Abstract:
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
