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For the grouped frequency distribution below, what are the first and third quartiles?
Marks interval | Number of students
0–10 | 4
10–20 | 8
20–30 | 11
30–40 | 15
40–50 | 12
50–60 | 6
60–70 | 3
- 21.5, 43.8
- 26.26, 49.69
- 22.5, 45.2
- 23, 45
Correct answer: 22.5, 45.2
Solution
N=59, so Q1 lies at N/4=14.75 in class 20-30 (L=20, cf=12, f=11): Q1=20+(14.75-12)/11*10=22.5. Q3 lies at 3N/4=44.25 in class 40-50 (L=40, cf=38, f=12): Q3=40+(44.25-38)/12*10=45.2. So Q1=22.5, Q3=45.2.
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