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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:
| Variate | 10 | 11 | 12 | 13 | 14 | 15 | 16 | 17 | 18 | 19 | 20 |
| Frequency | 1 | 2 | 3 | 1 | 2 | 4 | 2 | 1 | 1 | 2 | 1 |
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Solution
| Variate | Frequency (f) | Cumulative frequency |
| 10 | 1 | 1 |
| 11 | 2 | 3 |
| 12 | 3 | 6 |
| 13 | 1 | 7 |
| 14 | 2 | 9 |
| 15 | 4 | 13 |
| 16 | 2 | 15 |
| 17 | 1 | 16 |
| 18 | 1 | 17 |
| 19 | 2 | 19 |
| 20 | 1 | 20 |
No. of terms = 20
Lower Quartile (Q1) = `"n"/4 = 20/4` = 5th term = 12
Upper Quartile (Q3) = `("n" xx 3)/4 = (20 xx 3)/4` = 15th term = 16
Interquartile range = Q3 - Q1 = 16- 12 = 4
Semi-Interquartile range = `(Q_3 - Q_1)/2 = (16-12)/2 = 2`
Hence, Lower quartile = 12, upper quartile = 16, interquartile range = 4, semi-interquartile range = 2
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