Question

There are $40$ students in Joe's class. In a $20$ marks class test, $10$ students got $16$ marks, $20$ students got $15$ marks and rest $10$ students got $10$ marks. The weighted average of marks in Joe's class is .

Answer 1

As per the question, in a $20$ marks class test
$\bullet$ number of students got $16$ marks= $10$
$\bullet$ number of students got $15$ marks= $20$
$\bullet$ number of students got $10$ marks= $10$

The above data can be represented in table format as

Number of students	Marks
$10\left(w_1\right)$	$16\left(x_1\right)$
$20\left(w_2\right)$	$15\left(x_2\right)$
$10\left(w_3\right)$	$10\left(x_3\right)$

In the above table, the weighted factors $(w_1,w_2,w_3)$ are the number of students $(10,20,10)$, and the corresponding data points $(x_1,x_2,x_3)$ are the student's marks $(16,15,10)$.

$\therefore$ Weighted average of marks

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

$=\frac{(10\times 16)+(20\times 15)+(10\times 10)}{10+20+10}$

$=\frac{160+300+100}{40}$

$=\frac{560}{40}=14$

$\therefore$ The weighted average of marks in Joe's class is $14$.