Why is mathematically different to create a program that creates one random number from 2 to 12 as opposed to two random numbers from 1 to 6 and adding them together?

Question

Why is mathematically different to create a program that creates one random number from 2 to 12 as opposed to two random numbers from 1 to 6 and adding them together?

Answer 1

The mean average is different...

For random stats in the range 2 to 12, the mean average is 7...

For random stats in the range 1 to 6, the mean average is 3.5