The Petersen Capture-Recapture Method
Learn The Petersen Capture-Recapture Method for GCSE Statistics with this free worksheet and full mark scheme — Higher tier exam-style questions with worked answers for AQA and Edexcel. The Petersen capture-recapture method estimates a population size by marking, releasing and then re-sampling.
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This is a Higher tier only topic, so there's no Foundation paper — only the Higher worksheet and mark scheme below.
Topic overview
The Petersen capture-recapture method estimates the size of a population that cannot be counted directly, such as fish in a lake. This is a Higher-only topic.
A first sample is captured, marked and released. Later a second sample is captured, and the number of marked individuals within it is counted. The proportion marked in the second sample is assumed to equal the proportion marked in the whole population.
The formula is \(N = \frac{n_1 n_2}{m}\), where \(n_1\) is the size of the first sample, \(n_2\) the size of the second, and \(m\) the number of marked individuals recaptured. Several assumptions must hold for the estimate to be valid, and stating them is examined as often as the calculation itself.
Revision notes
The method
Capture a first sample of size \(n_1\), mark them and release them.
Allow time for them to mix back into the population. Capture a second sample of size \(n_2\) and count how many are marked, giving \(m\).
The formula
\(N = \frac{n_1 n_2}{m}\), where \(N\) is the estimated population size.
With 60 marked, a second sample of 80 containing 12 marked gives \(N = \frac{60 \times 80}{12} = 400\). Write the formula, substitute, then calculate.
The assumptions
The population is closed — no births, deaths, immigration or emigration between the samples.
The marks do not come off, and do not affect the chance of being recaptured. The marked individuals mix fully back into the population. Both samples are random.
Key points
- Capture, mark and release a first sample.
- Capture a second sample and count the marked.
- \(N = \frac{n_1 n_2}{m}\).
- The population must be closed.
- Marks must not come off or affect recapture.
- Marked individuals must mix back fully.
Worked examples
Example 1
In a capture-recapture study, 50 fish are marked. A later sample of 90 contains 15 marked fish. Estimate the population. [3 marks]
Working
Example 2
State two assumptions made when using the capture-recapture method. [2 marks]
Working
Example 3
Explain why the marked individuals must be allowed to mix before the second sample is taken. [2 marks]
Working
Common mistakes
Dividing by the wrong quantity.
Divide by \(m\), the number recaptured that were marked.
Not stating the assumptions.
They are examined as often as the calculation.
Forgetting to write the formula first.
It usually carries a method mark.
Giving a non-whole-number answer without rounding.
Round to a sensible whole number, since you cannot have part of an animal.
Exam tips
- Write the formula before substituting.
- Learn at least three assumptions.
- Show each step separately for method marks.
- Remember this is a Higher-only topic.
Key terms
- Capture-recapture
- A method estimating population size using marked individuals.
- Closed population
- A population with no births, deaths or migration.
- Recapture
- Catching a second sample after marking the first.
- Estimate
- An approximate value calculated from a sample.
Related topics
Written and reviewed against the current AQA and Edexcel specifications. Spotted an error? Let us know.