In the following table, the toll paid by drivers and the number of vehicles is shown. Find the mean of the toll by 'assumed mean' method.
| Toll (Rupees) | 300–400 | 400–500 | 500–600 | 600–700 | 700–800 |
|---|---|---|---|---|---|
| No. of vehicles | 80 | 110 | 120 | 70 | 40 |
Answer: Mean toll ≈ ₹ 521.43
Take assumed mean \(A = 550\).
| Class | Class mark \(x_i\) | \(d_i = x_i - 550\) | \(f_i\) | \(f_id_i\) |
|---|---|---|---|---|
| 300–400 | 350 | -200 | 80 | -16000 |
| 400–500 | 450 | -100 | 110 | -11000 |
| 500–600 | 550 | 0 | 120 | 0 |
| 600–700 | 650 | 100 | 70 | 7000 |
| 700–800 | 750 | 200 | 40 | 8000 |
| Total | \(\sum f_i = 420\) | \(\sum f_id_i = -12000\) |
\[ \bar{d} = \frac{\sum f_id_i}{\sum f_i} = \frac{-12000}{420} \approx -28.57 \]
\[ \bar{X} = A + \bar{d} = 550 + (-28.57) \]
\[ \bar{X} \approx 521.43 \]
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