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The table shows information about the heights of 80 children - Edexcel - GCSE Maths - Question 1 - 2017 - Paper 3
Question 1
The table shows information about the heights of 80 children. Height (h cm) Frequency 130 < h ≤ 140 4 140 < h ≤ 150 11 150 < h ≤ 160 24 160 < h ≤ ... show full transcript
Worked Solution & Example Answer:The table shows information about the heights of 80 children - Edexcel - GCSE Maths - Question 1 - 2017 - Paper 3
Step 1
Find the class interval that contains the median.
Answer
To find the class interval that contains the median, we first need to determine the total frequency (N).
Total frequency, .
Next, we find the median position, which is given by the formula:
Now we calculate the cumulative frequency for each class:
- For 130 < h ≤ 140: Cumulative frequency = 4
- For 140 < h ≤ 150: Cumulative frequency = 4 + 11 = 15
- For 150 < h ≤ 160: Cumulative frequency = 15 + 24 = 39
- For 160 < h ≤ 170: Cumulative frequency = 39 + 22 = 61
- For 170 < h ≤ 180: Cumulative frequency = 61 + 19 = 80
The cumulative frequency reaches 40 between the classes of 150 < h ≤ 160 (39) and 160 < h ≤ 170 (61). Thus, the class interval that contains the median is:
160 < h ≤ 170.
Step 2
Draw a frequency polygon for the information in the table.
Answer
To draw the frequency polygon, we first calculate the midpoints for each class interval:
- Midpoint for 130 < h ≤ 140:
- Midpoint for 140 < h ≤ 150:
- Midpoint for 150 < h ≤ 160:
- Midpoint for 160 < h ≤ 170:
- Midpoint for 170 < h ≤ 180:
Next, we will plot the points corresponding to the midpoints and their frequencies:
- (135, 4)
- (145, 11)
- (155, 24)
- (165, 22)
- (175, 19)
Finally, we connect the points with straight lines to complete the polygon.