Question

Find the median of the following numbers $\;25,{\text{ }}27,{\text{ }}21,{\text{ }}23,{\text{ }}24$ is ------
$\left( {\text{A}} \right){\text{ }}21$
$\left( {\text{B}} \right){\text{ }}23$
$\left( {\text{C}} \right){\text{ }}25$
$\left( {\text{D}} \right){\text{ }}24$

Answer 1

Here, we have to find out the median of the given set of numbers.
We can say that the median is the middle number of the set of numbers and when we arranged in an ascending order.
First, we arrange the given number into an ascending order.
Then we find the middle value of the set of given numbers by using the formula.
Finally, we get the required answer.

Formula used: If the number of a term is odd, then the middle value of the number ${\left( {\dfrac{{\;n + 1}}{2}} \right)^{th}}$ term

Complete step-by-step solution:
It is given that the set of numbers $\;25,{\text{ }}27,{\text{ }}21,{\text{ }}23,{\text{ }}24$
Now we have to arrange the given number into an ascending order.
In the way of arranging ascending order to given number is written as the smallest number to the greatest number
So we can write it as, $21,{\text{ }}23,{\text{ }}24,{\text{ }}25,$ and $27$
Also, the number of terms we can write it as the total count of the set of arranging ascending order of the number,
So we can represent it as, $n = 5$
Now, if the number of terms is odd, then we will find the middle value of these numbers.
Here we use the formula ${\left( {\dfrac{{\;n + 1}}{2}} \right)^{th}}$ term.
Here $n = 5$, so we can write it as,
$\Rightarrow \left( {\dfrac{{{\text{5 + 1}}}}{{\text{2}}}} \right)$
On adding the numerator term and we get,
$\Rightarrow \dfrac{{\text{6}}}{{\text{2}}}$
Let us divide the term,
$\Rightarrow {{\text{3}}^{{\text{rd}}}}{\text{ term}}$
That is third term of the set of arranging ascending order of the number
So the third term is $24$

Hence the correct option is $\left( D \right)$

Note: The median value is to be fixed by its own position and it is not reflected by the given individual value.
If the total number of terms is even, then the median of the given number
Median=$\left[ {\dfrac{{{{\left( {\dfrac{{\text{n}}}{{\text{2}}}} \right)}^{{\text{th}}}}{\text{term + }}{{\left( {\dfrac{{\text{n}}}{{\text{2}}}{\text{ + 1}}} \right)}^{{\text{th}}}}{\text{ term}}}}{{\text{2}}}} \right]$ term, where n is the number of terms.