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प्रश्न
The weight of 60 boys are given in the following distribution table:
| Weight (kg) | 37 | 38 | 39 | 40 | 41 |
| No. of boys | 10 | 14 | 18 | 12 | 6 |
Find:
- Median
- Lower quartile
- Upper quartile
- Inter-quartile range
उत्तर
| Weight (kg) x |
No. of boys f |
Cumulative frequency |
| 37 | 10 | 10 |
| 38 | 14 | 24 |
| 39 | 18 | 42 |
| 40 | 12 | 54 |
| 41 | 6 | 60 |
Number of terms = 60
i. Median = The mean of the 30th and 31st terms
∴ Median = `(39 + 39)/2`
= `78/2`
= 39
ii. Lower quartile (Q1) = `60^(th)/4` term
= 15th term
= 38
iii. Upper quartile (Q3) = `(3 xx 60^(th))/4` term
= 45th term
= 40
iv. Inter-quartile range = Q3 – Q1
= 40 – 38
= 2
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संबंधित प्रश्न
An incomplete distribution is given as follows:
| Variable: | 0 - 10 | 10 - 20 | 20 - 30 | 30 - 40 | 40 - 50 | 50 - 60 | 60 - 70 |
| Frequency: | 10 | 20 | ? | 40 | ? | 25 | 15 |
You are given that the median value is 35 and the sum of all the frequencies is 170. Using the median formula, fill up the missing frequencies.
Compute the median for the following data:
| Marks | No. of students |
| Less than 10 | 0 |
| Less than 30 | 10 |
| Less than 50 | 25 |
| Less than 70 | 43 |
| Less than 90 | 65 |
| Less than 110 | 87 |
| Less than 130 | 96 |
| Less than 150 | 100 |
Estimate the median for the given data by drawing an ogive:
| Class | 0 – 10 | 10 – 20 | 20 – 30 | 30 – 40 | 40 – 50 |
| Frequency | 4 | 9 | 15 | 14 | 8 |
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| Class | 65 – 85 | 85 – 105 | 105 – 125 | 125 – 145 | 145 – 165 | 165 – 185 | 185 – 200 |
| Frequency | 4 | 5 | 13 | 20 | 14 | 7 | 4 |
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| Height(in cm) | 135 - 140 | 140 - 145 | 145 - 150 | 150 - 155 | 155 - 160 | 160 - 165 | 165 - 170 | 170 - 175 |
| Frequency | 6 | 10 | 18 | 22 | 20 | 15 | 6 | 3 |
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| Frequency | `f_1` |
5 |
9 | 12 | `f_2` | 3 | 2 | 40 |
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| Pocket expenses |
0 - 200 |
200 - 400 |
400 - 600 |
600 - 800 |
800 - 1000 |
1000 - 1200 |
1200 - 1400 |
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| Class interval | Frequency |
| 0 – 100 | 2 |
| 100 – 200 | 5 |
| 200 – 300 | x |
| 300 – 400 | 12 |
| 400 – 500 | 17 |
| 500 – 600 | 20 |
| 600 – 700 | y |
| 700 – 800 | 9 |
| 800 – 900 | 7 |
| 900 – 1000 | 4 |
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