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Modelling Geometric Measure of Variation About the Population Mean
American Journal of Theoretical and Applied Statistics
Volume 8, Issue 5, September 2019, Pages: 179-184
Received: Sep. 17, 2019; Accepted: Sep. 28, 2019; Published: Oct. 12, 2019
Authors
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
Article Tools Abstract PDF (320KB)
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 this paper was to model a geometric measure of variation about the population mean which could overcome the weaknesses of the existing measures of variation about the population mean. The study was able to formulate the geometric measure of variation about the population mean that obeyed the algebraic laws behind absolute numbers, which was capable of further algebraic manipulations as it could be used further to estimate the average variation about the mean for weighted datasets, probability mass functions and probability density functions. Lastly, the measure was not affected by outliers and skewed datasets. This shows that the formulated measure was capable of solving the weaknesses of the existing measures of variation about the mean.
Keywords
Standard Deviation, Geometric Measure of Variation, Deviation About the Mean, Average, Mean, Absolute Deviation
Troon John Benedict, Karanjah Anthony, Alilah Anekeya David, Modelling Geometric Measure of Variation About the Population Mean, American Journal of Theoretical and Applied Statistics. Vol. 8, No. 5, 2019, pp. 179-184. doi: 10.11648/j.ajtas.20190805.13
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