daniel Resende via Wikimedia Commons