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 have been able to develop measures of dispersion from the mean such
as mean deviation, mean absolute deviation, variance and standard deviation. Studies have shown that standard
deviation is currently the most efficient measure of variation about the mean and the most popularly used
measure of variation about the mean around the world because of its fewer shortcomings. However, studies have
also established that standard deviation is not 100% efficient because the measure is affected by outlier in the
datasets and it also assumes symmetry of datasets when estimating the average deviation about the mean a factor
that makes it to be responsive to skewed datasets hence giving results which are biased for such datasets. The
aim of this study is to make a comparative analysis of the precision of the geometric measure of variation and
standard deviation in estimating the average variation about the mean for various datasets. The study used paired
t-test to test the difference in estimates given by the two measures and four measures of efficiency (coefficient
of variation, relative efficiency, mean squared error and bias) to assess the efficiency of the measure. The results
determined that the estimates of geometric measure were significantly smaller than those of standard deviation
and that the geometric measure was more efficient in estimating the average deviation for geometric, skewed
and peaked datasets. In conclusion, the geometric measure was not affected by outliers and skewed datasets,
hence it was more precise than standard deviation.
Keywords:Standard Deviation, Geometric Measure of variation, deviation about the mean, average, mean,
measure of efficiency
