Determining the Unbiased Estimator of the Population Geometric Measures of Variation About the Mean

Abstract

Geometric Measures of Variation about the mean is a measure that uses the geometric averaging technique to average the deviations from the mean. From previous studies, it has been determined that the measure is more precise in estimating the average variation about the mean than the existing measures of variation about the mean. Given that the technique is a newly introduced technique of estimating the average variation about the mean, the actual sample estimator for the measure is still unknown, as a result, the study aimed at determining the unbiased estimator for the population geometric measure. The study used a mathematical estimation technique to determinethe unbiased estimator among the existing possible estimators as it assumed a simple random sampling without replacement technique. The study determined that the unbiased estimator of the population estimator was the sample estimator which did not allow one degree of freedom.