Question

The average marks of Smith and Max in a quiz is $62$. In the same quiz, the average marks of Ellen and Max is $65$ and that of Smith and Ellen is $64$. What will be the average marks of all three of them in the quiz?

• A. $64$
• B. $65.67$
• C. $63.67$
• D. $62.5$

Answer 1

The correct option is C $63.67$

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 tabular form as,


Here, the weighted factors are the number of students , i.e., $w_1=2$, $w_2=2$ and $w_3=2$ and their corresponding average marks $n_1=62$, $n_2=65$ and $n_3=64$ are the data points.

Substitute the given values in the formula of weighted average to calculate the average marks of Smith, Max, and Ellen.

$\begin{array}{cc}\text{Required average marks}& =\frac{(2\times 62)+(2\times 65)+(2\times 64)}{2+2+2}\\ & =\frac{124+130+128}{6}\\ & =\frac{382}{6}\\ & =63.67\end{array}$

Hence, the average marks of all three of them is $63.67$

So, option (c) is correct.