Statistical moments connect the mean, variance, skewness, and kurtosis into a unified framework for describing distributions. A moment is simply a quantitative measure of the shape of a set of points or a probability distribution. Raw moments are taken around zero, while central moments are taken around the mean.

The first raw moment is the mean itself, and the second central moment is the variance. Standardized moments divide by the standard deviation raised to the corresponding power, yielding skewness as the third standardized moment and kurtosis as the fourth. These metrics are not disjointed tools but interconnected measures rooted in the same mathematical structure.

The concept of moments extends beyond statistics into physics, where torque and the moment of inertia share the same foundational principles. Understanding moments provides deeper insight into distribution behavior, enabling more powerful analytical applications across fields like machine learning and data science.