International Journal of Statistics and Applications
pISSN: 21685193 eISSN: 21685215
2018; 8(6): 309315
doi:10.5923/j.statistics.20180806.04
Md. SirajUdDoulah
Department of Statistics, Begum Rokeya University, Rangpur, Bangladesh
Correspondence to: Md. SirajUdDoulah, Department of Statistics, Begum Rokeya University, Rangpur, Bangladesh.
Email: 
Copyright © 2018 The Author(s). Published by Scientific & Academic Publishing.
This work is licensed under the Creative Commons Attribution International License (CC BY).
http://creativecommons.org/licenses/by/4.0/
The Paper examines the performances of some popular and frequently used measures of dispersion such as standard deviation, coefficient of variation and standard error and survey that they may not perform as good as anticipating in the presence of nonnormality or outliers. The usefulness of the proposed measures is scrutinized with the frequently used measures of dispersion by bootstrap and jackknife computer based techniques as well as Monte Carlo simulation approach. In this paper, I propose new alternative measures of dispersion, namely DMstandard deviation, coefficient of deviation and DMstandard error. These measures should be fairly robust. The results demonstrate that DMstandard deviation, coefficient of deviation and DMstandard error outperforms than the standard deviation, coefficient of variation and standard error in a broad range of frequently occurring situations.
Keywords: Bootstrap, Coefficient of Variation, Coefficient of Deviation, DMstandard Deviation, DMstandard Error, Jackknife, Monte Carlo Simulation
Cite this paper: Md. SirajUdDoulah, Alternative Measures of Standard Deviation Coefficient of Variation and Standard Error, International Journal of Statistics and Applications, Vol. 8 No. 6, 2018, pp. 309315. doi: 10.5923/j.statistics.20180806.04.

Table 2. Bootstrap Results Comparison of Six Different Measures of Dispersion for Score Data set With Outliers and Without Outliers 
Table 3. Comparison of Percentile Length of Six Different Estimators of Dispersion for Score Data with Outliers and without Outliers by Bootstrap 
Table 4. Jackknife Results Comparison of Six Different Measures of Dispersion for Score Data set With Outliers and Without Outliers 
Table 5. Comparison of Percentile Length of Six Different Estimators of Dispersion for Score Data with and without Outliers by Jackknife 

