What does a positive value returned by the kurtosis function indicate about the distribution of data values?

A positive value returned by the kurtosis function indicates that the distribution of data values is peaked. Kurtosis provides insights into the tails and the sharpness of the peak of a distribution. Specifically, a higher kurtosis value signifies that the data has heavier tails and a sharper peak compared to a normal distribution. This means that there are more data values in the tails and a concentration of values near the mean, indicating that the distribution is more pronounced and distinct at its peak.

In contrast, a distribution with a kurtosis value close to that of a normal distribution would be characterized as mesokurtic, indicating a normal level of peakedness. A flat distribution would reflect low kurtosis, while skewness refers to asymmetry in the distribution rather than peak sharpness. Thus, the positive kurtosis signifies a level of peakedness that differentiates the data distribution from others.