Expectation and Standard Deviation of a Sample Average -- 2 different distributions

[xxMsJojoxx]

Hi there,
I have the below 2 questions in my Intro to Stats Course.

1)
Expectation & Standard Deviation is as followed -


2)
Expectation & Standard Deviation is as followed _




Question:
I don't get why the 2nd example isn't also a 'uniform distribution', like the 1st example.
A 'uniform distribution' is when the probability of each value is the same.
So the calculation should be the same?

 

[Harry_the_cat]

The first is continuous, the second is discrete.