I] Introduction \\\ 



(8) Midpanel Central Difference doubly Finial Formula (h and k botti limited). 



- i </> {(4 



These formulae will be found amply illustrated later in the present volume, 

 and it seems unnecessary to do more than cite them here. 



TABLE I. 



Ordinates of Normal Curve to five figures for each Permille of Frequency. 

 (Biometrika, Vol. xni. pp. 426428.) 



This table is an abbreviated form of that to 10 figures given as Table II 

 in this Part II. It is supplementary to Table I of Part I, which provides the 

 abscissae of the normal curve, while this provides the ordinates to each permille of 

 frequency. These tables to five figures are adequate for many statistical purposes, 

 and are particularly useful for representing frequency distributions on a normal 

 scale, when they are given in broad categories, and for plotting a graph in the 

 case of bivariate tables. The second variate may be given either quantitatively, 

 or as the first by broad categories. There is no assumption or approximation 

 made when we plot variates on a normal scale. It is, however, another question 

 whether a regression curve obtained by such plotting will or will not be a straight 

 line. Of course the real assumption comes in when we treat the array of y's for 

 a broad category of a; as itself a normal distribution in y. Assuming first that 

 the whole distribution is normal, the array of y's corresponding to a given broad 

 category of x, ranging from x to x%, will be given by 



__ 

 - L_ - e 21 



2-0- <r - 2 



/, 277-0-3 <r v VI -r 2 

 in the usual notation. 

 This may be written 



If we treat x as constant in the term y rx of the second exponential, we 



<T X 



can integrate out and there results, if n x be the total frequency in the category 

 and 25 the constant value given to x, 



l 1 / <r. V 



II * rr \ 

 ~ Q /I 'r?\ ' V / 



a normal distribution in y, with standard deviation that of the indefinitely small 



