Question

What is the median number for the numbers 4, 8, 10, 5, 9?

Answer 1

We need to find the median number for the numbers 4, 8, 10, 5, 9. We start to solve the question by arranging the given numbers in ascending order. Then, we find the median number which is the ${{\left( \dfrac{n+1}{2} \right)}^{th}}$ term of the arranged data set where n=5.

Complete step-by-step answer:
We are given a data set and are asked to find the median number for the numbers. We will be solving the given question by arranging the data set in ascending order and then finding the median term using the formula $\left( \dfrac{n+1}{2} \right)$
The median is the middlemost number of the data set. It is the center value in a sorted list of numbers.
We have to arrange the numbers 4, 8, 10, 5, 9 in ascending order.
Ascending order involves arranging the numbers from smallest to largest.
Arranging the numbers in ascending order, we get,
$\Rightarrow 4,5,8,9,10$
In our case, the total number of observations given is 5.
As the total number of observations is odd, the median for the data set is the ${{\left( \dfrac{n+1}{2} \right)}^{th}}$ term of the data set where n is the total number of observations.
Here,
n=5
$\Rightarrow median=\left( \dfrac{n+1}{2} \right)$
Substituting the value of n in the above formula, we get,
$\Rightarrow median=\left( \dfrac{5+1}{2} \right)$
Simplifying the above equation, we get,
$\Rightarrow median=\left( \dfrac{6}{2} \right)$
$\therefore median={{3}^{rd}}term$
The ${{3}^{rd}}$ term of the data set $4,5,8,9,10\;$ is 8.
$\therefore$ The median number for the numbers 4, 8, 10, 5, 9 is 8.

Note: The median is the mid-value in the sorted list of numbers. We must not forget to arrange the given numbers in ascending order before computing the median for the data. The formula of median depends upon the total number of observations(n).
If n is odd, then $median={{\left( \dfrac{n+1}{2} \right)}^{th}}term$
If n is even, then $median=\dfrac{\left( {{\left( \dfrac{n}{2} \right)}^{th}}term+\left( {{\left( \dfrac{n}{2} \right)}^{th}}+1 \right)term \right)}{2}$