Question

The marks distribution of $30$ students in a mathematics examination are as follows:

Class-interval of marks	$10-25$	$25-40$	$40-55$	$55-70$	$70-85$	$85-100$
Number of students	$2$	$3$	$7$	$6$	$6$	$6$

Find the mean by direct method and find also the mode of given data.

Answer 1

Let the mean be $\overline{x}$

Using the direct method$:\overline{x}=\frac{\sum x_i{n}_i}{\sum n_i}$

$=\frac{2\times 17.5+3\times 32.5+7\times 47.5+6\times 62.5+6\times 77.5+6\times 92.5}{30}$

$=\frac{1860}{30}=62$

Mode is the data point that occurs the most frequently in the data set.

Hence, the mode is class-interval $40-55.$