Question

The marks of $10$ students of a class in an examination arranged in ascending order is as follow. $13,35,47,46,x,x+4,55,61,71,80$.
If the median marks is $48$, find the value of $x$. Hence find the mode of the given data.

Answer 1

Now, the given numbers are : $13,35,47,46,x,x+4,55,61,71,80$

The number of marks are even and so the median is given by: $\frac{x+x+4}{2}=48$ .....(given)

Therefore, $2x+4=96$

$\Rightarrow 2x=92$

$\Rightarrow x=46$

Now, the mode of the given data is the number that is repeated the most number of times.

Thus the mode of the given data is $46$.