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Question
Find the lower quartile, the upper quartile, the interquartile range and the semi-interquartile range for the following frequency distributions:
| Marks | 25 | 30 | 35 | 40 | 45 | 50 |
| No. of students | 6 | 15 | 12 | 10 | 18 | 9 |
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Solution
| Marks | No. of students (f) | Cumulative frequency |
| 25 | 6 | 6 |
| 30 | 15 | 21 |
| 35 | 12 | 33 |
| 40 | 10 | 43 |
| 45 | 18 | 61 |
| 50 | 9 | 70 |
No. of terms = 70
Lower Quartile (Q1) = `n/4 = 70/4` = 17.5th term = 30
Upper Quartile (Q3) = `(n xx 3)/4 = (70 xx 3)/4` = 52.5th term = 45
Interquartile range = Q3 - Q1 = 45-30 = 15
Semi-Interquartile range = `(Q_3 - Q_1)/2 = (45-30)/2 = 7.5`
Hence, Lower quartile = 30, upper quartile = 45, interquartile range = 15, semi -interquartile range = 7.5
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