Efficiency Comparison of the Population Standard Deviation Estimation Methods for Data set with Normal Distribution and Containing Outlier
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Abstract
The objective of this research was to compare the efficiency of four population standard deviation estimation methods, mean absolute deviation, adjusted range, adjusted standard deviation and sample standard deviation – for a normal distribution when data set containing outlier when the lowest absolute bias and the lowest mean square error were used as criteria. Under 90 simulation scenarios that normal distribution with mean equals 30 and the population standard deviation equals 1, 5, 10, 15 and 20, sample size equals 10, 20, 30, 50, 70 and 100 with the percentage of outlier equals 0%, 10% and 20%. The results found that sample standard deviation was the most efficient when the data set not contain outlier and it was more efficient if the sample size was larger, but the efficiency would decrease when standard deviation was increase and found that adjusted standard deviation has more efficient than adjusted range in all situation which the data set not contain outlier and found that mean absolute deviation was the most efficient when the percentage of outlier equals 10% and 20%.
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References
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