Question

If the median of the following data is 78, then find the value of $x$.

44, 47, 63, 65, $x$ + 13, 87, 93, 99, 110.
(data is in ascending order)

Answer 1

Observations are already arranged in ascending order
44, 47, 63, 65, $x$ + 13, 87, 93, 99, 110

Since number of observations is 9 , the median will be the middle term.

So, median is the $(\frac{10}{2}{)}^{th}$ term =$5^{th}$ term
$\because 5^{th}$ term = $x$ + 13

$\Rightarrow$ Median = $x$ + 13
$\Rightarrow$ 78 = $x$ + 13
$\Rightarrow$ $x$ = 78 - 13
$\Rightarrow$ $x$ = 65
Thus, the value of $x$ is 65.