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The histogram gives information about the heights, in metres, of the trees in a park - Edexcel - GCSE Maths - Question 19 - 2019 - Paper 2
Question 19
The histogram gives information about the heights, in metres, of the trees in a park. The histogram is incomplete. 20% of the trees in the park have a height betwee... show full transcript
Worked Solution & Example Answer:The histogram gives information about the heights, in metres, of the trees in a park - Edexcel - GCSE Maths - Question 19 - 2019 - Paper 2
Step 1
Methods to find my frequency
Answer
To find the frequency for the interval 0-5 metres, we calculate the area of the bar:
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The height of the bar indicates a frequency density of 2.
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The width of the interval is 5 metres.
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Therefore, the frequency for this interval is:
Next, for the interval 5-10 metres:
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The height of the bar is 3.
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The width of the interval is also 5 metres.
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The frequency for this interval is:
Step 2
Methods to use areas
Answer
For the interval 10-12.5 metres, we know that 20% of the trees fall within this range. Assuming the total number of trees is represented as T, the frequency can be calculated as:
Now we calculate the total frequency for the intervals up to 25 metres. Since none of the trees exceed 25 metres, we can find total frequency:
- From the previous intervals, we have:
- 0-5 metres: 10
- 5-10 metres: 15
- 10-12.5 metres: 0.2T
Total frequency = 10 + 15 + 0.2T + Frequency for 12.5-25 metres.
Step 3
Complete the histogram
Answer
Finally, to ascertain the frequency for the interval 12.5-25 metres, we need to find:
Solving, we have:
- Let's calculate the total frequency again,
- At this point, frequency density for the final interval can be obtained by dividing this frequency by the width (12.5 metres):
For the complete histogram, ensure all bars accurately reflect these calculated frequencies.