Central Limits

The Central Limit Theorem (CLT) states that when independent, random variables are summed, their normalized sum tends toward a normal distribution as the number of variables increases, regardless of the original distributions’ shapes.

This emergence of the bell curve is due to the additive accumulation of small, random fluctuations balancing each other out—large deviations become increasingly unlikely.

The CLT explains why normal distributions appear in nature and statistics: even if individual phenomena are random and varied, their collective behavior converges to predictable patterns, with the mean and variance of the sum stabilizing around central, Gaussian-like tendencies.