The median of the data arranged in ascending order 8, 9, 12, 18, (x + 2), (x + 4), 30, 31, 34, 39 is 24. The value of x is
Question:

The median of the data arranged in ascending order 8, 9, 12, 18, (x + 2), (x + 4), 30, 31, 34, 39 is 24. The value of x is
(a) 22
(b) 21
(c) 20
(d) 24

Solution:

(b) 21

The given data is in ascending order.
Here, n is 10, which is an even number.
Thus, we have:

Median $=$ Mean of $\left(\frac{n}{2}\right)$ th $\&\left(\frac{n}{2}+1\right)$ th observations

$=\frac{1}{2}$ (5 th observation $+6$ th observation)

$=\frac{1}{2}(x+2+x+4)=(x+3)$

$=24$

Also,

$x+3=24$

$\Rightarrow x=21$