What does kurtosis indicate in statistics?

Kurtosis is a statistical measure that captures the "tailedness" of a probability distribution, which refers to how heavy or light the tails of the distribution are compared to a normal distribution. It provides information about the presence of outliers and the potential for extreme values in the dataset. For example, a distribution with high kurtosis has fatter tails and a sharper peak, indicating a higher likelihood of extreme scores, while a distribution with low kurtosis has thinner tails and a flatter peak.

This understanding of kurtosis is crucial in many fields, especially when assessing the risk of extreme events in financial markets or understanding the distribution of psychological test scores, as it helps identify the potential for atypical data points that could influence analysis and interpretation significantly.

The other options relate to different aspects of a dataset. The shape of the dataset's central peak primarily concerns skewness, the frequency of data points below the mean relates to measures such as percentiles or cumulative frequency, and the average dispersion refers to measures such as variance or standard deviation. Thus, none capture the specific function of kurtosis as effectively as the correct choice.