What does kurtosis evaluate in a statistical distribution?

Kurtosis evaluates the peakedness of a statistical distribution. It provides insight into the shape of the distribution's tails and the height of its peak compared to a normal distribution. High kurtosis indicates a distribution with sharper, taller peaks and fatter tails, suggesting that a dataset may have a higher probability of extreme values. Conversely, low kurtosis reflects a flatter peak and thinner tails, indicating less extreme deviations from the mean.

This concept helps in understanding not just the central tendency and variability of the data, but also how likely it is to encounter extreme values, which can have significant implications in statistical modeling and analysis.