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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:
| Shoe size | 5 | 6 | 7 | 8 | 9 | 10 | 11 |
| Frequency | 8 | 1 | 7 | 14 | 11 | 5 | 4 |
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Solution
| Shoe size | Frequency (f) | Cumulative frequency |
| 5 | 8 | 8 |
| 6 | 1 | 9 |
| 7 | 7 | 16 |
| 8 | 14 | 30 |
| 9 | 11 | 41 |
| 10 | 5 | 46 |
| 11 | 4 | 50 |
No. of terms = 50
Lower Quartile (Q1) = `n/4 = 50/4` = 12.5th term = 7
Upper Quartile (Q3) = `(n xx 3)/4 = (50 xx 3)/4` = 37.5th term = 9
Interquartile range = Q3 - Q1 = 9-7 = 2
Semi-interquartile range = `(Q_3 - Q_1)/2 = (9-7)/2 = 1`
Hence, Lower quartile = 7, upper quartile = 9, interquartile range = 2, semi-interquartile range = 1
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