What 5 numbers have a mean of 6 and range of 1?

Answer 1

There are infinitely many possible answers:

{5.8, 5.8, 5.8, 5.8, 6.8}

or {5.5, 6, 6.5, 6-a and 6+a} where a is any number less than or equal to 0.5

are two options.