Question

A class of 50 students is divided into 3 clubs A, B, and C. The 20 students of club A scored 90 marks on an average, the 15 students of club B scored 70 marks on an average, and the rest, who were in club C, scored 50 marks on an average. Find the weighted average of the marks of the class.

• A. 72
• B. 62
• C. 60
• D. 70

Answer 1

The correct option is A 72

As per the question, in a $100$ marks class test,

$\bullet$ Number of students who scored $90$ marks = $20$

$\bullet$ Number of students who scored $70$ marks = $15$

$\bullet$ Number of students who scored $50$ marks = $50-(20+15)=50-35=15$

The above data can be represented in table format as:

Number of students	Marks
$20\left(w_1\right)$	$90\left(x_1\right)$
$15\left(w_2\right)$	$70\left(x_2\right)$
$15\left(w_3\right)$	$50\left(x_3\right)$

In the above table, the weighted factors $(w_1,w_2,w_3)$ are the number of students $(20,15,15)$, and the corresponding data points $(x_1,x_2,x_3)$ are the students' marks $(90,70,50)$.

$\therefore$ Weighted average of marks

$=\frac{(w_1\times x_1)+(w_2\times x_2)+(w_3\times x_3)}{w_1+w_2+w_3}$

$=\frac{(20\times 90)+(15\times 70)+(15\times 50)}{20+15+15}$

$=\frac{1800+1050+750}{50}$

$=\frac{3600}{50}=72$

$\therefore$ The weighted average of marks in the class is $72$.