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Question
The mileage (km per litre) of 50 cars of the same model was tested by a manufacturer and details are tabulated as given below:
| Mileage (km/l) | 10 – 12 | 12 – 14 | 14 – 16 | 16 – 18 |
| Number of cars | 7 | 12 | 18 | 13 |
Find the mean mileage. The manufacturer claimed that the mileage of the model was 16 km/litre. Do you agree with this claim?
Solution
| Mileage (km/l) |
Class marks `(bb(x_i))` |
Number of cars `(bb(f_i))` |
`bb(f_i x_i)` |
| 10 – 12 | 11 | 7 | 77 |
| 12 – 14 | 13 | 12 | 156 |
| 14 – 16 | 15 | 18 | 270 |
| 16 – 18 | 17 | 13 | 221 |
| Total | `sumf_i = 50` | `sumf_i x_i = 724` |
Here, `sumf_i` = 50
And `sumf_i x_i` = 724
∴ Mean `(barx) = (sumf_i x_i)/(sumf_i)`
= `724/50`
= 14.48
Hence, mean mileage is 14.48 km/l.
No, the manufacture is claiming mileage 1.52 km/l more than average mileage.
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