A New Approach to Determine the Coefficient of Skewness and An Alternative Form of Boxplot

TL;DR

This paper introduces 'Rank skewness', a new measure for skewness that handles extreme values better, and proposes a simplified four-point boxplot that outperforms traditional methods.

Contribution

The paper presents a novel skewness measure called 'Rank skewness' and a simplified four-point boxplot, improving accuracy and simplicity over existing methods.

Findings

'Rank skewness' performs better for skewed distributions.

The four-point boxplot provides clearer insights than traditional boxplots.

New methods are based on all observations for better accuracy.

Abstract

To solve the problems in measuring coefficient of skewness related to extreme value, irregular distance from the middle point and distance between two consecutive numbers, "Rank skewness" a new measure of the coefficient of skewness has been proposed in this paper. Comparing with other measures of the coefficient of skewness, proposed measure of the coefficient of skewness performs better specially for skewed distribution. An alternative of five point summary boxplot, a four point summary graph has also been proposed which is simpler than the traditional boxplot. It is based on all observation and give better result than the five point summary.