Q-Ba-Maze by Mindwareis actually a pretty painful product. It’s hard to make things that stay upright and stay together. However, I was able to create a pretty good Galton Machine with it to demonstrate the central limit theorem.
It’s a little hard to explain how this works. The Q-Ba-Maze has several sorts of elements:
- Ones that drop straight through (straight-throughs)
- Ones that drop to one side (one-sides)
- Ones that drop to either side more-or-less randomly (either-sides)
By judicious arrangement of these elements — details left to the reader — it’s pretty easy to create a Galton Machine that’s essentially as large as you like.
Here’s Leo’s lab notebook for our first run of the device:
(Reader’s guide for 5.5 year old penmanship: Numbers down the left are the replication, and it says “Prob Exp” across the top. I wanted him to write out “probability experiment”, but could see that it was going to take up the whole page, so we did an impromptu lesson on abbreviations! Then there’s a bunch of math and carries, which is why all the ones along the top.)
First, make sure that you put one of the large columns and a straight-through element at the top so that you appropriately de-bias the initial drop. Here’s a close up that shows the top a little more clearly.
Second, use a set of straight-throughs at the base to catch the balls, otherwise they end up all over the place, and are hard to count. You can see that in the above picture as well.
Finally, use a straight-through element at each stage, otherwise the fall from the previous stage will tend to bias the either-side toward the side opposed to that from which the ball arrived, and will bias the results towards the outside of the machine. Here are a couple of close-ups that show this a bit more clearly:
Five balls is a good number to drop through the size machine depicted here. If you’ve balanced the machine well (an iPhone level helps a lot!), they will assort randomly just in the nice way predicted by the central limit theorem…statistically speaking, of course! 🙂