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Question
The following table gives the distribution of total household expenditure (in rupees) of manual workers in a city. Find the average expenditure (in rupees) per household.
| Expenditure (in rupees) (x1) |
Frequency(f1) |
| 100 - 150 | 24 |
| 150 - 200 | 40 |
| 200 - 250 | 33 |
| 250 - 300 | 28 |
| 300 - 350 | 30 |
| 350 - 400 | 22 |
| 400 - 450 | 16 |
| 450 - 500 | 7 |
Solution
Let the assumed mean (A) = 275
| Class interval |
Mid value (x1) | d1 = x1 - 275 | `"u"_1=(x_1-275)/50` | Frequency(f1) | f1u1 |
| 100 - 150 | 125 | -150 | -3 | 24 | -72 |
| 150 - 200 | 175 | -100 | -2 | 40 | -80 |
| 200 - 250 | 225 | -50 | -1 | 33 | -33 |
| 250 - 300 | 275 | 0 | 0 | 28 | 0 |
| 300 - 350 | 325 | 50 | 1 |
30 |
30 |
| 350 - 400 | 375 | 100 | 2 | 22 | 44 |
| 400 - 450 | 425 | 150 | 3 | 16 | 48 |
| 450 - 500 | 475 | 200 | 4 | 7 | 28 |
| N = 200 | `sumf_1"u"_1=-35` |
We have
A = 275, h = 50
Mean `=A+hxx(sumf_1"u"_1)/N`
`=275+50xx(-35)/200`
= 275 - 8.75
= 266.25
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