Question

The median of the observations 5, 8 , 12 , (x+2) , (x + 4) , 24 , 26 , 30 arranged in ascending order is 18.

Find the Value of x .

• A. 16
• B. 15
• C. 14
• D. 19

Answer 1

The correct option is B

15

Number of terms (n) is even = 8

Median = $\frac{(\frac{n}{2}{)}^{th}term+(\frac{n}{2}+1{)}^{th}term}{2}$

Median will be average of 4th and 5th Observation

$\Rightarrow$ Median = $\frac{(x+2)+(x+4)}{2}$

Median is given as 18

$\therefore$ $\frac{(x+2)+(x+4)}{2}$ = 18

$\Rightarrow$ 2x + 6 = 18 $\times$ 2 = 36

$\Rightarrow$ 2x = 30

$\Rightarrow$ x = $\frac{30}{2}$ = 15