THEORY OF STATISTICS, 
EXERCISES. 
1. (Ref. 4: total of columns of all the 13 tables given.) 
Compare the actual with the theoretical mean and standard-deviation for 
the following record of 6500 throws of 12 dice, 4, 5, or 6 being reckoned 
as a ‘‘ success.” 
Successes. Frequency. Successes. Frequency. 
0 1 7 1351 
14 3 844 
103 9 391 
302 10 117 
71 11 21 
1231 12 3 
: 1411 - = 
Total 6500 
2. (Ref. 1.) 
Balls were drawn from a bag containing equal numbers of black and white 
balls, each ball being returned before drawing another. The records were then 
grouped by counting the number of black balls in consecutive 2’s, 3’s, 4’s, 5’s, 
etc. The following give the distributions so derived for grouping by 5%, 6, 
and 7’s. Compare actual with theoretical means and standard-deviations. 
(a) Groupin (6) Groupin ¢) Grouping 
Successes by F a 2 by or 2 oe es 
= 30 17 9 
125 65 34 
277 i 166 104 
224 | 192 | 151 
136 166 148 
27 69 95 
— 40 
— — 4 
Total E ) 
3. (Ref. 2, p. 22.) 
Ten thousand drawings of a ball from a bag containing equal numbers of 
black and white were made in the same manner as in the preceding example, 
and then grouped into 100 sets of 100. The following gives the resulting 
frequency of different numbers of white balls. Compare mean and standard- 
deviation with theory. 
Number, Frequency. ~ Number. Frequency: Number. Frequency. 
34 1 44 54 R 
35 - 45 : 55 
36 —- 46 56 ) 
o - a 4 7 7 , 
3 . 
; : be 9 = 
4 i) , JO ? 
4. Li 5 ol y 
42 52 1 62 ’ 
43 53 63 
274 
81y 683 5QF