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,
$x+3=24$
$\Rightarrow x=21$