It seems like the tendency for the beads to cluster around the middle is mostly because they were dropped right above the middle. If you move the funnel to either side, then the distribution will be correspondingly skewed.
For anyone who is not familiar with a Galton board: [https://en.wikipedia.org/wiki/Galton_board](https://en.wikipedia.org/wiki/Galton_board)
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In: 5
Where it’s dropped is the average. The sides show the distribution from the average.
If you move the funnel, the average will be different, but the distribution around the average will be the same.
Well the Wikipedia article explains it quite nicely.
The board demonstrates the property of binomial distribution (the result on a population where each member undergoes a series of random yes/no choices). Each level presents each bead with two possibilities: move left one step, or move right one step.
The board demonstrates the probability that any particular bead will accumulate a particular proportion of left or right outcomes.
In extension to the other answers: if you want a board where the average is different from the dropping point, take one where the pins of each consecutive row are not next rows is not centered, but off from the middle. As long as it is off in a consistent way (say always 1mm to the left), you still get the results it is used to demonstrate.
The important thing about a Galton board is the shape of the distribution, not where its peak is.
There are lots of ways something could be clustered near the funnel. Things could be clustered in a linear way. Or they could disperse around the funnel in a negative quadratic way.
But they don’t. Even though you can’t make any reasonable prediction about any individual bead, you can reliably predict that the overall shape will look very close to a theoretical binomial distribution. And you can do it just by reasoning about the situation!
Neat!
*How many* of the beads drop in the middle? What percentage? Or better yet, what percentage drop in the outer edges? Coincidence?
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