Sept. IS, I9I9 Variation in Milk of Ayrshire Cows 311 



24.7018 , V 172.7511 



'+16:6^; (^-^6:7;^; Pearson's Type I. 



(^ .16.6417/- ^ X32-07SS 



—34/ 3;2 \ -36-1987 147.9872 tan-'^^— 



10 years. .>'=9.6682 X 10 ( i4" ) e ' Pearson's Type IV 



11 years. .7=24.9882(^1-^3^-^^ J Pearson's Type II. 



~^°/ X- \— 32.0148 106.7238 tan-i^y^g— 



12 years. .)'=2. 5479 X 10 ( i-j ^-7 — j g " Pearson 'sTypelV. 



From Tables VII and VIII and the accompanying curves the follow- 

 ing points are to be noted : 



1. It is apparent that the fitted curves give very good graduations 

 of the data throughout. Pearson's generalized probability curve has 

 been shown by experience to be applicable in one or another of its types 

 to so wide a range of cases that a new application calls for no special 

 mention. However the continued addition of new classes of data 

 easily and perfectly graduated by these curves is the best refutation 

 of the criticisms which were formerly made against them. 



2. The general tendency of these milk production and fat percentage 

 variation curves is plainly toward positive skewness. All of these 

 curves show a positive skewness, with the single exception of the mean 

 weekly yield curve for cows 1 1 years old. There the skewness is minus 

 but in comparison with its positive error (on the basis of the normal 

 curve) is insignificant. In other words, this curve for 11 -year-old cows 

 is, within the limits of error of random sampling, a symmetrical distribu- 

 tion. All the others are skew in the positive direction, or, in other 

 words, the mean is greater than the mode. 



3. Considering the probable error of this skewness on the basis of a 

 normal curve, it is seen that in 7 out of the 10 curves for the mean weekly 

 yield the skewness is three or more times its probable error. In 2 cases 

 it is somewhat less than three times its probable error, while in i case 

 the skewness is certainly insignificant — that for 11 years, as already 

 noted. In the case of fat content 9 out of the 11 curves show a skew- 

 ness three or more times the probable error. In 2 of the remaining 

 cases the skewness is nearly three times the probable error, while in i 

 case — that of the 12-year-old cows where the number of individuals 

 concerned is small — the skewness is distinctly less than three times its 

 probable error. From these figures it is plain that in general these 

 Ayrshire milk variation cur\^es show a significant tendency toward 

 an asymmetry indicated by a positive skewness. 



