What does skewness measure in a probability distribution?

Skewness is a statistical measure that quantifies the degree of asymmetry or deviation from the normal distribution in a set of data. When a distribution is perfectly symmetrical, it has a skewness of zero. Positive skewness indicates that the tail on the right side of the distribution is longer or fatter than the left side, while negative skewness indicates that the tail on the left side is longer or fatter than the right side. Understanding skewness helps analysts determine whether the mean, median, and mode of the data differ, which can influence decision-making and risk assessments in a variety of contexts.

The other choices address different aspects of a distribution. The average value pertains more to the measure of central tendency, specifically the mean. The spread of data points relates to the concept of variance or standard deviation, which capture the extent of variation in the data. Concentration within quartiles refers to the distribution of data across specific segments, which is more associated with measures like the interquartile range. Hence, skewness specifically focuses on the asymmetry and is accurately represented by the statement regarding the symmetry of the distribution around its mean.