Question

5. The following 9 observations are arranged in the
ascending order as follows:
3, 5, 8, 13, x - 1, 16, 18, 21, 23.
If the median of the data is 15, find the value of x.
​

Answer 1

given observations : 3, 5, 8, 13, x - 1, 16, 18, 21, 23.

median means middle number (x-1)

x-1=15

x=15+1

x=16

Answer 2

Given :

3, 5, 8, 13, x - 1, 16, 18, 21, 23

Number of items = 9

Median = 15

To find : the value of x = ?

Solution :

N = 9 which is odd

$Median=(\dfrac{N+1}{2})^{th}\\\\=(\dfrac{9+1}{2})^{th}\\\\=\dfrac{10}{2}^{th}\\\\=5^{th}\ term\\\\=x-1$

So, it becomes,

$15=x-1\\\\15+1=x\\\\16=x$

Hence, the value of x is 16.