## Estimating a Population

There is a way though to estimate and monitor a changing population. Suppose from a population of a species of total size

\[N\]

, \[n\]

animals are tagged. The fraction of animals that are tagged is \[\frac{n}{N}\]

.The tagged animals are freed, and a second sample of size

\[m\]

is then taken. \[x\]

of these animals are wearing the tag. Assuming the proportion of animals wearing the tag is the same as the proportion of animals that were tagged, \[\frac{n}{N}=\frac{x}{m}\]

. Rearranging this gives \[N=\frac{nm}{x}\]

.200 wild pandas are tagged and released, and a year later, a sample of 300 is taken, of which 50 are wearing a tag. The population estimate is then

\[N=\frac{200 \times 300}{50}=1200\]

.This estimate assumes that there have not been any births or deaths since the animals were tagged, and the tagged and untagged animals are properly mixed.