Essay on the Interpretation of Milk Records^. 157 



Details of Method. — A class unit of 100 gallons was taken 

 for totals. In all other cases the unit was two quarts. 



The mode was calculated from the formula — 

 Mode = mean— 3 (mean — median), 

 which gives a reasonably close value in most cases.^ ^ 



The modal coefficient is the percentage of variates falling 



on the empirical mode. It thus gives a measure of conformity 



, , _,, . mean — mode ^ 

 to type. Skewness is • 



The probable errors of the various constants have been 

 calculated from the following formulae : — 



P.E.^ean == ± 0-6745-^. 

 V n 



P.E.niedian=± 0-84535-^ H 



= ± 1-25332 XP.E.naean. O 



P.E.o- = ± 0-6745 -^ C) 



P.E.^.„e.- ±0-6745 V'l, v^T+Wn " 

 P.E.r, = ± 0-6745 V n_^2('— V]* 



These formulie are only strictly correct in cases of normal distribution. 



From the table of constants it is seen that the mean of the 

 revised maximum is about one quart above the mean of the 

 averages, while the mean maximum is about one pint higher 

 still. 



Both median and mode are less than the mean in every 

 case, showing the curves to have positive skewness. It is least 



> K. Pearson : Blometriha, Vol. I., page 260. 1902. 



' C. V. L. Charlier : Meddelandenfran Lundi AttronomisTta Ohserratorium, 

 Series II., No. 4 Kongl. Fysiografiska Sallskapets Handlingar, Bd. 16, pp. 

 1-51. Lund, 1906. 



' K. Pearson : " Skew Variation in Homogeneous Material," Pkil. Trant. 

 Roy. iSoc, clxxxvi., 1895, page 370. 



" W. F. Sheppard : Phil. Trans. Boy. Soc, clxlii., 1898, page 101. 



•'■ Raymond Pearl : " Biometric Study of Egg Production," U.S. Bureau 

 Animal InduKtry, Bull, 110, page 23. 



" Raymond Pearl: Biometrika. Vol. VI., pp. 112-117, 1908. This author 

 shows that this formula can only be used when curves approximate to the 

 normal. 



" L. N. G. Filon and K. Pearson : Phil. Trans. Boy. Soc, clxli., 1898, 

 page 229. 



