1: THEORY OF STATISTICS. 
6. (Data from census of 1901.) The table below shows the population of 
the rural sanitary districts of Essex, the urban sanitary districts (other than 
the borough of West Ham), and the borough of West Ham, at the censuses 
of 1891 and 1901. Estimate the total population of the county at a date 
midway between the two censuses, (1) on the assumption that the percentage 
rate of increase is constant for the county as a whole, (2) on the assumption 
that the percentage rate of increase is constant in each group of districts and 
the borough of West Ham. 
Population. 
Es<ex, 5 
1891. 1901. 
Rural districts . 232,867 240,776 
West Ham . ; . . 204,903 267,358 
Other urban districts . 345,604 575,864 
Total 783,374 1,083,998 
7. (Data from Agricultural Statistics for 1905, Cd. 8061, 1906.) The 
following statement shows the monthly average prices of eggs in Great 
Britain in 1905, as compiled from the weekly returns of market prices for 
first and second quality British eggs, per 120 :— 
First Second 
Benth. Quality. Quality. 
snd. snd. 
January . > . 13 Opry 11 0 
February . . . 110: 90 
March . ; ; : 890 Bao 
Aprilia. 3 ; . 7 13 
Mays =, L a 2 i 
June . : . oe To 
; July . . . i . 
August . 3 . IE 10 9 
September . : TIES ERIE 1048 
October . 2 : . 14 0 12:3 
November . ‘ : 18 0 16 0 
December . : 1756 15 0 
Mean for year 11 5% | 10 0% 
What would have been the mean price for the year in each case if the whole- 
sale prices had been recorded in the same way as retail prices, 7.c. at so many 
eggs per shilling ? State your answer in the form of the equivalent price per 
120, and obtain it in the shortest way by taking the harmonic mean of the 
above prices (¢f. § 27). : 
8. Supposing the frequencies of values 0, 1, 2, . . . of a variable to be 
given by the terms of the binomial series 
n(n —1) 
a n.qr=1,p, w= Dp p8 so 6 8 
where p+¢=1, find the mean. 
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