Question

A student obtained $60,75$ and $85$ marks respectively in three monthly examinations in Mathematics and $95$ marks in the final examination. The three monthly examinations are of equal weightage whereas the final examination is weighted twice as much as a monthly examination. The mean marks of Mathematics are

• A. $81$
• B. $82$
• C. $80$
• D. $85$

Answer 1

Answer: (B)

We have
$x_1=60,x_2=75,x_3=85,x_4=95,w_1=1,w_2=1,w_3=1$ and $w_4=2$
$\therefore \overline{X_w}=\frac{w_1{x}_1+w_2{x}_2+w_3{x}_3+w_4{x}_4}{w_1+w_2+w_3+w_4}$
$\Rightarrow \overline{X_w}=\frac{1\times 60+1\times 75+1\times 85+2\times 95}{1+1+1+2}=\frac{410}{5}=82$