Editing Kurtosis (section)

=== Interpretation ===
The interpretation of the Pearson measure of kurtosis (or excess kurtosis) was once debated, but it is now well-established. As noted by Westfall in 2014{{r|Westfall2014}}, "...''its unambiguous interpretation relates to tail extremity.'' Specifically, it reflects either the presence of existing outliers (for sample kurtosis) or the tendency to produce outliers (for the kurtosis of a probability distribution). The underlying logic is straightforward: Kurtosis represents the average (or [[expected value]]) of standardized data raised to the fourth power. Standardized values less than 1—corresponding to data within one standard deviation of the mean (where the “peak” occurs)—contribute minimally to kurtosis. This is because raising a number less than 1 to the fourth power brings it closer to zero. The meaningful contributors to kurtosis are data values outside the peak region, i.e., the outliers. Therefore, kurtosis primarily measures outliers and provides no information about the central "peak".

Numerous misconceptions about kurtosis relate to notions of peakedness. One such misconception is that kurtosis measures both the “peakedness” of a distribution and the  [[heavy-tailed distribution|heaviness of its tail]] .{{r|Balanda1988}} Other incorrect interpretations include notions like “lack of shoulders” (where the “shoulder” refers vaguely to the area between the peak and the tail, or more specifically, the region about one [[standard deviation]] from the mean) or “bimodality.” {{r|Darlington1970}}   Balanda and [[Helen MacGillivray|MacGillivray]] argue that the standard definition of kurtosis “poorly captures the kurtosis, peakedness, or tail weight of a distribution.”Instead, they propose a vague definition of kurtosis as the location- and scale-free movement of [[probability mass]] from the distribution’s shoulders into its center and tails. {{r|Balanda1988}}