aA THEORY OF STATISTICS.
Twelve Dice thrown 4096 times, a throw of 4, 5, or 6 points re-koned
a success (p. 258).
Expected
Observed P
No. of Frequency ’ (m' —m)?
Successes. F a (m) (m' =m) zon
i 4096(% +3)12
0 0 1 1 1°0000
! 7 12 25 2°0833
60 66 | 36 5455
198 220 484 2°2000
430 495 4225 85354
731 792 3721 4:6982
948 924 576 ‘6234
847 792 3025 38194
536 495 1681 3°3960
257 220 1369 6:2227
1 71 66 25 ‘3788
11 12 i 0833
12 0 1 1°0000
Totals £396 23 ed 34:5860 = y*
From the tables we find :—
n'. x. 2.
13 30 1002792
13 40 ‘000072
Hence, by interpolation for x2=34'5860, P="0015.
Twelve Dice thrown 4096 times, a throw of 6 points reckoned a success.
Expected
No. of el Frequency / 2 (m' =m)?
Frequency (m' —m)% ye iy
Successes. (m) (m) m
: 4096(% + #)'2
n 447 459 144 3137
1145 1103 1764 15993
1181 1213 1024 8442
796 809 x 169 2089
380 364 256 7033
115 116 11 *0086
24 27 J) *3333
7 and over 8] 5 9 1:8000
Totals 3 3 a 58113 ="
From the tables we find :—
n', x> 2
8 5 '659963
8 6 539750
Henee, by interpolation for x2=5'8113, P= 5624.

5 Ps
at 409r
409% 409¢