Mathematical Concept
The Central Limit Theorem, in Practice
- Published
- 11 APR 2026
- Reading
- 1 MIN
- Status
- DEMONSTRATION ENTRY
Where the normal approximation helps, where heavy tails make it fail, and how to tell the difference.
DEMONSTRATION NOTE — conceptual outline.
Statement
Sums of independent, identically distributed variables with finite variance converge to a normal distribution after scaling.
Where it bends
- Heavy tails slow convergence dramatically.
- Dependence changes the effective sample size.
- Finite samples differ from the limit in the tails first.
Takeaway
Use the approximation as a starting point, then check it by simulation.