Question

The following observation are arranged in ascending order. If the median of the data is $17$, find $x$ if the observations are $6,8,9,15,x,x+2,21,22,25,29.$

• A. $x=11$
• B. $x=13$
• C. $x=15$
• D. $x=16$

Answer 1

Answer: (D)

$x=16$

The observations are: $6,8,9,15,x,x+2,21,22,25,29$
The number of observations are $10$. Since, the observations are even, the median will be the mean of $\frac{n}{2}$ and $\frac{n}{2}+1$ observations
median $=$ mean of $\frac{10}{2}$ and $\frac{10+2}{2}$ observations
median $=$ mean of $5^{th}$ and $6^{th}$ observations
median = $\frac{x+x+2}{2}$
$17=x+1$
$x=16$