GATE CS 2024 Set 1 — Question 3

To find the median, we first arrange the given numbers in ascending order:$$9, 10, 11, 11, 13, 14, 15, 17, 18, 69$$The number of observations is $n = 10$, which is an even number.
For an even number of observations, the median is the average of the $\left(\frac{n}{2}\right)^{th}$ and $\left(\frac{n}{2} + 1\right)^{th}$ terms.Here, $\frac{n}{2} = \frac{10}{2} = 5$. So, we take the average of the $5^{th}$ and $6^{th}$ terms.$5^{th}$ term $= 13$
$6^{th}$ term $= 14$Median $= \frac{13 + 14}{2} = \frac{27}{2} = 13.5$