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C\\ll 



Theoretical values of the moment coefficients of the sampling dihtribution of 

 the range, w, have been given by Tippett, but lengthy computation in required to 

 put these results into numbers; Tippett however carried through the following 

 work : 



(1) Computed the mean range, w, in terms of the population standard deviation 

 as unit for samples of sizes 2 to 1000. This is given in Table XXII. 



(2) Calculated the values of the standard deviation of range, <r w , for samples 

 of a few selected sizes. 



(3) Gave approximations to the moment constants fti and ft t for certain larger 

 samples. 



The problem of smaller samples was considered later more fully by E. S. Pearson 

 who obtained the numerical values for the first four moment coefficients of the distri- 

 bution of range for n = 2, 3, 4, 5 and 6, and suggested a method of approximating 

 to /?i and /3 2 between n 6 and n = 100. A summary of these combined results is 

 given below; the values of w are given more fully in the main table, XXII. Inter- 

 mediate values for <r w , & and $ 2 for n >10 may be found with reasonable accuracy by 



Moment Constants of the Distribution of Range, w. 



graphical interpolation. Using these values for the moment constants "Student 

 has calculated Pearson curves to represent the distribution of range in the cases 

 n = 2, 3, 4, 5, 6, 10, 20 and 60. The equations of these curves referred to their 

 modes as origin are given on p. 163 of his paper referred to above. Partly from 

 these curves and partly from interpolation he obtained the following table, in 



