Range (of variation of a sample)

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The difference

between the largest and smallest values in the ordered sample

obtained by taking independent measurements of the same random variable . Let be the distribution function of the random variable . Then the probability distribution for the range is


[1] B.L. van der Waerden, "Mathematische Statistik" , Springer (1957)
[2] L.N. Bol'shev, N.V. Smirnov, "Tables of mathematical statistics" , Libr. math. tables , 46 , Nauka (1983) (In Russian) (Processed by L.S. Bark and E.S. Kedrova)


The range of variation of a sample is also called the sample range.


[a1] D.B. Owen, "Handbook of statistical tables" , Addison-Wesley (1962)
How to Cite This Entry:
Range (of variation of a sample). Encyclopedia of Mathematics. URL:
This article was adapted from an original article by T.Yu. Popova (originator), which appeared in Encyclopedia of Mathematics - ISBN 1402006098. See original article