Finding Median in a distribution

Question

What does it mean by "find all medians"? I thought there could only be one median. Also, how would you approach solving this question?

Suppose $P(X = x) = \displaystyle\tfrac{x}{21}$ for $x = 1, 2, 3, 4, 5, 6.$

Find all medians of this distribution.

Answer 1

The median is $P(X\geq m)\geq 1/2$ and $P(X\leq m)\geq 1/2$. This definition suggests that there can be more than one median. But in your example $5$ seems to be the only number which satisfies both inequalities.

Answer 2

Means and medians are different things.

I would approach this question by looking up the definition of both in a textbook or wikipedia. Then you will see that a distribution can have more than one median. And then you can answer the question.