Question

The teacher divided the students of grade $7$ into $4$ groups and conducted a test. The number of students in the $4$ groups formed were $12,16,13$, and $15$ and the corresponding average score of these groups were $23,25,19$, and $27$.

What will be the weighted average score of the students of grade $7$?

• A. $19$
• B. $23.71$
• C. $27.21$
• D. $25$

Answer 1

The correct option is B $23.71$

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 given data can be represented in the tabular form as follows:


Here, number of students are the weighted factors and the average score are the data points and hence can be denoted as,


Thus, the weighted average scores of grade $7$ students will be calculated as,

$\begin{array}{cc}\text{Weighted average score}& =\frac{(w_1\times n_1)+(w_2\times n_2)+(w_3\times n_3)+(w_4\times n_4)}{w_1+w_2+w_3+w_4}\\ & =\frac{(12\times 23)+(16\times 25)+(13\times 19)+(15\times 27)}{12+16+13+15}\\ & =\frac{276+400+247+405}{56}\\ & =\frac{1328}{56}\\ & =23.71\end{array}$

Hence, the weighted average score of grade $7$ students is $23.71$.

So, option (b) is correct.