[discia] GCSE Maths › Statistics › Capture Recapture

Capture Recapture

discia.org 10 questions · 38 marks
Name Date
  1. Either paper 3 marks

    Amara wants to estimate how many trout there are in the reservoir.

    She catches 198 trout, tags them and puts them back.

    A week later she catches 77 trout. Of these, 11 are tagged.

    Use Amara's results to estimate the number of trout in the reservoir.

    Show answer
    \(1386\)
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  2. Either paper 4 marks

    Reuben is estimating the number of ladybirds in the hedgerow.

    He catches 54 ladybirds, marks them and releases them.

    Later that month he catches 78 ladybirds, of which 6 are marked.

    (a)

    Use Reuben's results to estimate the number of ladybirds in the hedgerow.

    (b)

    Write down one assumption you have made.

    Show answer
    (a) \(702\)
    (b) e.g. no ladybirds entered or left the hedgerow between the two samples
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  3. Either paper 3 marks

    There are thought to be about 280 carp in the lake. 40 of them are tagged.

    Joel catches a sample of 56 carp.

    Estimate how many of his sample are tagged.

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    \(8\)
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  4. Either paper 4 marks

    Nadia wants to estimate how many ladybirds there are in the hedgerow.

    She catches 171 ladybirds, marks them and puts them back. Later she catches 36 ladybirds. Of these, 9 are marked.

    Using these numbers, Nadia estimates that there are 684 ladybirds in the hedgerow.

    Now think about two ways the study could have played out differently.

    (a)

    Suppose she had found more than 9 marked ladybirds in the second catch — the size of each catch stays the same.

    Would this make the estimate bigger or smaller than 684? Give a reason for your answer.

    (b)

    Between the two catches, suppose the marked ladybirds become easier to catch a second time, drawn back to wherever they were caught before. Nadia still uses the same calculation as before.

    Would this make Nadia's estimate of 684 ladybirds bigger or smaller than the true number of ladybirds actually living in the hedgerow? Give a reason for your answer.

    Show answer
    (a) Smaller — marked ladybirds would then be a bigger share of the second catch, so the same 171 marked ladybirds from the first catch must stand for a smaller population
    (b) Smaller — the second catch ended up with more marked ladybirds than a fair sample would, so the 9 out of 36 makes the marked share of the second catch look bigger than it really is, so the calculation underestimates the number of ladybirds in the hedgerow
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  5. Either paper 4 marks

    Idris catches 60 sparrows in the reserve, rings them and puts them back.

    (a)

    A month later he catches 50 sparrows from the reserve. 5 of them are ringed.

    Estimate the number of sparrows in the reserve.

    (b)

    What percentage of that estimate had been ringed?

    Show answer
    (a) \(600\)
    (b) \(10\%\)
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  6. Either paper 3 marks

    Yusuf is estimating the number of rabbits in a field.

    He catches some rabbits, tagged all of them, and returns them to a field.

    Later he catches \(50\) rabbits. \(5\) of them are tagged.

    Using these results, he estimates that there are \(600\) rabbits in a field.

    (a)

    Work out how many rabbits he tagged the first time.

    (b)

    Write down one assumption that has been made.

    Show answer
    (a) \(60\ \text{rabbits}\)
    (b) The tagged rabbits had mixed evenly back into the population before the second catch
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  7. Either paper 3 marks

    Isla is trying to estimate the number of beetles in the hedge bank.

    She catches 45 beetles, marks them and puts them back. Later she catches 30 beetles. Of these, 5 are marked.

    Here is her working:

    \( 45 \times 30 = 1350 \)

    She says there are about 1350 beetles in the hedge bank.

    (a)

    Write down the mistake Isla has made.

    (b)

    Find the correct estimate for the number of beetles in the hedge bank.

    Show answer
    (a) She multiplied the two catch sizes together but forgot to divide by the number that were marked
    (b) \(270\)
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  8. Calculator 5 marks

    Hafsa estimates the number of stick insects in the greenhouse using capture-recapture.

    She catches 180 stick insects, marks them and puts them back. Later she catches 72 stick insects. Of these, 9 are marked.

    (a)

    Use Hafsa's results to estimate the number of stick insects in the greenhouse.

    (b)

    A complete count later found 2648 stick insects in the greenhouse.

    Work out the difference between Hafsa's estimate and the true number of stick insects, as a percentage of the true number. Give your answer correct to 1 decimal place.

    Show answer
    (a) \(1440\)
    (b) \(45.6\%\)
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  9. Either paper 6 marks

    Amara wants to estimate the number of snails living across the whole of Hollow Wood, an area of 3 hectares (\(1\) hectare \(= 10\,000\) m²).

    To do this, she fences off a smaller plot of 125 m² within Hollow Wood so the snails cannot move in or out, and studies them there.

    Inside the plot, she catches 18 snails, marks them and releases them. Later she catches 12 snails in the same plot, of which 3 are marked.

    (a)

    Work out Amara's estimate for the number of snails in the 125 m² plot.

    (b)

    Hollow Wood covers 3 hectares in total. Using \(1\) hectare \(= 10\,000\) m², use Amara's plot estimate to estimate the number of snails across the whole of Hollow Wood, giving your answer to 2 significant figures.

    (c)

    State one assumption Amara is making when scaling the plot estimate up to the whole of Hollow Wood.

    Show answer
    (a) \(72\)
    (b) \(17000\)
    (c) That snails are spread evenly across Hollow Wood, so the density found in the plot is typical of the wood as a whole
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  10. Either paper 3 marks

    Omar wants to estimate how many trout there are in the reservoir.

    He catches 60 trout, tags them and puts them back.

    A week later he catches 36 trout. Of these, 6 are tagged.

    Use Omar's results to estimate the number of trout in the reservoir.

    Show answer
    \(360\)
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discia.org Capture Recapture · sheet 1
Answers Capture Recapture · sheet 1
  1. \(1386\)
  2. (a) \(702\)
    (b) e.g. no ladybirds entered or left the hedgerow between the two samples
  3. \(8\)
  4. (a) Smaller — marked ladybirds would then be a bigger share of the second catch, so the same 171 marked ladybirds from the first catch must stand for a smaller population
    (b) Smaller — the second catch ended up with more marked ladybirds than a fair sample would, so the 9 out of 36 makes the marked share of the second catch look bigger than it really is, so the calculation underestimates the number of ladybirds in the hedgerow
  5. (a) \(600\)
    (b) \(10\%\)
  6. (a) \(60\ \text{rabbits}\)
    (b) The tagged rabbits had mixed evenly back into the population before the second catch
  7. (a) She multiplied the two catch sizes together but forgot to divide by the number that were marked
    (b) \(270\)
  8. (a) \(1440\)
    (b) \(45.6\%\)
  9. (a) \(72\)
    (b) \(17000\)
    (c) That snails are spread evenly across Hollow Wood, so the density found in the plot is typical of the wood as a whole
  10. \(360\)
discia.org Capture Recapture · sheet 1