Theory:

Problem \(1\)
Find the median of the following numbers.
 
\(45\), \(57\), \(87\), \(23\), \(35\), \(46\), \(94\)
 
Let us now find the solution.
 
Step \(1\): Arrange the numbers either in ascending order or descending order.
 
Here we have arranged the numbers in ascending order.
 
\(23\), \(35\), \(45\), \(46\), \(57\), \(87\), \(94\)
 
Step \(2\): Find the total number of terms.
 
The total number of terms \(= 7\)
 
Step \(3\): Find the median.
 
Since the total number of terms is odd:
 
\(\text{Median} =\) N+12th \(\text{term}\)
 
\(\text{Median} = \Big( \frac{7+ 1}{2} \Big)^{th}\) \(\text {term}\)
 
\(\text{Median} = 4^{th}\) \(term\)
 
\(\text{Median} = 46\)
 
Problem \(2\)
Find the median of the following numbers.
 
\(54\), \(25\), \(75\), \(65\), \(97\), \(31\), \(55\), \(84\)
 
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:
 
\(\text{Median} =\) \(\frac{1}{2}\)\(\Bigg[\)N2th\(\text{term}\)\(+\)N2+1th\(\text{term}\)\(\Bigg]\)
 
\(\text{Median}\) \(=\) \(\frac{1}{2}\) \(\Bigg[\) \(\Big(\frac{8}{2}\Big)^{th}\) \(\text{term}\) \(+\) \(\Big(\frac{8}{2} + 1 \Big)^{th}\) \(\text {term})\) \(\Bigg]\)
 
\(\text{Median}\) \(=\) \(\frac{1}{2}\) \([4^{th} \text{term} + 5^{th} \text{term}]\)
 
\(\text{Median} = \frac{55 + 65}{2}\)
 
\(\text{Median} = \frac{120}{2}\)
 
\(\text{Median} = 60\)