Gaussian - Standard Normal Distribution

thingiverse

This Visualization was created using the profile of the Standard normal distribution revolved around the Z axis. It's an approximation, that I drew freehand (tracing a screen capture from https://www.desmos.com/calculator/2kmx0enkkz) to get a rough idea of how the percent per sigma differs from the percent per sigma by volume. I used Blender to measure the volumes (before making space between each cylinder so they could nest). The running percent totals (by volume) are roughly as follows: 1 sigma - 36% 1.25 sigma ~ 50% 2 sigma - 81% 3 sigma - 97% 4 sigma ~ 100% Individually, they are: 1 sigma - 36% 1 sigma to 1.25 sigma - 14% 1.25 sigma to 2 sigma - 31% 2 sigma to 3 sigma - 16% 3 sigma to 4 sigma - 3% I made it so you could arrange 50% of the total distribution by volume in two parts by nesting the first piece inside the second piece. Some things that I learned: for a 2D Gaussian, the 50%, by volume, mark is at .6745*sigma, but for a 3D Gaussian, it's closer to around 1.25*sigma, which I didn't expect like the previous, 1 sigma for a 2D contains 68% while for a 3D it only contains roughly 36% This wasn't meant to be an exact calculation, nor was it generated using a formula. It does make a decent approximation and a nice demo piece. I think this helps demonstrate that distributions are different when going from 2D to 3D.