Down-voted for not acknowledging or not realizing that you were also lucky.
As people make their guesses, the mean of their guesses will fluctuate. This doesn't mean the number of jellybeans is fluctuating, of course. You were lucky that your well-educated guess happened to be closer than any other guess.
Suppose people's guesses were normally distributed about the true number of jellybeans with a specific standard deviation. Even with these ideal assumptions, the average of N guesses doesn't converge that quickly to the mean, and I don't suppose it converges faster than the probability that any one guess is closer to the true number than your mean.
The guesses in most contests won't be normally distributed, period, so they won't be normally distributed around the true number. They'd be closer to log-normal or some such distribution, I would guess.
A couple of years ago my workplace was running one of those guess-the-number-of-jellybeans-in-the-jar competitions. I don't even like jellybeans all that much, but nonetheless, I held aloft my nonmagic calculator and said "by the power of Galton!" Taking the mean of all the previous guesses, I put that down as my answer. I was out by one bean, and won the jar. I don't think my colleagues have ever been so interested in statistics as they were that afternoon, and I doubt they ever will be again.
I'm going to admit something a bit silly and embarrassing now: that made me feel like a wizard. Not because of the scope of what I'd done, since it was an utterly trivial piece of arithmetic, but because of the reaction it got. I had drawn on arcane lore unknown to my colleagues, and used it to exercise power over the world.
Personally, I think something like solid state semiconductor technology is about as impressive a real-world miracle as one could ever want by way of demonstrating the whole Science Works/Rationality Is Systematised Winning/Maths Has Manifold Real-World Applications thing, but for most people it will never have the impact of intentionally winning a jar full of jellybeans.
So I ask you, LW-readership: what other impressive nonmagical powers do we have, that we can casually demonstrate to everyday people in everyday circumstances?