The Best Unbiased Estimate of Population Standard Deviation Based on Group Ranges

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Abstract
In order to better the efficiency of the statistic range for sample sizes greater than eleven, a method, which possesses practical efficiency, is given in this paper for dividing a sample into groups so that an estimate of the standard deviation of the normal population sampled can be formed from a linear function of the group ranges. The estimate so obtained is “best” in the sense that it is unbiased and has a smaller variance than any other estimate which is based on a linear compound of group ranges. In dividing a sample into groups for using the range of groups, it is shown in the Appendix that the most efficient group size is eight. Table I of this paper gives the approximate percentage points for the best unbiased estimate based on group ranges and Table II gives approximate percentage points for the estimate based on mean range determined from r groups or samples of equal size n.

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