Estimating Average Variation About the Population Mean Using Geometric Measure of Variation

Troon John Benedict; Karanjah Anthony; Alilah Anekeya David

doi:doi:10.11648/j.ijsd.20200602.11

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Estimating Average Variation About the Population Mean Using Geometric Measure of Variation

Troon John Benedict, Karanjah Anthony, Alilah Anekeya David

Published in International Journal of Statistical Distributions and Applications (Volume 6, Issue 2)

Received: 17 September 2019 Accepted: 16 October 2019 Published: 25 August 2020

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Abstract

Measures of dispersion are important statistical tool used to illustrate the distribution of datasets. These measures have allowed researchers to define the distribution of various datasets especially the measures of dispersion from the mean. Researchers and mathematicians have been able to develop measures of dispersion from the mean such as mean deviation, variance and standard deviation. However, these measures have been determined not to be perfect, for example, variance give average of squared deviation which differ in unit of measurement as the initial dataset, mean deviation gives bigger average deviation than the actual average deviation because it violates the algebraic laws governing absolute numbers, while standard deviation is affected by outliers and skewed datasets. As a result, there was a need to develop a more efficient measure of variation from the mean that would overcome these weaknesses. The aim of the paper was to estimate the average variation about the population mean using geometric measure of variation. The study was able to use the geometric measure of variation to estimate the average variation about the population mean for un-weighted datasets, weighted datasets, probability mass and probability density functions with finite intervals, however, the function faces serious integration problems when estimating the average deviation for probability density functions as a result of complexity in the integrations by parts involved and also integration on infinite intervals. Despite the challenge on probability density functions, the study was able to establish that the geometric measure of variation was able to overcome the challenges faced by the existing measures of variation about the population mean.

Published in	International Journal of Statistical Distributions and Applications (Volume 6, Issue 2)
DOI	10.11648/j.ijsd.20200602.11
Page(s)	23-35
Creative Commons	This is an Open Access article, distributed under the terms of the Creative Commons Attribution 4.0 International License (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted use, distribution and reproduction in any medium or format, provided the original work is properly cited.
Copyright	Copyright © The Author(s), 2020. Published by Science Publishing Group

Keywords

Standard Deviation, Geometric Measure of Variation, Deviation About the Mean, Average, Mean, Absolute Deviation, Estimation

References

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[18]	Roberson, Q. M., Sturman, M. C., & Simons, T. L., (2007). Does the Measure of Dispersion Matter in Multilevel Research? A Comparison of the Relative Performance of Dispersion Indexes. Cornell University School of Hotel Administration. The Scholarly Commons.
[19]	Roenfeldt, K., (2018). Better than average: Calculating Geometric Means Using SAS. Henry. M. Foundation for the Advancement of Military Medicine.
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Troon John Benedict, Karanjah Anthony, Alilah Anekeya David. (2020). Estimating Average Variation About the Population Mean Using Geometric Measure of Variation. International Journal of Statistical Distributions and Applications, 6(2), 23-35. https://doi.org/10.11648/j.ijsd.20200602.11

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ACS Style

Troon John Benedict; Karanjah Anthony; Alilah Anekeya David. Estimating Average Variation About the Population Mean Using Geometric Measure of Variation. Int. J. Stat. Distrib. Appl. 2020, 6(2), 23-35. doi: 10.11648/j.ijsd.20200602.11

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AMA Style

Troon John Benedict, Karanjah Anthony, Alilah Anekeya David. Estimating Average Variation About the Population Mean Using Geometric Measure of Variation. Int J Stat Distrib Appl. 2020;6(2):23-35. doi: 10.11648/j.ijsd.20200602.11

