Calculate a sampled population density

Supplied materials

• All measurements and observations below are supplied classroom examples. They are not data from actual learners or a claim about a particular real site.
• Paper or browser document; an ordinary calculator is optional.
• Rule: Sample density equals counted individuals divided by sampled square meters. Formula: a/b. Variable key: a = counted individuals, b = sampled area (m²)
• Distinct worked inputs and result: A distinct plot has 18 counted plants in 3 m²: 18/3=6 plants/m².
• Assessment case 1: Supplied case 1: counted individuals=24; sampled area (m²)=6, using the explicitly named quantities. Sample density equals counted individuals divided by sampled square meters. What result follows?
• Assessment case 2: Supplied case 2: counted individuals=40; sampled area (m²)=8, using the explicitly named quantities. Sample density equals counted individuals divided by sampled square meters. What result follows?
• Assessment case 3: Supplied case 3: counted individuals=30; sampled area (m²)=5, using the explicitly named quantities. Sample density equals counted individuals divided by sampled square meters. What result follows?
• Assessment case 4: Supplied case 4: counted individuals=54; sampled area (m²)=9, using the explicitly named quantities. Sample density equals counted individuals divided by sampled square meters. What result follows?
• Assessment case 5: Supplied case 5: counted individuals=72; sampled area (m²)=12, using the explicitly named quantities. Sample density equals counted individuals divided by sampled square meters. What result follows?
• Assessment case 6: Supplied case 6: counted individuals=84; sampled area (m²)=14, using the explicitly named quantities. Sample density equals counted individuals divided by sampled square meters. What result follows?

Learn the idea

Density uses a count divided by a sampled area. It is not a census of every habitat. Sampling method and patchiness affect how well an estimate describes a wider population.

Sample density equals counted individuals divided by sampled square meters. The formula in the supplied model is a/b. Variable key: a = counted individuals, b = sampled area (m²). Use sampled area as denominator. Do not extrapolate without representative sampling assumptions.

A distinct plot has 18 counted plants in 3 m²: 18/3=6 plants/m². Count individuals, not species kinds. Track the quantity and unit before calculating. Explain the meaning of a positive, negative or fractional result when relevant. A numerical answer supports the stated model calculation; broader claims require the additional measurements and assumptions described here.

1. Name the measured quantities and their units before substituting values.
2. Write the stated rule and use the variable key to match each symbol to its explicitly named quantity.
3. Calculate each supplied case separately, keeping intermediate arithmetic and the result unit.
4. Explain the result in context and identify the assumption that would invalidate direct use of the rule.

Check your reasoning

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Take it further

Changed-input task: use the same stated model with counted individuals=25; sampled area (m²)=6. Expected result: approximately 4.1666667 individuals/m². Explain what changes and keep this assumption: Count individuals, not species kinds.

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