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 , Find the mean mileage. The manufacturer claimed that the mileage of the model was $16\mathrm{km}/\mathrm{litre}$. Do you agree with this claim?

S.N	Mileage (km L-1)	Class –Marks (xi)	Number of cars (fi)
$1$	$10–12$	$11$	$7$
$2$	$12–14$	$13$	$12$
$3$	$14–16$	$15$	$18$
$4$	$16–18$	$17$	$13$

Answer 1

Find the mean mileage of the cars.

Given,

The mileage of $50$cars put through testing by a manufacturer.

S.N	Mileage (km L-1)	Class –Marks (xi)	Number of cars (fi)	fixi
$1$	$10–12$	$11$	$7$	$77$
$2$	$12–14$	$13$	$12$	$156$
$3$	$14–16$	$15$	$18$	$270$
$4$	$16–18$	$17$	$13$	$221$
			$\sum _{i=1}^4{f}_i=50$	$\sum _{i=1}^4{f}_i{x}_i=724$

Step 1: Apply direct method
$\mathrm{Mean}=\frac{\sum {\mathrm{f}}_{\mathrm{i}}{\mathrm{x}}_{\mathrm{i}}}{\sum {\mathrm{f}}_{\mathrm{i}}}$
From the table,

$$\begin{gathered} \mathrm{Mean}=\frac{724}{50} \\ =14.48 \end{gathered}$$
Thus, the mean mileage is $14.48\mathrm{km}/\mathrm{litre}$.

Step 2: Find mean mileage less than the manufacturers claim.
Given, the manufacturer claimed that the mileage of the model was $16\mathrm{km}/\mathrm{litre}$ .
Difference in mileage

$$\begin{gathered} \mathrm{Difference}\mathrm{in}\mathrm{mileage}=16-14.48 \\ =1.52\mathrm{km}/\mathrm{litre} \end{gathered}$$
Hence, the mean mileage is $1.52\mathrm{km}/\mathrm{litre}$ less than the manufacturers claim.