An Original New Statistical Chart: Polar Coordinate and Cumulative Distribution Function (CDF)-Based Individual and Central Tendency Deviation Statistical Chart Method

Abstract

In empirical economic and managerial analysis, data visualization serves as a crucial bridge between theoretical modeling and policy decision-making. However, traditional descriptive tools often fail to present complex multi-dimensional distribution characteristics effectively. In descriptive statistics, traditional histograms, box plots, and density curves often suffer from a lack of dimensional intuitiveness or overlapping confusion when simultaneously displaying population central tendencies (mean, median, mode) and individual relative positions. This paper proposes a novel statistical chart representation method based on the polar coordinate system. This method uses central tendency measures as the "zero-angle reference line" (angle axis) in polar coordinates. By calculating the proportion of the area integral of individual values under the population cumulative frequency distribution function (CDF), it maps it into the deviation angle θ in polar coordinates. Additionally, by combining concentric circles corresponding to radii of different central tendency measures, it achieves a multi-dimensional visualization of the overall distribution shape and the relative positions of individuals.

Keywords: descriptive statistics; polar coordinate; cumulative distribution function (CDF); measures of central tendency; skewness; data visualization; empirical distribution function

DOI: 10.7176/EJBM/18-8-01

Publication date: August 30^th 2026