What is the interpretation of skewness in a probability distribution?

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Skewness provides a crucial insight into the shape of a probability distribution, specifically focusing on its symmetry. A distribution is considered symmetric if it has the same shape on both sides of the mean, exhibiting that the data points are evenly distributed. However, when skewness is present, it indicates that the distribution leans towards one side. Positive skewness suggests that the tail on the right side of the distribution is longer or fatter, while negative skewness indicates that the tail on the left is longer or fatter. By understanding skewness, one can interpret how data points are distributed relative to the mean, gaining insight into potential outliers and the overall behavior of the dataset. Thus, skewness is fundamentally about the asymmetry of the probability distribution rather than just clustering or spread of data.