VIL—AVERAGES. 125 
24. The use of the geometric mean finds its simplest application 
in estimating the numbers of a population midway between two 
epochs (say two census years) at which the population is known. 
If nothing is known concerning the increase of the population 
save that the numbers recorded at the first census were P, and at 
the second census n years later P,, the most reasonable assump- 
an is gil 2% F719] 1901 
300 ‘1-300 
Qunbdertand 
2 — 250 
Dorset 
Dag —- 200 
150 - = 150 
Cumberland 
Dorset - Hereford 
00 - —100 
Hereford 
os iC 2 
o. eS O 
. ‘ : I ‘ 
JECT Lo oi =r $i, S81 el. qt. 81 91. i904 
Census year. 
F16. 24.— Showing the Populations of certain rural counties of England 
for each Census year from 1801 to 1901. 
tion to make is that the percentage increase in each year has 
been the same, so that the populations in successive years form a 
geometric series, Pr being the population a year after the first 
census, £;r* two years after the first census, and so on, and 
P, =P. 7” . (15) 
The population midway between the two censuses is therefore 
Pop=Pyr"?=(P,.P,)} 7m 
5 
o¢ 
50 Sr 
(lo