What does skewness measure in a probability distribution?

Skewness is a statistical measure that describes the degree of asymmetry or distortion in a probability distribution. When examining a distribution, skewness indicates whether it leans to one side of the mean or is evenly distributed around it. A skewness value of zero suggests a perfectly symmetrical distribution, while a positive skew indicates that the tail on the right side (higher value side) of the distribution is longer or fatter than the left side. Conversely, a negative skew implies that the left tail (lower value side) is longer or fatter than the right side.

Understanding skewness is crucial in various applications, as it can influence decision-making processes, risk assessment, and predictions based on the data. It provides insights beyond basic measures of central tendency like the mean or median, which do not capture the shape of the distribution effectively.

In contrast, the other options—variance, mean, and dispersion—pertain to different characteristics of a distribution. Variance measures the spread or variability of data points relative to the mean, mean represents the average of a data set, and dispersion refers to how far apart the data points are within a given dataset. These metrics do not convey the asymmetry or directionality of a distribution, making skewness a unique and