Question

A school conducted $5$ terminals. The average score of John in first two terminals is $90$, while in the remaining terminals his average score is $120$. What will be his average score in all the $5$ terminals?

• A. $108$
• B. $105$
• C. $42$
• D. $270$

Answer 1

The correct option is A $108$

The formula to calculate the weighted average is,

$\text{Weighted Average}=\frac{(w_1\times n_1)+(w_2\times n_2)+\dots +(w_l\times n_l)}{w_1+w_2+\dots +w_l}$,

where $w_1,w_2,\dots w_l$ are the weighted factors and $n_1,n_2,\dots n_l$ are the data points.

The tabular representaion of the given information will be given as,


Here the number of terminals are the weighted factors and are denoted as $w_1=2$ and $w_2=3$, while the corresponding average score are the data points and is depicted as $n_1=90$ and $n_2=120$.

Thus, the average score in all the $5$ terminals will be calculated as,

$\begin{array}{cc}\text{Weighted average score}& =\frac{(2\times 90)+(3\times 120)}{2+3}\\ & =\frac{180+360}{5}\\ & =\frac{540}{5}\\ & =108\end{array}$

Hence, John's average score in all $5$ terminals is $108$.

So, option (a) is correct.