Question

The percentage of marks obtained by the students in a class of $50$ are given below. Find the mean for the following data.

Marks$\left(\%\right)$	$40-50$	$50-60$	$60-70$	$70-80$	$80-90$	$90-100$
Number of students	$6$	$12$	$14$	$8$	$6$	$4$

• A. $64.6\%$
• B. $65.6\%$
• C. $66.6\%$
• D. $67.6\%$

Answer 1

The correct option is C $66.6\%$

Marks $f_i$ $x_i$ $f_i{x}_i$

$40-50$ $6$ $45$ $270$

$50-60$ $12$ $55$ $660$

$60-70$ $14$ $65$ $910$

$70-80$ $8$ $75$ $600$

$80-90$ $6$ $85$ $510$

$90-100$ $4$ $95$ $380$

$\Sigma f_i=50$ $\Sigma f_i{x}_i=3330$

We know that, the arithmetic mean using direct method is

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

$\overline{x}=\frac{3330}{50}$

$\Rightarrow 66.6$

Therefore, the mean for the given data is $66.6\%$.