What does kurtosis indicate in a data set?

Kurtosis is a statistical measure that specifically quantifies the "tailedness" of a probability distribution. This characteristic of a data set indicates how heavy or light the tails of the distribution are in comparison to a normal distribution. High kurtosis suggests that a distribution has heavy tails, meaning that there are more extreme values or outliers than in a normal distribution. Conversely, low kurtosis indicates that the distribution has lighter tails and less extreme values.

Understanding kurtosis is important in risk modeling as it provides insights into the likelihood and potential severity of extreme outcomes. This can be crucial for decision-making in fields such as finance and insurance, where the risk of extreme losses must be effectively managed.

The other options address different statistical concepts. For instance, spread is typically measured by variance or standard deviation; average refers to the central tendency, often measured by the mean; and mode concerns the most frequently occurring value in a data set. Hence, kurtosis is distinctively focused on the nature and frequency of extreme values rather than these other properties.