512 On the Distribution of the Means of Samples 
TABLE IV. 
Actually Observed Frequencies of the Samples from 20,000 Cells. 
Samples of 25 
Samples of 50 
AMPLER OF 
100 

Number of 
Number of 
Number of 
Number of 

JNumoer 01 
Number of 
Bacilli per Sample 
Samples 
Bacilli per Sample 
Samples 
Bacilli pel' Sample 

Samples 
44- 51 
1 
112—123 
2 
267 — 282 
2 
52— 59 
U 
124-135 
9 
283 — 298 
9 
60— 67 
38 
136—147 
21 
299 — 314 
4 
68— 75 
74 
148—159 
30 
315 — 330 
13 
76— 83 
128 
160—171 
58 
331—346 
29 
gj 
145 
H ■y2 1 83 
83 
36 
92— 99 
147 
184—195 
71 
363—378 
34 
100—107 
113 
196—207 
64 
379—394 
34 
108—115 
74 
208—219 
31 
395—410 
15 
116—123 
37 
220—231 
15 
411-426 
11 
124—131 
19 
232—243 
10 
427—442 
5 
132—139 
7 
244—255 
3 
443— 4B8 
3 
140—147 
2 
256—267 
1 
459—474 
1 
148—155 
0 
268—279 
0 
475—490 
1 
156—163 
0 
280- 291 
1 
491—506 
2 
164—171 
0 
292—303 
1 
507—522 
1 
172—179 
1 
Totals 
800 
400 
200 
includes samples with 76 and samples with 83 bacilli per 25 cells. For convenience 
of calculation, we took an arbitrary origin and unit of grouping in each case. In 
obtaining the moment coefficients Sheppard's corrections were used in all cases ; 
Table V gives the constants and equations, Graphs 3, 4, 5 illustrate the curves. 
TABLE V. 
Curves Resulting from an Analysis of the 20,000 Cells. 
Material 
Number of 
Samples 
Mean (in terms 
of Bacilli per 
Sample) 
Mode (in terms 
of Bacilli per 
Sample) 
<r (in terms 
of Bacilli) 
P. 
ft 
Samples of 25 
Samples of 50 
Samples of 100 
800 
400 
200 
92-04 
184-07 
367-62 
89-7488 
181-3964 
360-2632 
16-7184 
25-7496 
39-9824 
-1033 
-1467 
-3004 
3- 4321 
4- 0907 
4-3500 
Material 
m 
Skewness 
P(Fit) 
Samples of 25 
Samples of 50 
Samples of 100 
■1436 
•0665 
•1367 
25-2068 
10^1436 
10-1723 
13-6033 
6-0718 
6-0862 
10 -.3220 
2-7070 
- 4-0483 
9-5149 
6- 2691 
7- 0316 
-4321 
1 -0907 
1 -3500 
-1:571 
-1066 
-1840 
-9765 
-8673 
•1727 
