What is skewness a measure of in a distribution?

Skewness is a statistical measure that describes the degree of asymmetry of a distribution around its mean. When a distribution is perfectly symmetrical, it has a skewness of zero. However, in real-world data, distributions often exhibit skewness, indicating that one tail is longer or fatter than the other.

Positive skewness indicates that the right tail (higher values) is longer, suggesting that there are relatively few high outliers in the data. Conversely, negative skewness indicates that the left tail (lower values) is longer, pointing to few low outliers. This understanding of asymmetry is crucial in statistics, as it influences how we interpret the data and the relevance of different statistical measures, such as the mean and median.

The other options do not accurately describe skewness: symmetry pertains to when the left and right sides of a distribution are mirror images, frequency of occurrence relates to how often data points appear within the dataset, and the mean value refers to a central tendency measure rather than the nature of the distribution's shape.