Question

Numbers 50, 42, 35, 2x + 10, 2x − 8, 12, 11, 8, 6 are written in descending order and their median is 25, find x.

Answer 1

Here, the number of observations n is 9. Since n is odd , the median is the ${\left(\frac{n+1}{2}\right)}^{th}$ observation, i.e. the 5^th observation.
As the numbers are arranged in the descending order, we therefore observe from the last.
Median = ​5^th observation.
$\Rightarrow$ 25 = 2x -8
$\Rightarrow$ 2x = 25 +8
$\Rightarrow$ 2x = 33
$\Rightarrow$x = $\frac{33}{2}$
$\Rightarrow$x = 16.5
Hence, ​x = 16.5.