5. Some problems on median

Let us now find the solution.

 

Step $1$: Arrange the numbers in ascending order or descending order.

 

$25$, $31$, $54$, $55$, $65$, $75$, $84$, $97$

 

Step $2$: Find the total number of terms.

 

The total number of terms $= 8$

 

Step $3$: Find the median.

 

Since the total number of terms is even:

 

$\text{Median} =$ $\frac{1}{2}$$\Bigg[$${\left(\frac{N}{2}\right)}^{\mathit{th}}$$\text{term}$$+$${\left(\frac{N}{2}+1\right)}^{\mathit{th}}$$\text{term}$$\Bigg]$

 

$\text{Median}$ $=$ $\frac{1}{2}$ $\Bigg[$ $\Big(\frac{8}{2}\Big)^{th}$ $\text{term}$ $+$ $\Big(\frac{8}{2} + 1 \Big)^{th}$ $\text {term})$ $\Bigg]$

 

$\text{Median}$ $=$ $\frac{1}{2}$ $[4^{th} \text{term} + 5^{th} \text{term}]$

 

$\text{Median} = \frac{55 + 65}{2}$