AQA GCSE · Question 11.3 · Statistical Measures and Calculations
Calculate an estimate of the number of squirrels in the forest.
How to approach this question
1. **Identify the formula or proportion**: The core idea is that the proportion of tagged squirrels in the second sample should be equal to the proportion of tagged squirrels in the whole population.
(Tagged in 2nd sample) / (Total in 2nd sample) = (Total tagged in population) / (Total population N)
11 / 40 = 50 / N
2. **Rearrange the formula to solve for N**:
N = (50 * 40) / 11
3. **Substitute the values**:
* Total tagged in population (size of 1st sample) = 50
* Total in 2nd sample = 40
* Tagged in 2nd sample = 11
4. **Calculate the result**:
* N = (50 * 40) / 11
* N = 2000 / 11
* N ≈ 181.82
5. **State the final answer**: Since the number of squirrels must be an integer, round the answer to the nearest whole number, which is 182.
Full Answer
Let N be the estimated total population size.
The formula for capture-recapture is:
N = (Number in 1st sample × Number in 2nd sample) / (Number tagged in 2nd sample)
Given values:
- Number in 1st sample (tagged) = 50
- Number in 2nd sample = 40
- Number tagged in 2nd sample = 11
N = (50 * 40) / 11
N = 2000 / 11
N = 181.8181...
Since we cannot have a fraction of a squirrel, we round to the nearest whole number.
Estimated population ≈ 182 squirrels.
The capture-recapture method estimates the total population (N) by assuming that the proportion of marked individuals in the second sample is representative of the proportion of marked individuals in the entire population.
This can be set up as a proportion:
(Number marked in second sample) / (Total size of second sample) = (Total number marked in population) / (Total population size, N)
Let's plug in the numbers:
11 / 40 = 50 / N
To solve for N, we can rearrange the equation:
11 × N = 50 × 40
11 × N = 2000
N = 2000 / 11
N ≈ 181.818...
Since we are estimating a number of squirrels, the answer must be a whole number. Rounding to the nearest integer gives:
N ≈ 182
So, the estimated squirrel population is 182.
Common mistakes
✗ Getting the proportion upside down (e.g., 40/11 = 50/N).
✗ Errors in multiplication or division.
✗ Leaving the answer as a decimal or fraction instead of rounding to a whole number.
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