ANSWERS ETC., TO EXERCISES GIVEN. 403 
intervals does not affect the sum of deviations, except for the interval in which 
the mean or median lies: for that interval the sum is n, (0°25 +2), hence the 
entire correction is 
a(n; — ng) +n5(0°25 + d?). 
In this expression d is, of course, expressed as a fraction of the class-interval, 
and is given its proper sign. Notice that the », and ny of this question are 
not the same as the NV; and A, of § 16. 
CHAPTER IX, 
lL. 0:=1'414, ¢,=2'280, r= +081. X=05¥Y+0'5. }=13X+1l 
2. Using the subscripts 1 for earnings, 2 for pauperism, 3 for out-relief ratio, 
My=579, 03=809 : rig= — 0°13, 7p3= + 0°60. 
CHAPTER XI. 
1. 1232 per cent. (against 1240 per cent.): 2'556 in. against 2572 in. 
2. The corrected standard-deviation is 0°9954 of the rough value. 
3. Estimated true standard-deviation 6-91: standard-deviation of fluctua- 
tions of sampling 9°38. (The latter, which can be independently calculated, 
is too low, and the former consequently probably too high. €f. Chap. XIV. 
§ 10.) 
4. 043. 
5. 58 per cent. 
6. oo?N/(o® + a®)(og® + 037). 
7 dado of =" 
ERNE RE 
8. 0-30. 
ea 2.2 72 2 2 
9. dl oy -b 09 + cog Y 
The others may be written down from symmetry. : 
10. (1) No effect at all. (2) If the mean value of the errors in variables is 
d, and in the weights e, the value found for the weighted mean is— 
The true value +d — 7.0, 0w0——r. 
w(w +e) 
If is small, d is the important term, and hence errors in the quantities are 
usually of more importance than errors in the weights. If » become consider- 
able, errors in the weights may be of consequence, but it does not seem probable 
that the second term would become the most important in practical cases, 
11. @Q=2/3. 
12. HE 077. 
CHAPTER XII 
1. res3= +0°759, rize= + 0097, rey = — 0436. 
0123 =2'64, 0213=0°594, 0312=70"1. 
X,=9'31+3'37 X,+0'00364 X..