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.
||Rishav Bhattacharjee [aut],
Siddhanta Phuyal [aut, cre],
Mamunur Rashid [aut],
Jyotirmoy Sarkar [aut]
||Siddhanta Phuyal <siddhantaphuyal7159 at gmail.com>
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