A Polyplot for Visualizing Location, Spread, Skewness, and Kurtosis

A plot that includes multiple location and spread statistics can provide useful information about the shape of a distribution, not only with respect to location and variability but also with respect to skewness and kurtosis. We propose a plot containing the interquartile range, mean absolute deviation, standard deviation, and range of a dataset. The comparison of the spread statistics gives information about kurtosis and the comparison of the location statistics gives information about skewness. After the distribution has been divided into two parts by the median, the interquartile range can be thought of as the distance between the medians in each half of the distribution. We explain how the mean absolute deviation with respect to the median can similarly be visualized as half the distance between the means in each half of the distribution. An R function to produce the polyplot is available as an online supplement.