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Yes, they are. A uniform distribution is one in which the probability of each outcome is the same and, as a result, the mean and median are the same. A uniform distribution should not be confused with a set of random variables, all with the same distributions - much less the same values!

For example, the median of a Poisson distribution is not the same as its mean. So if you have a number of random variables (RVs), each with the same Poisson distribution, their mean and median will be different. This is true of any set of RVs whose distributions are asymmetric.


And it is very easy to see that the mode need not be the same. The outcome of a single roll of a regular die is the uniform distribution over the numbers {1, 2, 3, 4, 5, 6}. The mean and median are 3.5 but the mode cannot be 3.5 since that is not a value that can ever be observed.

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Yes, since all the values of the variable are the same. That value is also the mode.

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Q: In an uniform distribution is the mean and median the same?
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