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Median Height 17Ecaa

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Median Height 17Ecaa


1. The problem is to estimate the median height of 60 trees using the histogram data. 2. The median corresponds to the 30th tree when the data is ordered by height. 3. Calculate the frequency (area) of each bar: frequency = frequency density \times class width. 4. For 0-10 m: $1 \times 10 = 10$ trees. 5. For 10-15 m: $5 \times 5 = 25$ trees. 6. Cumulative frequency up to 15 m: $10 + 25 = 35$ trees. 7. The median tree (30th) lies in the 10-15 m interval. 8. Use linear interpolation in 10-15 m interval: Class width = 5 m, frequency density = 5, frequency in class = 25. Trees before class = 10. Position in class = $30 - 10 = 20$. 9. Median height = lower boundary + $\frac{\text{position in class}}{\text{frequency in class}} \times \text{class width}$ = $10 + \frac{20}{25} \times 5 = 10 + 4 = 14$ m. 10. Final answer: median height is 14.0 m.