PROJECT

Galton Board: Visualizing Normal Distribution

March 15 2018
Vector graphic of a pascal's triangle

TOOLS USED

  • HTML & CSS
  • JavaScript

Order Among Chaos

I took my first statistical analysis class in late 2017 and was blown away by the concept of normal distribution . The idea of chaos resulting in order was something I had difficulty wrapping my head around.

A few online tutorials later I came across the Galton Board, a device that helped me visualize the concept of normal distribution. This device contains hundreds of small beads/balls that are dropped from the top of the device and are allowed to scatter randomly by hitting several rows of pegs in the middle.

As the balls fall down and collect in the slots at the bottom, you can see a pattern emerge. Every single time you flip the Galton Board. You will see a Normal Distribution.

Why does this happen??

When the balls fall through the machine, they hit the pegs in the first row. Once they do that, they have a 50-50 chance of falling to the left or right. As they hit the second row, they again get an equal chance to fall either to the right or left. This process continues all the way down to the last row.

In the long run, across a large number of trials (Law of Large Numbers), we expect balls whose complete paths contain about the same number of left and right turns to be the most common. This means that most balls will land right below where they started while only a handful will travel to the sides. We cannot guess where a particular ball will land, but can make a pretty good estimate about the general behavior that all balls will follow.

This results in Normal Distribution.

To help understand this concept better, I created a digital Galton Board for students to play with. I hope this tool could prevent you from pulling your hair the night before your stat finals. I will update the site with more visual tools in the coming months to make it a more comprehensive guide

Where can I learn more??

Michael Stevens, from the youtube channel VSauce has an amazing video explaining normal distribution and more interesting probability concepts using the Pascal's Triangle.