standupmaths: How to estimate a population using statisticians

How could you estimate population size? Catch random sample of individuals to be "marked" (capture). Catch another random sample and count proportion of the "marked" (recapture). The proportion of the "marked" in the second sample is statistically equivalent to the proportion of the "marked" in whole population.

Given that we have marked \( S_1 \) individuals during capture phase and have later recaptured \( M_2 \) of them together with \( S_2 - M_2 \) unmarked individuals, the total size of population \( N \) is given by \begin{equation} N = \frac{S_1 S_2}{M_2} . \end{equation} This formula should give a rather good approximation of \( N \) if samples sizes are large and enough and the sampling is truly random.

You can find two exemplary experiments in a video by Matt Parker (one of the most well-known standup mathematicians).