📈 Normal Distribution

The normal (Gaussian) distribution with mean μ and standard deviation σ arises naturally wherever many small independent effects add up. The Central Limit Theorem (CLT) guarantees that the average of n independent draws from any distribution converges to a normal distribution as n → ∞ — the most powerful theorem in statistics. 🇺🇦 Українська

Mode

Distribution

Statistics

Mean—
Std Dev—
Area [x₁,x₂]—
Samples—

Why the Normal Distribution?

The 68–95–99.7 rule: about 68% of data falls within ±1σ, 95% within ±2σ, and 99.7% within ±3σ. In the CLT demo, roll n dice and sum their faces — even though each die is uniform, the distribution of sums quickly approaches a bell curve. Applications include: measurement errors, financial returns, height distributions, IQ scores, noise in electronics, and as the limiting distribution in countless statistical tests (z-tests, t-tests, ANOVA).