clviii Tables for Statisticians and Biometricians [XXXII XXXIV 



Interspace between ordinates in terms of s.D. 



X-81 + -x -19 = -2254. 



2279 -1994 



We have put down this method of obtaining these quantities in order that the 

 reader may understand what their nature is, but they are more accurately and 

 more readily obtained from Table XXXIV, p. 220. Here for n = 13, p = -5 and p = '6 

 we have 



Origin to Mean 2-123,6943, 2-925,3194, 



and Abscissal Unit . -219,3627, '250,7341. 



Hence interpolating* -19 to -81, Origin to Mean in terms of s.D. 



= 2-123,6943 x -81 + 2'925,3194 x -19 = 2'2763. 

 Abscissal Unit of interspace between ordinates 



= -219,3627 x -81 + -250,7341 x -19 = "2253. 



The present values are to be preferred as Table XXXIV is based on more 

 figures for mean and standard deviations than are provided in Table XXXII. 

 Accordingly for our present data with standard deviation = 13*5078 we have 



Distance from Origin to Mean = 2'276,000 x 13-5078 = 307438, 

 Abscissal Unit = '225,323 x 13-5078 = 3'0436. 

 We may determine in the same way the position of the mode. 

 Distance of Mode from Oriin 



Now one point needs attention. The /* 3 of the r-frequency curve is negative, 

 but that of our data is positive', the r-frequency curve must therefore be reversed 

 and we thus obtain 53*5799 for the origin in units of our original data, to which we 

 add abscissal units 3'0436 to obtain the abscissae on the positive side, i.e. the side 

 of decreasing frequencies, and subtract the same 3*0436 continuously to obtain 

 the abscissae on the negative side. Column (i) in the following table gives these 

 abscissae in actual units of the data. On this scale the mode will be at 



53-5799 - 37*2082 = 16*3717. 



In Columns (ii) and (iii) we have the ordinates, y ti and y Hi , of each of the 

 distributions n = 13, p = '5 and p = "6; in Column (iv) we have the interpolated 

 values 2/ iv . But these are not what we require, for they are based on an abscissal 



* The differences of the table are too unsatisfactory, the intervals of n being large, to stand more 

 than linear interpolation. But the result shown in the diagram on p. clx below indicates that this 

 interpolation is sufficient. 



6093 x 13*5078 



f As found from the value the distance is 36-991, a difference of only 0'4 / . 



' 



