Almost all naturally occurring properties can be arranged in a Gaussian distribution. We don't necessarily know what that curve looks like, but it's going to be big in the middle and small on the sides. So if you pick one object at random from that group of things, you're more likely to be getting an item from the middle. You're most likely to get the object that is perfectly average. So even when you only have one data point, you can still know that you most likely have something within 1 standard deviation of the mean, and almost certainly have something within 2 standard deviations of the mean. It's possible it's further away, but if you just assume you're within 2 standard deviations you'll be right 19 times out of 20. You still don't get an idea of what a standard deviation is or even which side of the mean you're on, but it gives a good starting point for what you should expect to see lots more of.Originally Posted by BalticSailor
This works with the number of times something should occur, too. So if we spend 5 years looking for a thing before we find the first one, we can safely assume that 5 years is within two standard deviations of the average amount of time it'll take to find another of those things the way we're doing it. We also have a nice lower bound since you can't take less than 0 time to find something, so that gives us a bounds for what the standard deviation will most likely look like.
In this case specifically, we found this faster than our models said we should have. So either our models are wrong, we just experienced a lottery-winning low-probability event, or this isn't part of the natural phenomena that we modeled. And, comeon, isn't it more fun to think about what it would mean if it's from outside our model, instead of just going with 'our models are wrong'?
Fun fact: If you take all natural phenomena that can be fit to a Gaussian distribution, and measure how far they deviate from ideal form of one, those measurements will form a Gaussian distribution.
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