# Find the median given a table of relative frequencies

I came across the following GRE question. I had no problem finding the mean. However, the answer for the median is given to be 1. I don't understand how they arrive at this.

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I don't either. It looks like the answer should be 0 to me. Perhaps the book has a mistake. –  mtiano Mar 31 '13 at 12:57
I'm curious -- why do you think it should be zero? I don't see that. –  Joebevo Mar 31 '13 at 13:02
Put the values of $X$ in order or relative frequency. Zero is the value in the middle. –  mtiano Mar 31 '13 at 13:20

Imagine that there were $100$ observations. We got the result $0$ a total of $18$ times, and the result $1$ a total of $33$ times, and so on. Thus $51$ of the observations are $\le 1$. It follows that the median is $\le 1$. But only $18$ of the observations are $\le 0$. It follows that the median is $1$.
Remark: Our data are coarse-grained, and a small change in them could produce a large change in median. So although the answer of $1$ is technically correct, it feels uncomfortable.