APPLICATION OF STATISTICAL METHODS 81 



nidnu-nts anil tin- factors, such as the average, standard dexiation, 

 k and fii should be given. These factors provide us with measures of 

 the lack of syninu'trv', and can be used as pointed out in the previous 

 sections of this paper. Recording this amount of data makes it 

 possible for anyone interested, either to check the calculations of the 

 theoretical frwjuencics anti the conclusions derived therefrom, or to 

 calculate a different theoretical distribution based upon fundamentally 

 different hypotheses in a way such as has been illustrated already 

 in the iliscussion of the distribution of measurements of the cephalic 

 index, as given in Fig. 11. 



In most instances, ho\ve\er, it is liighK" probable that the man who 

 originally prepares the chart is charged with the responsibility of 

 choosing the best distribution, and, therefore, the chief interest of 

 those reailing the report is centered upon the conclusions indicated 

 therein. The graphical representation of the observed distribution 

 by means of the histogram is hopeful. The comparison of this with 

 the theoretical curve represented by a solid line shows qualitatively 

 whether or not the product is changing. The probability of fit gives 

 a quantitative measure of the degree of fit. The set of curves given 

 in Fig. 12 is drawn to illustrate a condition which may sometimes 

 happ)en when, for example, the standards used in the machines have 

 been changed. This is only typical of the results which may be 

 expected. Obviously, the form of such reports designed to meet 

 sf)ecific conditions will vary. That presented above is only typical 

 of one which has been found to be of value in presenting the analysis 

 of the results of inspection of certain types of apparatus. 



so.me .^dv.^ntages derived from a compar.\tively complete 

 Statistical Analysis 



It has been pointed out that the value of either a physical or an 

 engineering interpretation of data depends upon the success attained 

 in deriving the best theoretical distribution. This is the equation 

 which fits the observed points best, and which, if possible, can be 

 interpreted physically. The previous discussion indicates the way 

 in which different causal relationships tend to produce typical fre- 

 quency distributions, and also the way in which statistical methods 

 may be used in finding a theoretical distribution which yields a 

 physical interpretation. 



This point has been illustrated by several examples. It has been 

 shown that by a proper choice of theoretical curve a ver\' close ap- 

 proximation to an obser\x'd distribution can be obtained. This 