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@article{10.11648/j.ijsd.20200602.11,
  author = {Troon John Benedict and Karanjah Anthony and Alilah Anekeya David},
  title = {Estimating Average Variation About the Population Mean Using Geometric Measure of Variation},
  journal = {International Journal of Statistical Distributions and Applications},
  volume = {6},
  number = {2},
  pages = {23-35},
  doi = {10.11648/j.ijsd.20200602.11},
  url = {https://doi.org/10.11648/j.ijsd.20200602.11},
  eprint = {https://article.sciencepublishinggroup.com/pdf/10.11648.j.ijsd.20200602.11},
  abstract = {Measures of dispersion are important statistical tool used to illustrate the distribution of datasets. These measures have allowed researchers to define the distribution of various datasets especially the measures of dispersion from the mean. Researchers and mathematicians have been able to develop measures of dispersion from the mean such as mean deviation, variance and standard deviation. However, these measures have been determined not to be perfect, for example, variance give average of squared deviation which differ in unit of measurement as the initial dataset, mean deviation gives bigger average deviation than the actual average deviation because it violates the algebraic laws governing absolute numbers, while standard deviation is affected by outliers and skewed datasets. As a result, there was a need to develop a more efficient measure of variation from the mean that would overcome these weaknesses. The aim of the paper was to estimate the average variation about the population mean using geometric measure of variation. The study was able to use the geometric measure of variation to estimate the average variation about the population mean for un-weighted datasets, weighted datasets, probability mass and probability density functions with finite intervals, however, the function faces serious integration problems when estimating the average deviation for probability density functions as a result of complexity in the integrations by parts involved and also integration on infinite intervals. Despite the challenge on probability density functions, the study was able to establish that the geometric measure of variation was able to overcome the challenges faced by the existing measures of variation about the population mean.},
 year = {2020}
}

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TY  - JOUR
T1  - Estimating Average Variation About the Population Mean Using Geometric Measure of Variation
AU  - Troon John Benedict
AU  - Karanjah Anthony
AU  - Alilah Anekeya David
Y1  - 2020/08/25
PY  - 2020
N1  - https://doi.org/10.11648/j.ijsd.20200602.11
DO  - 10.11648/j.ijsd.20200602.11
T2  - International Journal of Statistical Distributions and Applications
JF  - International Journal of Statistical Distributions and Applications
JO  - International Journal of Statistical Distributions and Applications
SP  - 23
EP  - 35
PB  - Science Publishing Group
SN  - 2472-3509
UR  - https://doi.org/10.11648/j.ijsd.20200602.11
AB  - Measures of dispersion are important statistical tool used to illustrate the distribution of datasets. These measures have allowed researchers to define the distribution of various datasets especially the measures of dispersion from the mean. Researchers and mathematicians have been able to develop measures of dispersion from the mean such as mean deviation, variance and standard deviation. However, these measures have been determined not to be perfect, for example, variance give average of squared deviation which differ in unit of measurement as the initial dataset, mean deviation gives bigger average deviation than the actual average deviation because it violates the algebraic laws governing absolute numbers, while standard deviation is affected by outliers and skewed datasets. As a result, there was a need to develop a more efficient measure of variation from the mean that would overcome these weaknesses. The aim of the paper was to estimate the average variation about the population mean using geometric measure of variation. The study was able to use the geometric measure of variation to estimate the average variation about the population mean for un-weighted datasets, weighted datasets, probability mass and probability density functions with finite intervals, however, the function faces serious integration problems when estimating the average deviation for probability density functions as a result of complexity in the integrations by parts involved and also integration on infinite intervals. Despite the challenge on probability density functions, the study was able to establish that the geometric measure of variation was able to overcome the challenges faced by the existing measures of variation about the population mean.
VL  - 6
IS  - 2
ER  -

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Author Information

Troon John Benedict

Department of Mathematics and Physical Science, Maasai Mara University, Narok, Kenya
Karanjah Anthony

Department of Mathematic, Multimedia University, Nairobi, Kenya
Alilah Anekeya David

Department of Mathematics and Statistics, Masinde Muliro University of Science and Technology, Kakamega, Kenya

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Plain Text BibTeX RIS

APA Style

Troon John Benedict, Karanjah Anthony, Alilah Anekeya David. (2020). Estimating Average Variation About the Population Mean Using Geometric Measure of Variation. International Journal of Statistical Distributions and Applications, 6(2), 23-35. https://doi.org/10.11648/j.ijsd.20200602.11

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ACS Style

Troon John Benedict; Karanjah Anthony; Alilah Anekeya David. Estimating Average Variation About the Population Mean Using Geometric Measure of Variation. Int. J. Stat. Distrib. Appl. 2020, 6(2), 23-35. doi: 10.11648/j.ijsd.20200602.11

