By Student 
307 
Putting n = 8 we get the equation y = y„ (1 — x-f and 
■1429 ± -0050 instead of actual -1392, 
•0476 ± -0038 „ „ -0454, 
C7 = -3780 ± -0066 „ „ -3731, 
= 2T 
/3, = 3 -§ = 2-333 + -012 
2-336. 
3 021 
The equation calculated from the actual moments is y = ?/„ — . ^^q^ ) whence 
the calculated range is r98, whereas it is known to be 2. 
The foUoAving tables compare the actual distributions with those calculated from 
the equations. 
Distribution of r from samples of 4 coinjxtred luith the equation 
i-^il-xj. 
00 
'O 
1 
o 
1 
c 
00 
+ 
O 
+ 
^2 
4- 
o 
+ 
+ 
o 
+ 
op 
+ 
Actual . . . 
Calculated 
Difference 
64 
65 
45^ 
56" 
-m 
56 
67 
56 
59 
56 
62 
56 
+ 11 
+ 3 
+ 6 
63 
56 
+ 7 
58 
56 
60 
56 
64 
56 
5U 
56" 
+ 4 +8 
-41 
4U 
56" 
54 
65 
14* 
11 
From this we get = 13'30, P = •34. It will however be noticed that the grouping 
has caused all the middle compartments to contain more than the calculated, as 
pointed out above. 
Distribution of r front samples of 8 compared ivith the equatioji 
750 X 1.5 
2/=— . 
00 
I 
o 
-1.3 
00 
SO 
+ 
+ 
o 
+ 
o 
+ 
4- 
o 
00 
+ 
Actual ... 
Calculated 
2 
4i 
27 
204 
44 
43 
60 
67 
96 
87 
114i 
100| 
103 
105 
lOOi 
98h 
87" 
65 
67 
374 
43" 
14* 
20| 
3 
Difference 
•2* 
+ 6i 
+ 1 
-7 +9 
+ 14 
154 
+ 1U 
-2 
54 
-6 
-IJ 
whence x" = 13 94, P = -30. 
39—2 
