On the Statistical Usefulness and Application of Sample Range

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We gave so far the g.l.b. and the l.u.b. of the second moment centered at the mean, so called s.s., by using the range R, and similar basic formulae for various data structures mathematically. We also devised the ways to prove them. In order to investigate the relation statistically, we give a table of correction multipliers of R to give unbiased estimates of the population standard deviation σ, a table of enciency of estimation by R compared with estimation by the sample standard deviation、 s, etc. Thereafter illustrative examples by practical data and a consideration to effective usage of the range R are given

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