Question

Ten observations 6, 14, 15, 17, x+1, 2x-13, 30, 32, 34, 43 are written in ascending order. If the median of the given data is 24 then find the value of x.

• A. 17
• B. 20.33
• C. 30
• D. 20

Answer 1

The correct option is D 20

The ten observations are 6, 14, 15, 17, x+1, 2x-13, 30, 32, 34, 43

Since the number of terms is 10 which is even, the median will be average of the 5th and 6th terms

5th term = x +1, 6th term = 2x - 13

$\text{Median}=\frac{(x+1)+(2x-13)}{2}\Rightarrow 24=\frac{(x+1)+(2x-13)}{2}\Rightarrow \frac{3x-12}{2}=24$
$\Rightarrow 3x-12=48$
$\Rightarrow 3x=60$
$\Rightarrow x=20$