Visualizing the Mean and the Standard Deviation Using R/RStudio Shiny Package

Abstract

Many of us have experienced an unpleasant situation in which only the mean and the standard deviation of a data set are reported, but we are expected to know everything about the dataset as if those two values were all we needed to know. We would learn so much more if there were easy ways to create and share graphical representations and interpretations of the entire raw data. Here we not only explain what the mean and the standard deviation tell us about a data set, but also describe how to include additional information on the data. We utilize the work of Sarkar and Rashid (2016) that introduced a geometric visualization of the sample mean based on the empirical cumulative distribution function of the raw data. They also extended the idea to visualize measures of spread such as the mean deviation, the root mean square deviation and the standard deviation. Our research involves creating interactive applications of these methods using R/RStudio Shiny, an open source package that provides an elegant and powerful web framework for building web applications. We hope, upon publication of these tools, users all over the world will use such interactive visualization methods for learning, teaching, and building more advanced tools.