420 
Miscellanea 
The following table gives the theoretical frequencies of this curve compared with the observed 
frequencies and the theoretical frequencies for the two curves fitted by Professor Edgeworth. 
These last being obtained by multiplying the values he gives of the theoretical relative frequencies 
by 25,000. 
TABLE II. 
Number of trumps 
-7 
0 
1 
2 
3 
4 
5 
6 
7 
8 
9 
10 
Totals 
Observed frequency 
215 
1724 
5262 
7440 
6371 
2950 
852 
166 
20 
25000 
Type I 
4-91 
202-85 
1698-32 
5201 -23 
7643-49 
6218-30 
2993- 16 
871-65 
152-89 
15-34 
•85 
•02 
25003 
Sum = 
='207-76 
Sum 
= 16-21 
Prof. Edgeworth's 
1st curve, p. 461 
5120 
7338 
6128 
3028 
Prof. Edgeworth's 
2nd curve, p. 467 
258 
1778 
5093 
7420 
6183 
3098 
965 
208 
25003 
For the Type I curve = 13-60 while n' = 9 so that P = -0938. 
Professor Edgeworth's first curve gives x~ = 1'7'48, n' = 4 and P= -000574*. His second 
curve gives x- = 41-55 for n' = 8 so that P is less than -000001. If in the second curve we take 
the four central compartments only (i.e. 2 to 5 trumps) we have x^ = 19-48, v' = 4 so that 
P = -000222. 
Judged by the usual criterion then, both of Professor Edgewortli's curves are a very much 
poorer fit than Pearson's Type I. If we calculate tlio value of tlie criterion proposed by Pi-ofessor 
Edgeworth we find that 
8 {e-/U) is -000814 for Professor Edgeworth's first cm-ve (four compartments), 
-00181 for eight compartments of his second curve, 
and -00077 for the four central compartments of the second curve. 
These values of S (e^/U) may be compared with -000544 for nine compartments or -000420 for 
four compartments for Pearson's Type I. 
Professor Edgeworth says (p. 467) of this example that "the correspondence between fact 
and theory is very satisfactory." 
Example II. The theorelical Frequency Distribution of black Balls in 210 Draws 
of four Balls out of a Bag containing four ivMte and six blach Balls. 
The frequencies are 
TABLE III. 
0 
•5 
3 
4 
Total 
i 
i 1 
24 
90 
80 
15 
210 
The mean is at 2-4 black balls, the moments about the mean are fx^ = '64, /X3 = - -032, = 1^- 
so that I3i = -00390625, /3., = 2-747768. The corresponding Pearsonian frequency curve is of 
Type II, 
9.,')938124 
represented by the continuous line in Fig. 2. The origin is at mode = mean = 2-4. 
* Professor Edgeworth calls this x^=40, n' =6 but only states the calculated (relative) frequencies 
for four compartments. 
y = 101-06905 
(3-7341772)2 
