[Verse 1]
Roll a single die and watch it land
Flat and uniform, no pattern planned
But gather up your samples, let them multiply
Something magical starts to mystify
[Pre-Chorus]
Independent draws with the same mean mu
Variance sigma squared running through
As n climbs higher, watch the transformation
From any shape to perfect constellation
[Chorus]
Central Limit's calling, order from the storm
X-bar minus mu, divided by sigma over root n
No matter where you started, bell curve is the norm
The universe converges to that beautiful form
Normal distribution, gravity of math
Every average finds the same sacred path
[Verse 2]
Heights of people, scores on every test
Stock returns and errors at their best
All these scattered numbers seem so wild
Till averaging tames them, chaos reconciled
[Pre-Chorus]
Sample size expanding, variance shrinks down
By the factor n underneath the ground
Standard error falling as we climb
Normal shape emerging every time
[Chorus]
Central Limit's calling, order from the storm
X-bar minus mu, divided by sigma over root n
No matter where you started, bell curve is the norm
The universe converges to that beautiful form
Normal distribution, gravity of math
Every average finds the same sacred path
[Bridge]
Skewed distributions, uniform and strange
All surrender to the normal range
Z-tests and confidence intervals reign
'Cause averaging washes out the pain
From triangular dice to perfect bell
Sample means have stories they will tell
[Final Chorus]
Central Limit's calling, theorem of the ages
X-bar approximately normal on the pages
Mu the center, sigma squared over n
The most important truth you'll ever pen
Statistics works because this law holds true
Averages converge, no matter what you do
[Outro]
Independent, identical, the magic starts to grow
As n approaches infinity, the normal truth will show