@toby3d so, since there are only 21 distinct numbers from 1.0 to 3.0 i'm guessing you don't mean *set*, since in maths this implies distinct elements.

if you want a list of say x=3 elements to average 2.35. this means you want r[0]+r[1]+r[2]=2.35*3 ±(3*0.5). r[] being the elements of the resulting list.
i'd start with 2.35*3=7.05, choose one element at random (e.g. 1.4), subtract the number 7.05-1.4=5.65, memoize the result.
repeat until the result of the subtrction is between 1.0 and 3.0.