xcvi Tables for Statisticians and Biometricians [XV 



As a rule the probable error of the mode is greater than that of the mean, and 

 can, as we approach J -shaped curves, become very great. On the other hand in the 

 case of U-shaped curves, the probable error of the mode, in this case an "anti- 

 mode," can be less than that of the mean. 



Notwithstanding the labour involved in the preparation of Table XV, first 

 difference interpolation is for the most part inadequate and higher difference 

 formulae must be used. 



Illustration (i). For the distribution of 4018 observations of the barometric 

 height at Laudale the following constants were found by Yasukawa * : 



Mean = 29"'85699, a = 0"'3845285, 

 & = -203,9448, fa = 3-200,5312. 



The midpanel central difference formula was used. The interpolate divides 

 the square formed by the four nearest interpolants in the #-ratio 6, </> (= 1 6) 

 and the y-ratio %, i/r (= 1 %). (See diagram on p. xviii of this Part II.) The re- 

 quired formula is 



) o 



Whence from the table we have 



3 



4. 2-1187 1-9797 



and for the differences we get 



S%o = '0160, 

 S 2 * 1)0 = -0281, 

 S%i = '0126, 



S 2 *!,! = '0210, 

 * Data from Phil. Trans. Vol. 190, A (1897), p. 429; Biometrika, Vol. xvin. pp. 283285. 



