Question

The mean mark of 10 boys is 58.If the mean mark of 7 of them is 61, what is the mean mark of the remaining 3 boys

Answer 1

As for the 10 boys altogether,

$\begin{gathered} \operatorname{mean}=58 \\ \text{and} \\ \operatorname{mean}=\frac{1}{10}\sum ^{10}_{i=1}\text{mark}_i \end{gathered}$

Thus,

$\Rightarrow580=\sum ^{10}_{i=1}\text{mark}_i$

On the other hand, as for seven of the boys

$\begin{gathered} \operatorname{mean}=61=\frac{1}{7}\sum ^7_{j=1}\text{mark}_j \\ \Rightarrow427=\sum ^7_{j=1}\text{mark}_j \end{gathered}$

Thus, regarding the remaining three boys,

$\Rightarrow\sum ^3_{k=1}mark_k=580-427=153$

Finally, the mean of those remaining three kids is

$\begin{gathered} \text{MEAN}=\frac{1}{3}\sum ^3_{k=1}mark_k=\frac{1}{3}\cdot153=51 \\ \Rightarrow\text{MEAN}=51 \end{gathered}$

Thus, the mean mark of the remaining 3 boys is 51