Question

The median of the following data set is $56.5$.

$3$	$x$	$9$	$5$	$17$
$1$	$10$	$13$	$16$	$7$

What is the value of $x$?

• A. 8

Answer 1

The correct option is A 8
Let's arrange the given data set in ascending order, except the unknown $x$.

$1$	$3$	$5$	$7$	$9$
$10$	$13$	$16$	$17$	$x$

As the data set has even number of elements, median is the mean of two central values.

As per the question, the median is $8.5$, which is less than $9$.

$\therefore$ $x$ must be placed just before $9$, such that the mean of $x$ and $9$ can be $8.5$.

The correct arrangement becomes

$1$	$3$	$5$	$7$	$\underset{–}{x}$
$\underset{–}{9}$	$10$	$13$	$16$	$17$

$\text{Median}=\text{Mean of}x\text{and}9=8.5$

$\Rightarrow \frac{x+9}{2}=8.5$
$\Rightarrow \frac{x+9}{2}\times 2=8.5\times 2$

(multiplying $2$ on both sides)

$\Rightarrow x+9=17$

$\Rightarrow x+9-9=17-9$

(substracting $9$ from both sides)

$\Rightarrow x=8$

Hence, the modified ordered data

$1$	$3$	$5$	$7$	$\underset{–}{8}$
$\underset{–}{9}$	$10$	$13$	$16$	$17$

And, the value of $x$ is $8$.