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AMA Style

Troon John Benedict, Karanjah Anthony, Alilah Anekeya David. Estimating Average Variation About the Population Mean Using Geometric Measure of Variation. Int J Stat Distrib Appl. 2020;6(2):23-35. doi: 10.11648/j.ijsd.20200602.11

Copy | Download

@article{10.11648/j.ijsd.20200602.11,
  author = {Troon John Benedict and Karanjah Anthony and Alilah Anekeya David},
  title = {Estimating Average Variation About the Population Mean Using Geometric Measure of Variation},
  journal = {International Journal of Statistical Distributions and Applications},
  volume = {6},
  number = {2},
  pages = {23-35},
  doi = {10.11648/j.ijsd.20200602.11},
  url = {https://doi.org/10.11648/j.ijsd.20200602.11},
  eprint = {https://article.sciencepublishinggroup.com/pdf/10.11648.j.ijsd.20200602.11},
  abstract = {Measures of dispersion are important statistical tool used to illustrate the distribution of datasets. These measures have allowed researchers to define the distribution of various datasets especially the measures of dispersion from the mean. Researchers and mathematicians have been able to develop measures of dispersion from the mean such as mean deviation, variance and standard deviation. However, these measures have been determined not to be perfect, for example, variance give average of squared deviation which differ in unit of measurement as the initial dataset, mean deviation gives bigger average deviation than the actual average deviation because it violates the algebraic laws governing absolute numbers, while standard deviation is affected by outliers and skewed datasets. As a result, there was a need to develop a more efficient measure of variation from the mean that would overcome these weaknesses. The aim of the paper was to estimate the average variation about the population mean using geometric measure of variation. The study was able to use the geometric measure of variation to estimate the average variation about the population mean for un-weighted datasets, weighted datasets, probability mass and probability density functions with finite intervals, however, the function faces serious integration problems when estimating the average deviation for probability density functions as a result of complexity in the integrations by parts involved and also integration on infinite intervals. Despite the challenge on probability density functions, the study was able to establish that the geometric measure of variation was able to overcome the challenges faced by the existing measures of variation about the population mean.},
 year = {2020}
}

Copy | Download

TY  - JOUR
T1  - Estimating Average Variation About the Population Mean Using Geometric Measure of Variation
AU  - Troon John Benedict
AU  - Karanjah Anthony
AU  - Alilah Anekeya David
Y1  - 2020/08/25
PY  - 2020
N1  - https://doi.org/10.11648/j.ijsd.20200602.11
DO  - 10.11648/j.ijsd.20200602.11
T2  - International Journal of Statistical Distributions and Applications
JF  - International Journal of Statistical Distributions and Applications
JO  - International Journal of Statistical Distributions and Applications
SP  - 23
EP  - 35
PB  - Science Publishing Group
SN  - 2472-3509
UR  - https://doi.org/10.11648/j.ijsd.20200602.11
AB  - Measures of dispersion are important statistical tool used to illustrate the distribution of datasets. These measures have allowed researchers to define the distribution of various datasets especially the measures of dispersion from the mean. Researchers and mathematicians have been able to develop measures of dispersion from the mean such as mean deviation, variance and standard deviation. However, these measures have been determined not to be perfect, for example, variance give average of squared deviation which differ in unit of measurement as the initial dataset, mean deviation gives bigger average deviation than the actual average deviation because it violates the algebraic laws governing absolute numbers, while standard deviation is affected by outliers and skewed datasets. As a result, there was a need to develop a more efficient measure of variation from the mean that would overcome these weaknesses. The aim of the paper was to estimate the average variation about the population mean using geometric measure of variation. The study was able to use the geometric measure of variation to estimate the average variation about the population mean for un-weighted datasets, weighted datasets, probability mass and probability density functions with finite intervals, however, the function faces serious integration problems when estimating the average deviation for probability density functions as a result of complexity in the integrations by parts involved and also integration on infinite intervals. Despite the challenge on probability density functions, the study was able to establish that the geometric measure of variation was able to overcome the challenges faced by the existing measures of variation about the population mean.
VL  - 6
IS  - 2
ER  -

Copy | Download