I have a "source" the claims to return small sets of values (size<10) where each set is uniformly distributed in some range $[n,m]$.

What is the simplest to perform test that would be able to test if this is a reasonable claim?

My first thought was to take the sample standard deviation and compare it to the expected value but how close would be close enough? (and for that matter I don't remember what the expected value is.)

As a sub issue, the small sample size is going to make the results noisy so I will need to run it many time, how should I aggregate the results; Union a bunch of sets? Keep an average of the computed statistics?