Definition

Normal distribution

The symmetric, bell-shaped distribution that arises whenever many small independent influences add up — the default assumption behind parametric statistics.

The normal (Gaussian) curve is fully described by its mean and SD, with the familiar 68/95/99.7% rule for one, two and three SDs. Heights, measurement errors, and averages of almost anything approximate it — the central limit theorem guarantees that means of large samples do, regardless of the raw data’s shape.

That last fact is why parametric tests are robust: they assume normal sampling distributions of means, not normal raw data. Genuinely skewed outcomes (income, counts, reaction times) still deserve a look — transformation, appropriate models, or rank-based tests.