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In statistics, there are various sampling methods used to collect data and estimate population characteristics. Two common techniques are **stratified sampling** and **capture-recapture**. Both methods aim to improve the accuracy of estimates, but they are used in different contexts.

**Stratified sampling** is a method where the population is divided into subgroups, called **strata**, that share similar characteristics. A random sample is then taken from each stratum, ensuring that each subgroup is proportionally represented in the overall sample.

**Strata** are based on specific characteristics, like age, gender, or income level. Each stratum is sampled separately, and the results are combined to represent the whole population.

Stratified sampling increases precision by ensuring that key subgroups are adequately represented.

**Capture-recapture** is a method used to estimate the size of a population, particularly in wildlife studies. It involves capturing a sample of individuals, marking them, and then releasing them back into the population. After some time, another sample is captured, and the number of marked individuals is counted.

The population size \(N\) can be estimated using the formula:

\[N = \frac{M \times C}{R}\]

\(M\) = the number of marked individuals in the first capture.

\(C\) = the total number of individuals captured in the second sample.

\(R\) = the number of marked individuals recaptured.

This method assumes random mixing between captures and that the marking does not affect an individual's chance of recapture.

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