# 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

This question appears to be off-topic. The users who voted to close gave this specific reason:

• "This question is missing context or other details: Please improve the question by providing additional context, which ideally includes your thoughts on the problem and any attempts you have made to solve it. This information helps others identify where you have difficulties and helps them write answers appropriate to your experience level." – Did, J. M. is a poor mathematician, José Carlos Santos, Namaste, JonMark Perry
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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

## 1 Answer

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