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The table shows information about the distances 570 students travelled to a university open day - Edexcel - GCSE Maths - Question 19 - 2018 - Paper 3
Question 19
The table shows information about the distances 570 students travelled to a university open day. Distance (d miles) Frequency 0 < d ≤ 20 120 20 < d ≤ 50 90 50 < d ≤... show full transcript
Worked Solution & Example Answer:The table shows information about the distances 570 students travelled to a university open day - Edexcel - GCSE Maths - Question 19 - 2018 - Paper 3
Step 1
Draw a histogram for the information in the table.
Answer
To draw the histogram based on the provided data, follow these steps:
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Set up the axes:
- The x-axis (Distance in miles) should include intervals: [0, 20], [20, 50], [50, 80], [80, 150], and [150, 200].
- The y-axis (Frequency) should scale from 0 to the maximum frequency (which is 140).
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Create bars for each interval:
- For the interval [0, 20]: Draw a bar from 0 to 20 with height 120.
- For the interval [20, 50]: Draw a bar from 20 to 50 with height 90.
- For the interval [50, 80]: Draw a bar from 50 to 80 with height 120.
- For the interval [80, 150]: Draw a bar from 80 to 150 with height 140.
- For the interval [150, 200]: Draw a bar from 150 to 200 with height 100.
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Ensure accurate bar widths: Each bar’s width should correspond to the respective interval’s range.
Step 2
Estimate the median distance.
Answer
To estimate the median distance:
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Calculate cumulative frequency
- [20, 50]: 120 + 90 = 210
- [50, 80]: 210 + 120 = 330
- [80, 150]: 330 + 140 = 470
- [150, 200]: 470 + 100 = 570
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Find the median position:
- The median position is given by: ( \frac{570}{2} = 285 ).
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Identify the interval containing the median:
- The cumulative frequency shows that the 285th student falls within the interval [50, 80], since it exceeds 210 but is less than 330.
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Use proportional method to calculate:
- This interval has a frequency of 120. The position of the median within this interval can be estimated proportionally based on the cumulative data we’ve calculated.
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Estimate median value:
- The median distance can be approximated between 66 to 71 miles.