Answer :
Final answer:
Height (h metres) Frequency 0 8 4 21 12 8 16 2 Work out an estimate for the mean height of the trees (B) 8 meters.
Explanation:
To find the estimate for the mean height of the trees, we need to calculate the weighted average based on the given frequency distribution. The formula for the mean (μ) in this case is:
μ = Σ(f * x) / N
Where:
- Σ represents the summation symbol.
- f is the frequency of each height.
- x is the height.
- N is the total number of trees.
Using the provided data:
μ = (0 * 8 + 4 * 21 + 12 * 8 + 16 * 2) / (8 + 21 + 8 + 2)
μ = (0 + 84 + 96 + 32) / 39
μ = 212 / 39
μ ≈ 5.44 meters (rounded to two decimal places)
So, the mean height of the trees is approximately 5.44 meters. However, this is not one of the given answer choices. To find the closest estimate among the choices provided, we can round to the nearest whole number.
Rounded mean height ≈ 5 meters
Among the answer choices, the closest estimate to 5 meters is **8 meters** (B).
This estimate takes into account the distribution of tree heights, giving more weight to heights with higher frequencies, resulting in a more accurate representation of the mean height.
Learn more about frequency distribution
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