What does a higher kurtosis value suggest about a dataset?

A higher kurtosis value indicates that the dataset has a sharp peak and heavy tails. This means that the distribution has more extreme values or outliers compared to a normal distribution. In other words, a high kurtosis suggests that the data is more concentrated around the mean and that there are significant deviations from the mean—some observations that are much higher or lower than the average. Such a distribution is often referred to as leptokurtic, where the presence of heavy tails can imply an increased risk for extreme outcomes, which is especially relevant in fields such as finance and psychology, where understanding variability and risk is crucial.

A distribution with high kurtosis contrasts with one that has a lower kurtosis, which would typically have a flatter peak and lighter tails, indicating fewer extreme values and thus a more uniform spread of data around the mean. This sharp peak and heavy tails characteristic of higher kurtosis makes it important for statistical analyses that involve predictions or risk assessments based on data behavior.