Ten observations 5,9,14,15,x+1,2x−13,28,30,32,34 are written in ascending order. The median of the data is 24. Find the value of x.

The total count of data observations given is n=10, which is an even number.
For an even number of observations sorted in ascending sequence, the median is calculated as the average of the two middle terms, located at positions
2
n
​
and (
2
n
​
+1):

Middle terms positions=
2
10
​
=5
th
 termand5+1=6
th
 term
From the sorted list:

5
th
 term=x+1

6
th
 term=2x−13

Formulating the median equation:

Median=
2
(x+1)+(2x−13)
​
=24
2
3x−12
​
=24
3x−12=48
3x=60⟹x=20