Values in List $P$ are distinct from values in List $Q$. List $R$ consists of all the values in list $P$ and all the values in list $Q$.
Find the median of list $R$.
My logic: Here the total number of elements is $100$, which implies that the median is the average of the $50^{\text{th}}$ and $51^{\text{st}}$ elements. So, according to me that should be $\frac{6+6}{2} = 6$. However the answer is $5.5$.
What confuses me is that the question specifies that elements in $P$ are distinct from elements in $Q$, and an answer of $5.5$ can be achieved only if we consider the $5$'s and $6$'s of both the tables to be same!
There are $50$ elements of $R$ that are $5$ or below: $44$ from $P$ and $6$ from $Q$. There are also $50$ elements of $R$ that are $6$ or above: $16$ from $P$ and $34$ from $Q$. The median is halfway between $5$ and $6$, or $5.5$. The statement that the items are distinct means that $R$ has $16$ items in the $5$ bin because we can add $10+6$. If some of the items were the same we would have to deduct the matches from $16$.