The mileage $(km/l)$ 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 $16 \, km/l$. Do you agree with this claim?
| 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 $16 \, km/l$. Do you agree with this claim?
(A)
Here,$\Sigma f_i = 50$ and $\Sigma f_i x_i = 724$.
Mean $\bar{x} = \frac{\Sigma f_i x_i}{\Sigma f_i} = \frac{724}{50} = 14.48$.
Hence,the mean mileage is $14.48 \, km/l$.
No,$I$ do not agree with the manufacturer's claim,as the calculated mean mileage $(14.48 \, km/l)$ is significantly less than the claimed $16 \, km/l$.
| Mileage $(km/l)$ | Class marks $(x_i)$ | Number of cars $(f_i)$ | $f_i x_i$ |
| $10-12$ | $11$ | $7$ | $77$ |
| $12-14$ | $13$ | $12$ | $156$ |
| $14-16$ | $15$ | $18$ | $270$ |
| $16-18$ | $17$ | $13$ | $221$ |
| Total | - | $\Sigma f_i = 50$ | $\Sigma f_i x_i = 724$ |
Here,$\Sigma f_i = 50$ and $\Sigma f_i x_i = 724$.
Mean $\bar{x} = \frac{\Sigma f_i x_i}{\Sigma f_i} = \frac{724}{50} = 14.48$.
Hence,the mean mileage is $14.48 \, km/l$.
No,$I$ do not agree with the manufacturer's claim,as the calculated mean mileage $(14.48 \, km/l)$ is significantly less than the claimed $16 \, km/l$.
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