Geometric mean
The arithmetic mean tells us that in a
population of 1000 deer increasing 10%
one year and 20% the next, the average
increase is 15%. However, this gives us
1322.5 deer when the actual population
increase is to 1320 deer.
, If we use the geometric mean instead, the
calculations are as follows…
10% and 20% increase is the same as 1.10 and 1.20
Take the natural log of these to get:
ln(1.10) = 0.09531 and ln(1.20) = 0.18232
The arithmetic average of these two is 0.138815
(.09531 + 0. = 0.138815)
Take the antilog of the arithmetic mean:
e 0.138815 = 1.14891
Multiply this by the population size each year to get a total end
population of 1319.99 – closer to the 1320 actual deer.
The arithmetic mean tells us that in a
population of 1000 deer increasing 10%
one year and 20% the next, the average
increase is 15%. However, this gives us
1322.5 deer when the actual population
increase is to 1320 deer.
, If we use the geometric mean instead, the
calculations are as follows…
10% and 20% increase is the same as 1.10 and 1.20
Take the natural log of these to get:
ln(1.10) = 0.09531 and ln(1.20) = 0.18232
The arithmetic average of these two is 0.138815
(.09531 + 0. = 0.138815)
Take the antilog of the arithmetic mean:
e 0.138815 = 1.14891
Multiply this by the population size each year to get a total end
population of 1319.99 – closer to the 1320 actual deer.
