516 On the Distribution of the Means of Samples 
We next treated, for purposes of comparison, the selected count of 15,000 cells 
in a similar fashion. Table VI contains the actual frequencies, Table VI A the 
constants and equations. Let us now consider in detail points suggested by these 
analytical results. The values of P show that in all cases the fit is close except in 
that of the sample hundreds. It appeared to us probable that in this case we had 
adopted too fine a unit of grouping, so that we re-worked, using a coarser unit 
which gave 11 groups, with the following result, 
y = 29-9734 (l + ^-^t^^)^) ^ ''''''' ^^"'''''^ ' 
which gives P= -232. 
This finding confirms the suggestion to some extent, but it must be admitted 
that the lOO's are still definitely less satisfactory than the smaller samples ; the 
explanation of this is not clear. Table VI B, which gives all the actual and 
calculated frequencies reduced to a common scale, will show the reader how little 
change was effected by the rejection of 5000 cells. 
TABLE VI. 
Actually Observed Frequencies of the Samples from 15,000 Cells. 
Samples of 25 
Samples of 50 
Samples of 100 
Number of Bacilli 
Number of 
Number of Bacilli 
Number of 
Number of Bacilli 
Number of 
per Sample 
Samples 
per Sample 
Samples 
per Sample 
Samples 
44- 51 
1 
112—123 
1 
267—282 
2 
52— 59 
11 
124—135 
8 
283—298 
8 
60— 67 
29 
136—147 
15 
299—314 
3 
68— 75 
62 
148—159 
25 
315—330 
10 
76— 83 
98 
160-171 
48 
331—346 
21 
84— 91 
115 
172—183 
66 
347—362 
27 
92— 99 
107 
184—195 
50 
363—378 
30 
100—107 
78 
196—207 
47 
379—394 
27 
108—115 
56 
208—219 
22 
395—410 
10 
116—123 
23 
220—231 
9 
411-426 
6 
124—131 
15 
232—243 
6 
427—442 
3 
132—139 
4 
244—255 
1 
443—458 
1 
140—147 
1 
256—267 
1 
459—474 
0 
268—279 
0 
475—490 
0 
280—291 
1 
491—506 
2 
Totals 
600 
300 
150 
