- THEORY OF STATISTICS. 
2. For all the districts in England and Wales included in the same table 
(Table VI., Chap. IX.) the standard-deviation of the proportion of male births 
per 1000 of all births is 7:46 and the mean proportion of male births 509-2. 
The harmonic mean number of births in a district is 5070. Find the signi- 
ficant standard-deviation oy. 
3. If for one half of » events the chance of success is p and the chance of 
failure g, whilst for the other half the chance of success is ¢ and the chance of 
failure p, what is the standard-deviation of the number of successes, the events 
being all independent ? 
4. The following are the deaths from small-pox during the 20 years 
1882-1901 in England and Wales : — 
1882 1317 1892 431 
83 957 93 1457 
84 2234 94 820 
85 2827 95 223 
86 275 96 541 
87 506 97 25 
88 1026 98 253 
89 23 99 174 
90 16 1900 85 
91 49 1901 356 
The death-rate from small-pox being very small, the rule of § 12, Chap. 
XIII., may be applied to estimate the standard-deviation of simple sampling. 
Assuming that the excess of the actual standard-deviation over this can be 
entirely accounted for by a correlation between the results of exposure to risk 
of the individuals composing the population, estimates. The mean population 
during the period may be taken in round numbers as 29 millions. 
200)