Package: EuclideanSD 0.1.0

EuclideanSD: An Euclidean View of Center and Spread

Illustrates the concepts developed in Sarkar and Rashid (2019, ISSN:0025-5742) <http://www.google.com/url?sa=t&rct=j&q=&esrc=s&source=web&cd=&cad=rja&uact=8&ved=2ahUKEwiH4deL3q3xAhWX73MBHR_wDaYQFnoECAUQAw&url=https%3A%2F%2Fwww.indianmathsociety.org.in%2Fmathstudent-part-2-2019.pdf&usg=AOvVaw3SY--3T6UAWUnH5-Nj6bSc>. This package helps a user guess four things (mean, MD, scaled MSD, and RMSD) before they get the SD. 1) The package displays the Empirical Cumulative Distribution Function (ECDF) of the given data. The user must choose the value of the mean by equating the areas of two colored (blue and green) regions. The package gives feedback to improve the choice until it is correct. Alternatively, the reader may continue with a different guess for the center (not necessarily the mean). 2) The user chooses the values of the Mean Deviation (MD) based on the ECDF of the deviations by equating the areas of two newly colored (blue and green) regions, with feedback from the package until the user guesses correctly. 3) The user chooses the Scaled Mean Squared Deviation (MSD) based on the ECDF of the scaled square deviations by equating the areas of two newly colored (blue and green) regions, with feedback from the package until the user guesses correctly. 4) The user chooses the Root Mean Squared Deviation (RMSD) by ensuring that its intersection with the ECDF of the deviations is at the same height as the intersection between the scaled MSD and the ECDF of the scaled squared deviations. Additionally, the intersection of two blue lines (the green dot) should fall on the vertical line at the maximum deviation. 5) Finally, if the mean is chosen correctly, only then the user can view the population SD (the same as the RMSD) and the sample SD (sqrt(n/(n-1))*RMSD) by clicking the respective buttons. If the mean is chosen incorrectly, the user is asked to correct it.

Authors:Rishav Bhattacharjee [aut], Siddhanta Phuyal [aut, cre], Mamunur Rashid [aut], Jyotirmoy Sarkar [aut]