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प्रश्न
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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उत्तर
| 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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संबंधित प्रश्न
Draw histogram for the following frequency distributions:
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| Frequency | 12 | 20 | 26 | 18 | 10 | 6 |
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| Class Interval | 30 – 39 | 40 – 49 | 50 – 59 | 60 – 69 | 70 – 79 |
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| Class Interval | 1-10 | 11-20 | 21-30 | 31-40 | 41-50 |
| Frequency | 11 | 23 | 30 | 20 | 16 |
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| Marks Scored | Number of Students |
| 0 - 20 | 6 |
| 20 - 40 | 9 |
| 40 - 60 | 14 |
| 60 - 80 | 16 |
| 80 - 100 | 5 |
Draw histogram for the above data.
Following table present educational level (middle stage) of females in Arunachal pradesh according to 1981 census:
| Age group | Number of females (to the nearest ten) |
| 10 - 14 | 300 |
| 15 - 19 | 980 |
| 20 - 24 | 800 |
| 25 - 29 | 380 |
| 30 - 34 | 290 |
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| Pocket expenses (in ₹) |
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| 0 - 5 | 10 |
| 5 - 10 | 14 |
| 10 - 15 | 28 |
| 15 - 20 | 42 |
| 20 - 25 | 50 |
| 25 - 30 | 30 |
| 30 - 35 | 14 |
| 35 - 40 | 12 |
Draw a histogram representing the above distribution and estimate the mode from the graph.
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| Overs | Runs scored |
| 20 – 30 | 37 |
| 30 – 40 | 45 |
| 40 – 50 | 40 |
| 50 – 60 | 60 |
| 60 – 70 | 51 |
| 70 – 80 | 35 |
Use graph sheet for this question.
Take 2 cm = 10 overs along one axis and 2 cm = 10 runs along the other axis.
- Draw a histogram representing the above distribution.
- Estimate the modal runs scored.
