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प्रश्न
Given below is the distribution of total household expenditure of 200 manual workers in a city:
| Expenditure (in Rs) | 1000 – 1500 | 1500 – 2000 | 2000 – 2500 | 2500 – 3000 | 3000 – 3500 | 3500 – 4000 | 4000 – 4500 | 4500 – 5000 |
| Number of manual workers |
24 | 40 | 31 | 28 | 32 | 23 | 17 | 5 |
Find the average expenditure done by maximum number of manual workers.
उत्तर
As the class 1500-2000 has the maximum frequency, it is the modal class.
Now, `x_k = 1500, h = 500, f_k = 40, f_k-1 = 24, f_k+1 = 31`
∴ Mode, `M_0 = x_k + {ℎ ×((f_k− f_k−1))/((2f_k− f_k−1−f_k+1))}`
=1500+ `{500 xx ((40-24))/((2 xx40-24-31))}`
=`1500+ {500xx 16/25}`
=(1500+320)
=1820
Hence, mode = Rs 1820
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| Age (in years) | 5 - 7 | 7 - 9 | 9 - 11 | 11 – 13 | 13 – 15 | 15 – 17 | 17 – 19 |
| Number of students | x | 15 | 18 | 30 | 50 | 48 | x |
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| f | 1 | 4 | 7 | 5 | 9 | 3 |
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| Class Interval | 50 - 55 | 55 - 60 | 60 - 65 | 65 - 70 | 70 - 75 | 75 - 80 | 80 - 85 | 85 - 90 |
| Frequency | 5 | 20 | 10 | 10 | 9 | 6 | 12 | 8 |
For the following distribution
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| Less than 20 | 4 |
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| Less than 80 | 56 |
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| Expenditure less than Rs. 10,000 | 15 |
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| 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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| Income (in Rs) | Number of families |
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| 30000 – 35000 | 2 |
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