Statistics for Business: Decision Making and Analysis, 3rd Edition

... indicating a nearly symmetric distribution. If we mix diamonds of varying quality, the skewness grows to K₃ ≈ 1.1. If K₃ > 1, there’s quite a bit of skewness and the data are not normally distributed.

Figure 12.21 The distribution of diamonds of varying quality is skewed to the right.

Kurtosis also captures a deviation from normality. Kurtosis measures the prevalence of outliers. The kurtosis is the average z-score raised to the fourth power, minus 3.

kurtosis

Prevalence of outliers in a distribution; average of the z⁴ minus 3. K₄ ≈ 0 for normal data.

$$K_4=\frac{z_1^4+z_2^4+\dots +z_n^4}{n}-3$$

Subtracting 3 makes K₄ ≈ 0 for normally distributed data. (This definition is ...