Question

Following $10$ observations are arranges in ascending order as follows.
$2,3,5,9,x+1,x+3,14,16,19,20$
If the median of the data is $11$, find the value of $x$.

Answer 1

Given that number of observations $\left(N\right)=10$

Median $\left(M_d\right)=11$ __(1)

the observations are arranges in ascending order as follows

$2,3,5,9,x+1,x+3,14,16,19,20$

we know that if the number of observations (N) is even then median is the average of the ${\frac{N}{2}}^{th}$ term and $\frac{N+1}{2}th$ term

$\therefore$ Median = $\frac{{\frac{N}{2}}^{th}term+{\frac{N+1}{2}}^{th}term}{2}$

$=\frac{{\left(\frac{10}{2}\right)}^{th}term+\frac{10}{2}+1^{th}term}{2}$

$=\frac{5^{th}term+6^{th}term}{2}$

from (1)

$11=\frac{(x+1)+(x+3)}{2}$

$22=2x+4$

$2x=22-4$

$2x=18$

$x=9$

The value of $x=9$