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 the sample variance. Sarkar and Rashid (2017) interpret the sample SD 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.
Nguyen, Hieu; Nguyen, Tom; Rashid, Mamunur; and Sarkar, Jyotirmoy, "SD Prisms 2D & 3D: Visualizing the Standard Deviation" (2022). Annual Student Research Poster Session. 107.