# Mode Median for discrete uniform [closed]

$X$ is a discrete uniform distribution on $1, 2, \ldots,n$. I know that the median is $\frac{n+1}2$ for odd $n$. I need to find median when $n$ is even. Would it be $\frac{n}2$ or $\frac{n}2+1$, whichever is greater?

Also, is every point mode as PDF has highest values there? So there are $n$ modes - $1,2,\ldots,n$?

## closed as off-topic by Did, J. M. is a poor mathematician, José Carlos Santos, Namaste, JonMark PerryNov 14 '17 at 5:11

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• – Henry Nov 8 '17 at 10:19
• And looking at some definitions is not an option because? – Did Nov 13 '17 at 23:47

Guide:

To answer the first question, think of how to handle the case where $n=2$.

what is the median for uniform distribution on $1,2$?

For the second question, yes, there are $n$ modes.

• 1 and 2 both will be the medians, right? – user492699 Nov 8 '17 at 6:58
• what is the definition of median to you? – Siong Thye Goh Nov 8 '17 at 6:59
• For median m, P(X<=m) = P(X>=m) = 1/2 – user492699 Nov 8 '17 at 7:00
• Here that point would be 0.5 – user492699 Nov 8 '17 at 7:00
• But as this is discrete random variable, we can choose only 1 or 2 – user492699 Nov 8 '17 at 7:00