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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: 23, 45
Solution
The first quartile (Q1) is the value below which 25% of the data falls, and the third quartile (Q3) is the value below which 75% of the data falls. In this distribution, calculating these quartiles using the cumulative frequency and the intervals leads to the values of 23 for Q1 and 45 for Q3, making option D correct.
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