Question

Frequency distribution of distance travelled in kms. per liter of petrol by different mopeds is given below.

$\begin{array}{cccccccc}\text{Distance travelled (in km/L)}& 62-65& 65-68& 68-71& 71-74& 74-77& 77-80& 80-83\\ \text{No.of mopeds}& 5& 8& 12& 28& 35& 10& 2\end{array}$

Find mean distance travelled per liter of petrol by a moped.

• A. $71.04$ kms/lit
• B. $73.04$ kms/lit
• C. $75.04$ kms/lit
• D. $79.04$ kms/lit

Answer 1

Answer: (B)

Lets form the frequency table for finding the mean,

$\begin{array}{cccc}\text{C.I}& \text{Frequency}\left(f_i\right)& x_i& f_i{x}_i\\ 62-65& 5& 63.5& 317.5\\ 65-68& 8& 66.5& 532\\ 68-71& 12& 69.5& 834\\ 71-74& 28& 72.5& 2030\\ 74-77& 35& 75.5& 2642.5\\ 77-80& 10& 78.5& 785\\ 80-83& 2& 81.5& 163\\ & \sum f_i=N=100& & \sum f_i{x}_i=7304\end{array}$

From the table,

$N=\Sigma f_i=100$

$\Sigma f_i{x}_i=7304$

Mean $\overline{x}=\frac{\Sigma f_i{x}_i}{N}$

$\Rightarrow \overline{x}=\frac{7304}{100}\overline{x}=73.04$

Mean distance travelled per liter of petrol by a moped is $73.04$ km/L

Hence, option $B$ is correct.