Third Central Moment and Skewness

*I make a mistake in saying that (2.41)^3=3.74...its approximately equal to that value not exactly equal to that value. Third Central Moment Explained | Skewness, Asymmetry, and Distribution Tails In this video, we continue our series on statistical moments by exploring the third central moment, the foundation of skewness. Previously, the second central moment (variance) squared deviations from the mean to measure dispersion. The third central moment takes a different approach by cubing deviations, allowing positive and negative values to be preserved while emphasizing larger deviations. This makes the third central moment useful for measuring asymmetry in a distribution. In this lesson, you'll learn: • What the third central moment measures • Why deviations are cubed instead of squared • How skewness differs from variance • How positive and negative skew arise in a distribution • The relationship between the third central moment and skewness • How standard deviation is used to standardize the third central moment • How to calculate skewness step-by-step using expectation operators Using a worked numerical example, we compute the third central moment, calculate skewness, and interpret what the result tells us about the shape of the distribution. You'll also learn how to identify: • Right-skewed (positively skewed) distributions • Left-skewed (negatively skewed) distributions • Symmetric distributions with skewness near zero This video builds directly on earlier lessons covering expectation operators, centering, the first central moment, and variance. In the next lesson, we move to the fourth central moment (kurtosis) and explore how statisticians measure tail behavior and distribution shape. #Statistics #Skewness #ThirdCentralMoment #StatisticalMoments #ProbabilityTheory #MathematicalStatistics #ExpectationOperator #Variance #Econometrics #DataScience #DistributionShape #StatisticsTutorial