SD Prism: Visualizing the Standard Deviation as the Size of a Prism Using R/RStudio

Abstract

SD Prism is a graphical R package used for visualizing the standard deviation of a data set. Given a raw data set, the standard deviation (SD) is defined as the square-root of twice the mean square of all pairwise half deviations between any two sample observations. This interpretation leads to a geometric visualization of the sample SD, and a more elementary explanation as to why the denominator in the sample variance is one less than the sample size. In this article we will explain step by step how to understand it mathematically and how the package implements the methodology to visualize the SD.