normal distribution

Normal Distribution (Bell Curve)

A symmetric, bell-shaped distribution where values cluster around the mean and the frequency of values decreases as distance from the mean increases — described by just two parameters: mean and standard deviation.

When you'd see it: In statistical test assumptions (T-tests and ANOVA assume approximately normal data), in regression error distributions, and in quality control (defect rates, measurement errors). Height, IQ scores, and measurement errors approximate normal distributions; most business data does not.

Why it matters: Many classical statistical tests assume normally distributed data, so knowing when your data violates that assumption matters. Intuitions like '95% of values fall within 2 standard deviations of the mean' are specific to the normal distribution and don't hold for skewed or heavy-tailed data.

Common mistakes: Assuming business data is normally distributed by default. Revenue, session lengths, deal sizes, and social sharing counts are typically right-skewed with heavy tails — not normal. Applying normal-distribution intuitions leads to systematic underestimation of extreme values.

Related mean, standard deviation, Z-score, T-test, outlier