Question

Given, $10,18,4,15,3,21,x$
If $x$ is the median of the $7$ numbers listed above, which of the following could be the value of $x$?

• A. $5$
• B. $8$
• C. $9$
• D. $14$
• E. $16$

Answer 1

The correct option is D $14$

Given numbers

$10,$ $18,$ $4,$ $15,$ $3,$ $21,$ $x$

Median is the middle value in the list of numbers. To find the median, the numbers have to be in the numerical order.

As $x$ is the given median, $x$ should be placed in the middle of the list in numerical order. The list contains $7$ numbers. So, $x$ should be placed in the $4^{th}$ position.

Rewriting the list in increasing order,

$3,$ $4,$ $10,$ $x,$ $15,$ $18,$ $21$

So, $x$ should lie between $10$ and $15$.

Possible values of $x$, $10$ $\le$ $x$ $\le$ $15$

From the given options,

Only $14$ satisfies the above condition.

Therefore, the value of $x$ is $14$.