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प्रश्न
Compare the modal ages of two groups of students appearing for an entrance test:
| Age (in years): | 16-18 | 18-20 | 20-22 | 22-24 | 24-26 |
| Group A: | 50 | 78 | 46 | 28 | 23 |
| Group B: | 54 | 89 | 40 | 25 | 17 |
उत्तर
| Age (in years) | Group ‘A’ | Group ‘B’ |
| 16–18 | 50 | 54 |
| 18–20 | 78 | 89 |
| 20–22 | 46 | 40 |
| 22–24 | 28 | 25 |
| 24–25 | 23 | 17 |
For group “A”
The maximum frequency is 78 so the modal class is 18–20.
Therefore,
l = 18
h = 2
f = 78
f1 = 50
f2 = 46
Mode `rArr=l+(f-f1)/(2f-f1-f2)xxh`
`=18+(78-50)/(156-50-46)xx2`
`=18+28/60xx2`
`=18+14/15`
= 18 + 0.93
= 18.93
For group “B”
The maximum frequency 89 so modal class 18–20.
Therefore,
l = 18
h = 2
f = 89
f1 = 54
f2 = 40
Mode `rArr=l+(f-f1)/(2f-f1-f2)xxh`
`=18+(89-54)/(178-54-40)xx2`
`=18+35/84xx2`
`=18+35/42`
`=18+5/6`
= 18 + 0.83
= 18.83
Thus, the modal age of group A is 18.93 years whereas the modal age of group B is 18.83 years.
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संबंधित प्रश्न
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| 0 – 5000 | 90 |
| 5000 – 10000 | 150 |
| 10000 – 15000 | 100 |
| 15000 – 20000 | 80 |
| 20000 – 25000 | 70 |
| 25000 – 30000 | 10 |
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| Area of land (in hectares) | 1 – 3 | 3 – 5 | 5 – 7 | 7 – 9 | 9 – 11 | 11 – 13 |
| Number of families | 20 | 45 | 80 | 55 | 40 | 12 |
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| Marks | 0 - 5 | 5 - 10 | 10 - 15 | 15 - 20 | 20 - 25 | 25 - 30 | 30 - 35 | 35 - 40 |
| No. of students | 3 | 7 | 15 | 24 | 16 | 8 | 5 | 2 |
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(ii) Which group has the least frequency?
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For the following distribution
| Monthly Expenditure (Rs.) | No. of families |
| Expenditure less than Rs. 10,000 | 15 |
| Expenditure les than Rs. 13,000 | 31 |
| Expenditure les than Rs. 16,000 | 50 |
| Expenditure les than Rs. 19,000 | 67 |
| Expenditure les than Rs. 22,000 | 85 |
| Expenditure les than Rs. 25,000 | 100 |
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| 0 – 5000 | 8 |
| 5000 – 10000 | 26 |
| 10000 – 15000 | 41 |
| 15000 – 20000 | 16 |
| 20000 – 25000 | 3 |
| 25000 – 30000 | 3 |
| 30000 – 35000 | 2 |
| 35000 – 40000 | 1 |
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0 − 20 | 20 − 40 | 40 − 60 | 60 − 80 | 80 − 100 |
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5 | 10 | − | 6 | 3 |
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7, 8, 6, 7, 7, 5, 9, 7, 6, 7, 8, 7
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| Class | 0 – 5 | 5 – 10 | 10 – 15 | 15 – 20 | 20 – 25 |
| Frequency | 10 | 15 | 12 | 20 | 9 |
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