Mathematics
Grade 8
15 min
Estimate population size using proportions
Estimate population size using proportions
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1
Introduction & Learning Objectives
Learning Objectives
Define key terms related to population estimation, such as 'population,' 'sample,' and 'proportion'.
Explain the principles behind the capture-recapture method for estimating population size.
Set up a proportion to model a capture-recapture scenario.
Solve proportions to estimate an unknown population size.
Identify and apply the formula for estimating population size using the capture-recapture method.
Interpret the estimated population size in the context of a real-world problem.
Ever wondered how scientists count all the fish in a lake or all the deer in a forest? 🦌 It's impossible to count every single one!
In this lesson, you'll discover a clever mathematical trick called the capture-recapture method, which u...
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Key Concepts & Vocabulary
TermDefinitionExample
PopulationThe entire group of individuals (animals, people, objects) that you are interested in studying or estimating the size of.All the salmon in a particular river; all the students in a school district.
SampleA smaller, representative group taken from the larger population. It's used to make inferences about the entire population.Catching 50 fish from a lake to tag them; surveying 100 students about their favorite subject.
ProportionAn equation that states that two ratios are equal. It's often used to find an unknown value when one ratio is known.If 1 out of 2 apples is red, then 5 out of 10 apples are red. This can be written as 1/2 = 5/10.
Capture-Recapture MethodA technique used to estimate the size of a population where it's impractical to cou...
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Core Formulas
Capture-Recapture Proportion
$$\frac{\text{Number of marked individuals in recapture}}{\text{Total individuals in recapture}} = \frac{\text{Total number of individuals initially marked}}{\text{Estimated total population size}}$$
This proportion forms the basis of the capture-recapture method. It assumes that the ratio of marked individuals in the second sample is representative of the ratio of marked individuals in the entire population. We use this to solve for the unknown total population size.
Solving for Estimated Population Size (N)
$$N = \frac{(\text{Total individuals initially marked}) \times (\text{Total individuals in recapture})}{\text{Number of marked individuals in recapture}}$$
This is the rearranged formula derived from the capture-recapture proportion, specifi...
5 more steps in this tutorial
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Challenging
A researcher tags 200 turtles. A month later, they recapture 100 turtles and find 10 are tagged. They later discover that the tags used were faulty and half of them likely fell off the turtles before the recapture. How would this flaw affect the population estimate?
A.It would likely cause an overestimate of the population size.
B.It would likely cause an underestimate of the population size.
C.It would have no effect on the estimate.
D.It would make the estimate perfectly accurate.
Challenging
Suppose some animals are 'trap-happy,' meaning they are not scared by the traps and are more likely to be caught again. How would this behavior affect the population estimate?
A.It would not affect the estimate because the sample size is the same.
B.It would lead to an overestimate of the population.
C.It would lead to an underestimate of the population.
D.It would make the estimate more accurate.
Challenging
A biologist performs two recaptures to improve her estimate of a snake population after initially marking 60 snakes. Recapture 1: 80 snakes caught, 12 marked. Recapture 2: 70 snakes caught, 10 marked. To get the best overall estimate, she pools the data. What is the estimated population size based on the combined data?
A.400
B.425
C.435
D.450
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