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The table shows information about the heights of 80 plants - Edexcel - GCSE Maths - Question 4 - 2019 - Paper 3
Question 4
The table shows information about the heights of 80 plants. Height (h cm) Frequency 10 < h ≤ 20 7 20 < h ≤ 30 13 30 < h ≤ 40 40 40 < h ≤ 50 12 50 < h ≤ 60 16 60 < h... show full transcript
Worked Solution & Example Answer:The table shows information about the heights of 80 plants - Edexcel - GCSE Maths - Question 4 - 2019 - Paper 3
Step 1
Find the class interval that contains the median.
Answer
To find the class interval containing the median, we first need to calculate the cumulative frequency (CF) for the height classes.
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The total frequency (n) is 80.
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The median position is given by:
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Now, we calculate the cumulative frequency:
- For 10 < h ≤ 20: CF = 7
- For 20 < h ≤ 30: CF = 7 + 13 = 20
- For 30 < h ≤ 40: CF = 20 + 40 = 60
- For 40 < h ≤ 50: CF = 60 + 12 = 72
- For 50 < h ≤ 60: CF = 72 + 16 = 88
- For 60 < h ≤ 70: CF = 88 + 18 = 106
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The cumulative frequency just greater than 40 is 60, which occurs in the interval: 30 < h ≤ 40.
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Therefore, the class interval that contains the median is: 30 < h ≤ 40.
Step 2
On the grid, draw a frequency polygon for the information in the table.
Answer
To draw the frequency polygon, follow these steps:
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Identify midpoints for each class interval:
- For 10 < h ≤ 20: Midpoint = 15
- For 20 < h ≤ 30: Midpoint = 25
- For 30 < h ≤ 40: Midpoint = 35
- For 40 < h ≤ 50: Midpoint = 45
- For 50 < h ≤ 60: Midpoint = 55
- For 60 < h ≤ 70: Midpoint = 65
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Plot the points based on frequency (y-axis) against midpoints (x-axis):
- (15, 7)
- (25, 13)
- (35, 40)
- (45, 12)
- (55, 16)
- (65, 18)
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Connect the points with straight lines:
- Start from (15, 7) to (25, 13) to (35, 40) to (45, 12) to (55, 16) to (65, 18).
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Ensure the polygon starts and ends at the x-axis (height 0), adding points (10, 0) at the left and (70, 0) at the right if required for clarity.