Question

Ten observations 6, 14, 15, 17, x+1, 2x – 13, 30, 32, 34 and 43 are written in an ascending order. The median of the data is 24. Find the value of x.

Answer 1

Given observations are 6, 14, 15, 17, x+1, 2x - 13, 30, 32, 34, 43
Here, total number of observations, n = 10 (even)
Since, n is even, so we use the formula for median,
Median $=\frac{\left(\frac{n}{2}\right)th\text{observation}+(\frac{n}{2}+1)th\text{observation}}{2}=\frac{\left(\frac{10}{2}\right)th\text{observation}+(\frac{10}{2}+1)th\text{observation}}{2}$
$=\frac{5th\text{observation}+6th\text{observation}}{2}$
$\Rightarrow 24=\frac{(x+1)+(2x-13)}{2}$ [given]
$\Rightarrow 3x-12=48\Rightarrow 3x=60\Rightarrow x=20$
Hence, the value of x is 20.