Estimating the Size of a Population

seed

1

sampling percentage

20

show

examples

percent estimation error

black lines: sample values

blue line: estimated size of population

red line: true size of population

Suppose that in a marathon each runner has a running number on their back but we do not know

N

, the total number of runners. At some point along the course we observe

n

random runners and write down their running numbers

X

i

,

i=1,2,…,n

. What would be our estimate of

N

? Let

m

be largest of the observed numbers

X

i

. It can be shown that a good estimate of

N

is

m+

m

n

-1

. The Demonstration shows examples of this estimate when

N

is 100. It also shows the frequency distribution of the percent estimation error, when the

N

is a random integer between 100 and 1000.