← Concept Lab

The Normal Distribution

The normal (Gaussian) curve f(x) = exp(-(x-mu)^2 / (2 sigma^2)) / (sigma sqrt(2 pi)) is set by just two numbers: the mean mu (where it is centered) and the standard deviation sigma (how wide it spreads). Drag them and watch the bell shift and stretch. The shaded band is one standard deviation each side of the mean - it always holds about 68% of the area, no matter the mean or the spread.

Peak height
0.399
1 sigma band
-1.0 / 1.0
Within 1 sigma
68.2%

This is a fixed demonstration concept (NOVA's interactive-visual study modality); the per-misconception, per-course generated version is the frontier work that follows.