A distribution free plotting position

Many plotting position formulae have been proposed for the past few decades. These formulae are derived or obtained under some specific assumption of probability distribution. Because in practice the data are often plotted in order to determine its probability distribution, it causes difficulty and confusion in selecting the plotting position formula. The objective of this study is to find a plotting position formula which is distribution free. In this study, the plotting position formulae corresponding to the order statistic mean, mode and median are investigated. The order statistic mean, mode and median values are determined by numerical integration and differentiation, and the corresponding plotting position formulae are obtained by regression analysis. The results indicate that both the plotting position formulae for the order statistic mean and mode vary with the distribution of data, but the plotting position formula for the order statistic median is distribution free. The distribution free plotting position formula for the order statistic median is proposed in this study as (i - 0.326)/(n + 0.348).