404 THEORY OF STATISTICS, 
2. To 34= + 0-680, Ti3.04= +0°803, T14.03= + 0-397. 
To3.14= — 0433, To413= ——" 0553, Tgqe10= = 0°149. 
010034 =917, 02.134 =49°2, Op 13=125, 04-103=105"4. 
xX; =53 + 0127 Xo+ 0-587 Xs + 0 ‘0345 X,. 
3. The correlation of the pth order is 7/(1 +7). Hence if » be negative, the 
correlation of order #—2 cannot be numerically greater than unity and r 
cannot exceed (numerically) 1/(n — 1). 
4, TE 719 
5. Ti9.3= — 1; Ti3.9=7T931= +1. 
6. T12.3=713.g=793.7= — 1. 
CHAPTER XIII. 
1. Theo. M=6, 0=1782 : Actual ¥=6°116, o=1"732. 
2. (a) Theo. M=2:5, ¢=1"118 : Actual M=2'48, c=1"14, 
(By, M=5, ‘g=1225. Y= 29] o=120. 
(eS), eM =313 Rr=11 3230: SNM = 3:47 So = 1-40. 
3. Theo. M=50, ¢=5 : Actual M=50°11, ¢=5"23. 
4. The standard deviation of the proportion is 000179, and the actual 
divergence is 54 times this, and therefore almost certainly significant. 
5. The standard deviation of the number drawn is 32, and the actual 
difference from expectation 18, There is no significance. 
6. p=1-02M, n=M/p : p=0'510, n=120 : p=0-454, n=110"4. 
8. Standard deviation of simple sampling 230 per cent. The actual 
standard-deviation does not, therefore, seem to indicate any real variation, but 
only fluctuations of sampling. 
9. Difference from expectation 75 : standard error 10:0. The difference 
might therefore occur frequently as a fluctuation of sampling. 
10. The test can be applied either by the formule of Case II. or Case III. 
Case II. is taken as the simplest. 
(2) (4B)/(B)=69"1 per cent.: (4B)/(B)=80'0 per cent. Difference 109 
per cent. (A)/N=71"1 per cent. and thence ,=12'9 per cent. The actual 
difference is less than this, and would frequently occur as a fluctuation of 
simple sampling. 
(0) (4B)/(B)=70°1 per cent. : (4B)/(B)=643 per cent. Difference 5:8 per 
cent. (4)/N=676 per cent., and thence e;,=38°40 per cent. The actual 
difference is 1°7 times this, and might, rather infrequently, occur as a fluctua- 
tion of simple sampling. 
CHAPTER XIV. 
Row. Ope Group of Rows. ape 
1 31 5, 6, and 7 2:1 
2 2:1 8,9, 10, and 11 16 
3 17 12, 13, and 14 1-2 
1 7 15 and upwards 11 
op is given in units per 1000 births, as s and s,. 
2. s,=7'02, and op=2'5 units. 
3. ¢2=n.pq as if the chance of success were p in all cases (but the mean is 
n/2 not p.n). 
4. Mean number of deaths per annum = ¢,*=680, 
a2=566,582, r=0°000029. 
1.