What Mean, Variance & Correlation Really Look Like

Why does the mean come from a projection? And why is correlation the cosine of an angle? In this animated walkthrough, we turn a dataset into a vector and discover the geometry connecting mean, variance, standard deviation, covariance, and Pearson correlation. Starting with a simple dataset, we build each idea step by step: • The mean: finding the closest vector whose coordinates are all equal. • Deviations: separating the common level from everything that varies. • Variance and standard deviation: measuring variation through vector length. • Covariance: measuring how two deviation…